tag:blogger.com,1999:blog-11983909323040683792024-03-19T07:11:15.072-04:00TrendXplorerUnknownnoreply@blogger.comBlogger83125tag:blogger.com,1999:blog-1198390932304068379.post-33813709063700783122023-02-17T06:35:00.031-05:002023-07-29T11:56:24.283-04:00Introducing Hybrid Asset Allocation (HAA)<div style="text-align: left;"><ul style="text-align: left;"><li>HAA aims to offer retail investors a tactical asset allocation strategy that is both balanced and aggressive at the same time.</li>
<li>HAA’s hybrid approach combines traditional dual momentum with canary momentum which results in robust crash protection with low cash-fractions.</li>
<li>HAA effectively selects assets only when they are most likely to appreciate.</li>
<li>HAA’s ability to obtain positive returns consistently is demonstrated by backtesting the strategy for over 50+ years covering various economic regimes.</li>
</ul>
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<p style="text-align: left;">
Hybrid Asset Allocation (HAA) is a novel approach which combines <i>“traditional”</i> dual momentum with <i>“canary”</i> momentum. Dual momentum is based on the concept of assets price trends and consists of absolute (trend following) and relative (cross-sectional) momentum. In addition to the traditional dual momentum framework HAA adds an extra layer for crash protection at the portfolio level based on a single canary asset in the protective (or canary) universe. HAA allows only for offensive investments when the canary asset is uptrending and switches in full to defensive investments if and for as long as this asset is not uptrending. Interested readers are referred to our paper published on <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4346906" target="_blank">SSRN</a> which offers a comprehensive explanation of the HAA methodology including explanations of the used jargon and abbreviations.
</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOEaVCZSp5QUPU6LH4oIQuhN9lF16ssOe7FRzlV7CGT4kmSL8277Ne81G1NHM8t7R3GU1639ALbyaXgKPBqyoaVbY-lvO4B-J_zP5zzV2kuxjD0FQPCAzN2eLmlmC6QYpkpOYVwJB2z0L1mbvve37VZNd3mOM6YUbq9SlvG2k6udllICovNgcnTKg0/s692/caleidoscope%20-%20123rf.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="692" data-original-width="692" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOEaVCZSp5QUPU6LH4oIQuhN9lF16ssOe7FRzlV7CGT4kmSL8277Ne81G1NHM8t7R3GU1639ALbyaXgKPBqyoaVbY-lvO4B-J_zP5zzV2kuxjD0FQPCAzN2eLmlmC6QYpkpOYVwJB2z0L1mbvve37VZNd3mOM6YUbq9SlvG2k6udllICovNgcnTKg0/s320/caleidoscope%20-%20123rf.jpg" width="320" /></a></div><br /><b><br /></b><div><b>Strategy layout</b><br /><p>HAA effectively utilizes the dual momentum framework for harvesting risk premia in financial markets by only allocating capital to assets when they are most likely to appreciate. To this effect three different universes are deployed: a protective, an offensive, and a defensive universe. </p><p>First for early crash warning the trend of the overall market is assessed through a single canary asset, for which we have taken into account the recent (2022) stagflation-like regime with low equity growth and rising yields/inflation, including possible recessions by ‘inverted- yield-curves’ from FED actions like interest hikes and tapering. Hence our choice for HAA’s dedicated canary asset needs to be sensitive not only to rising yields but to rising (expected) inflation too. When the canary momentum is positive, cross-sectional relative strength momentum is used for selecting the best assets with the highest performance while trend-following absolute momentum reduces potential drawdown by replacing best but <i>“bad”</i> (non-positive) risky assets to a safe harbor short-term or intermediate-term treasury bond fund, as is fully the case when canary momentum is “bad”. For all three universes one and the same momentum filter is applied.</p><p>The objective of HAA was to design an investment strategy that is both balanced and aggressive at the same time, while specifically aiming for low cash-fractions despite robust crash protection. We had to consider that small top sizes happen to be more aggressive but less balanced, while smaller universes tend to improve the effectiveness of absolute momentum based crash protection. To combine these opposite characteristics, we found a top size of four assets out of four different financial asset-classes with two assets per class for broad diversification to be a good compromise. </p><a name='more'></a><p>For <i>HAA-Balanced</i>, which is our preferred setup for HAA, four different financial asset-classes are equally present in a global <i>offensive</i> investment universe to achieve diversified portfolios:</p><div style="text-align: left;"><ul style="text-align: left;"><li><b>US Equities</b>: large cap S&P 500 (<b>SPY</b>) and small cap Russell 2000 (<b>IWM</b>)</li><li><b>Foreign Equities</b>: developed markets (<b>VEA</b>) and emerging markets (<b>VWO</b>)</li><li><b>Alternative Assets</b>: commodities (<b>DBC</b>) and US real estate (<b>VNQ</b>)</li><li><b>US Bonds</b>: 7-10y Treasury (<b>IEF</b>) and 20y Treasury (<b>TLT</b>)</li></ul></div><p style="text-align: left;">The <i>protective</i> (or canary) universe and the <i>defensive</i> universe for capital preservation are populated by one and two US Treasury funds, respectively, regardless of the size and composition of the offensive universe:</p><div style="text-align: left;"><ul style="text-align: left;"><li><b>Canary universe</b>: US Treasury Inflation Protected (<b>TIP</b>)</li><li><b>Defensive universe</b>: US 1-3m T-Bill (<b>BIL</b>) and 7-10y Treasury (<b>IEF</b>)</li></ul></div><p style="text-align: left;">Within the defensive universe, being able to (only) select the safe harbor fund with the highest momentum out of short-term T-Bills or intermediate-term Treasury bonds adds the benefit of alternation, making the safety module to a large extent immune to rising rates while allowing for the prospect of “crisis alpha” too.</p><p><b>The HAA recipe</b></p><p>On the close of the last trading day of each month t: </p><div style="text-align: left;"><ol style="text-align: left;"><li>Calculate the momentum of each asset in the offensive, defensive (BIL, IEF) and canary (TIP) universe, where momentum is the (unweighted) average total return over the past 1, 3, 6, and 12 months (13612U) and rank assets based on their momentums for each universe separately. </li><li>Select only the best defensive “cash” asset (BIL or IEF) when TIP’s momentum is non-positive (13612U <= 0), or else allocate 1/TopX of the portfolio to each of the best TopX half of the risky assets (equally weighted), while replacing each of those TopX assets by the best defensive “cash” asset when it has non-positive momentum. </li><li>Hold all positions until the final trading day of the following month. Rebalance the entire portfolio monthly, regardless of whether there is a change in positions. </li></ol></div><p style="text-align: left;">In our paper on <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4346906" target="_blank">SSRN</a> we selected the <i>HAA-Balanced</i> strategy with a Top4 out of 8 global assets in the offensive universe: SPY, IWM, VEA, VWO, VNQ, DBC, IEF, TLT (G8/T4) and the <i>HAA-Simple</i> strategy with just one US offensive asset (SPY only). Please refer to our paper for the demonstration of the robustness of HAA-Balanced with 4x4, 4x3, 4x2, and 4x1 sized <i>offensive</i> universes, for each of which our design objectives were met. As pointed out in our paper, HAA with only SPY as offensive asset might just be a <i>“lucky shot”</i>, since other choices for a single investment asset result in considerably higher drawdowns. With that out of the way, for both flavors of HAA performance details are shown below. </p><p><b>Performance overview</b></p><p>The following tables, charts, and diagrams provide a detailed view on the performance of (G8/T4) and HAA-Simple (SPY only). Results are derived from monthly total return ETF data extended with calibrated indices. Furthermore, risk-free rates, trading costs, slippage, and taxes are disregarded. Results are therefore purely hypothetical. Past performance is no guarantee of future results.</p><p>The key performance indicators for both of HAA’s flavors show that HAA-Balanced’s diversification over four different asset classes results in lower volatilities, drawdowns, and cash allocations for nearly all sample periods combined with higher reward/risk ratios when compared to HAA-Simple. Notice especially HAA-Balanced’s very low cash fraction CF on full sample, which was one of our main design objectives.</p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjumAFq8Ks3GoITRjFg41G_Bs5z3wGh_j8mdSyUgzRYq-TmLKS2ZYvEY6F97CgsTpJ3UHeGDZ16mEp24KCncY9ANAMACEIy52sSBtYP4TOLC_5GEgld1TNg_20rqeDl3wrCGaas_wsILjWhskSPlYC3Uw-jiqtkYpJbgtg_6yC8OX5ck-iNxnb-z_9j" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="332" data-original-width="1772" height="120" src="https://blogger.googleusercontent.com/img/a/AVvXsEjumAFq8Ks3GoITRjFg41G_Bs5z3wGh_j8mdSyUgzRYq-TmLKS2ZYvEY6F97CgsTpJ3UHeGDZ16mEp24KCncY9ANAMACEIy52sSBtYP4TOLC_5GEgld1TNg_20rqeDl3wrCGaas_wsILjWhskSPlYC3Uw-jiqtkYpJbgtg_6yC8OX5ck-iNxnb-z_9j=w640-h120" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjEks-rG_OKfMnRY3Aucshi-9e0lipDDmb4_eBU8-er69HsZyTSZB58_6bb2fgFtS6AsMzFrieePzup0De1qHwoWLpliQ1wAzRRzzCCX5Hb0zXm1s1gL04nAZAKa1nVGHAowtlJ2nKp1oGWzgsjC0hL5SGoNsA6XzSsz_Hn7XbryMdS8RQUS9luCfdv" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="336" data-original-width="1772" height="122" src="https://blogger.googleusercontent.com/img/a/AVvXsEjEks-rG_OKfMnRY3Aucshi-9e0lipDDmb4_eBU8-er69HsZyTSZB58_6bb2fgFtS6AsMzFrieePzup0De1qHwoWLpliQ1wAzRRzzCCX5Hb0zXm1s1gL04nAZAKa1nVGHAowtlJ2nKp1oGWzgsjC0hL5SGoNsA6XzSsz_Hn7XbryMdS8RQUS9luCfdv=w640-h122" width="640" /></a></div></div>
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<span><i>Key performance indicators for HAA-Balanced (above) and HAA-Simple (below)</i></span></div>
<p style="text-align: left;">The smooth upwards slope of especially HAA-Balanced’s portfolio equity curve reflects the consistent profitability as well as its low portfolio volatility. Notice however the deeper and at times prolonged troughs in HAA-Simple’s chart during drawdown periods.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2RGRRrbkRB9BxxUZwe0jJNRl8m8bBjy7wTc91DGIqxB4w5xC41vzqXRHwsiU7zSy00xWRg1zsy98Gf9ZLi1qFSWSfCcMpFW9e_VwfD2qaAFgYZ9cppDtqq8ZQUoiGT1zk_41Zfo47lKEFa9-LOeHXqq8uMueYSfhVU2444JsaTb8YizFXujwab7aN/s1400/1.2%20Portfolio%20Performance.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="700" data-original-width="1400" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2RGRRrbkRB9BxxUZwe0jJNRl8m8bBjy7wTc91DGIqxB4w5xC41vzqXRHwsiU7zSy00xWRg1zsy98Gf9ZLi1qFSWSfCcMpFW9e_VwfD2qaAFgYZ9cppDtqq8ZQUoiGT1zk_41Zfo47lKEFa9-LOeHXqq8uMueYSfhVU2444JsaTb8YizFXujwab7aN/w640-h320/1.2%20Portfolio%20Performance.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitkRFK8B6Us87F2vqF3j86VKj2byfmxSVhxSaPq-PU_85jTOS85N0yYhbyq5e5iPd1D5APMJ-o6qHxfvEj1TbT36Hp5MdKkba3N-yQ4q7hIXCtL6wnzf5e_wwPsrUGBX9ZHjEZ_9Dm9vJGcOqzDIggra8554L5v9QIudHbwMJTjkUKg9v13jI9mY0P/s1400/1.2%20Portfolio%20Performance.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="700" data-original-width="1400" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitkRFK8B6Us87F2vqF3j86VKj2byfmxSVhxSaPq-PU_85jTOS85N0yYhbyq5e5iPd1D5APMJ-o6qHxfvEj1TbT36Hp5MdKkba3N-yQ4q7hIXCtL6wnzf5e_wwPsrUGBX9ZHjEZ_9Dm9vJGcOqzDIggra8554L5v9QIudHbwMJTjkUKg9v13jI9mY0P/w640-h320/1.2%20Portfolio%20Performance.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><span><i>Portfolio equity curves for HAA-Balanced (above) and HAA-Simple (below)</i></span></div><div><br /></div><div>All rolling 3-year periods returns were positive for both versions of HAA, see the charts below.</div><div> </div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhn2KzCjXVDA_Qsldy52Zj8_sZCc-KgYUFsbjvP8YrzHfAdFOFCgWZp25VYnR-aE71OtfX4Caf-WWUNWhBsA9YlPhTglO6xVE1kcVr5uZYLDpoDXCJJvvb9ppDzfgE0SfkmL8cPG25TPvo-SzEHHQ9_DhPMsuzoKXF1hSj6OjJpH5npJglKtY9kwJ7R/s1400/9.6.%20Rolling%20Return%20(3%20year).png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="700" data-original-width="1400" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhn2KzCjXVDA_Qsldy52Zj8_sZCc-KgYUFsbjvP8YrzHfAdFOFCgWZp25VYnR-aE71OtfX4Caf-WWUNWhBsA9YlPhTglO6xVE1kcVr5uZYLDpoDXCJJvvb9ppDzfgE0SfkmL8cPG25TPvo-SzEHHQ9_DhPMsuzoKXF1hSj6OjJpH5npJglKtY9kwJ7R/w640-h320/9.6.%20Rolling%20Return%20(3%20year).png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWsO6eI-aDxeEez3pBAN_I1IIygebUsvwXMtn6dQ70Kf8lzz-tXbocW4B4YfLcBehwkmlbO_fqanNNfvHG3Ci7JqhNEPEufMbODq5i6mxhd6D5DTMQHPmUNX5Ij0Pfo_0qZExkQqjS0iaJzYwFmyZ5iOegJzsqBRuebn9mImI0Gx5jX62ZCm72eraq/s1400/9.6.%20Rolling%20Return%20(3%20year).png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="700" data-original-width="1400" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWsO6eI-aDxeEez3pBAN_I1IIygebUsvwXMtn6dQ70Kf8lzz-tXbocW4B4YfLcBehwkmlbO_fqanNNfvHG3Ci7JqhNEPEufMbODq5i6mxhd6D5DTMQHPmUNX5Ij0Pfo_0qZExkQqjS0iaJzYwFmyZ5iOegJzsqBRuebn9mImI0Gx5jX62ZCm72eraq/w640-h320/9.6.%20Rolling%20Return%20(3%20year).png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><span><i><span style="text-align: left;">Charts with returns for 3-year rolling periods </span>for HAA-Balanced (above) and HAA-Simple (below)</i></span></div><div><br /></div><div>The annual return distribution for HAA-Balanced shows only one (limited) down year over a 50+ year period compared to 7 negative against 45 positive annual returns for HAA-Simple.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXNdeHi9TzrUIEknC1jE-PXM7PtlbOCYd_BH7EfL_gEVHl1YkJdxUTCO9q0KOYJTqQFkExyudNeTV-pSA1wnc_rUVAVJhRUmWSjsVuwxI0s1cSSpv8hh5zf2C6AzqFQf_uv7xxRGbCVlUG2LIFYNI0GhpFySIwAM28romZ1PWJEG4XWlCt62SbJF8D/s1400/4.%20Annual%20Profits.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="700" data-original-width="1400" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXNdeHi9TzrUIEknC1jE-PXM7PtlbOCYd_BH7EfL_gEVHl1YkJdxUTCO9q0KOYJTqQFkExyudNeTV-pSA1wnc_rUVAVJhRUmWSjsVuwxI0s1cSSpv8hh5zf2C6AzqFQf_uv7xxRGbCVlUG2LIFYNI0GhpFySIwAM28romZ1PWJEG4XWlCt62SbJF8D/w640-h320/4.%20Annual%20Profits.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj10SHMLwG2RTeAm8cKD4VI4Wj7JmVFKT35d2dXzN-FidPVgMEgsklalTMaGrFYhbEzmAvudexrtd1cG7yuwulNph86U6_nRJMckLVDuDxx--mylU5GurR9ypVUjCIpYh7zPnHMxdnzdmz2-sXvNhfleUasmsvLONyuOD55Pkwiw6b2E8MRaYKtt14j/s1400/4.%20Annual%20Profits.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="700" data-original-width="1400" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj10SHMLwG2RTeAm8cKD4VI4Wj7JmVFKT35d2dXzN-FidPVgMEgsklalTMaGrFYhbEzmAvudexrtd1cG7yuwulNph86U6_nRJMckLVDuDxx--mylU5GurR9ypVUjCIpYh7zPnHMxdnzdmz2-sXvNhfleUasmsvLONyuOD55Pkwiw6b2E8MRaYKtt14j/w640-h320/4.%20Annual%20Profits.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><span><i><span style="text-align: left;">Annual return distributions for HAA-Balanced (above) and HAA-Simple (below)</span></i></span></div><p>The histograms depicting profit contributions clearly illustrate the difference between the Balanced and Simple versions. All four market sectors contribute to HAA-Balanced’s performance, while by design HAA-Simple almost entirely depends on its singular offensive asset SPY. </p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi40G5HAk01PJ6LNlvDF9bUqJ2f0GxEn0vjuHKYF_chhOcaqDzzzS9Ixm0HgQtW8ABr_C0m1ygTTWGm1rGPXxvVdfa_G6SKUv2cotbU4JlHNeps7I9HdCZtTGg2fB8ZNkTZjV2222nyEC95zPI7ahVNQ3g7484QV60dZi-FGaQNyS-hxp7HymE6CqZg/s1400/5.%20Profit%20Contribution.png" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="700" data-original-width="1400" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi40G5HAk01PJ6LNlvDF9bUqJ2f0GxEn0vjuHKYF_chhOcaqDzzzS9Ixm0HgQtW8ABr_C0m1ygTTWGm1rGPXxvVdfa_G6SKUv2cotbU4JlHNeps7I9HdCZtTGg2fB8ZNkTZjV2222nyEC95zPI7ahVNQ3g7484QV60dZi-FGaQNyS-hxp7HymE6CqZg/w640-h320/5.%20Profit%20Contribution.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidBgHT7rvXQqcroVsprrC1lGUzlMxM-bU_Wbv20oF_u6l2Ul59zP_y9mRLSuUUtvYlCkVzNqD6uFb8hFY1Fi_Qsb9g0FKBhtzHWAzy4tnJxd63QLevIdU2eV44yBWTffJpMbmO3RNTe_rHaiQ01_rcJREJdXjbLKKzsXQ5WcRGBMMSmgeeVl9wtULg/s1400/5.%20Profit%20Contribution.png" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="700" data-original-width="1400" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidBgHT7rvXQqcroVsprrC1lGUzlMxM-bU_Wbv20oF_u6l2Ul59zP_y9mRLSuUUtvYlCkVzNqD6uFb8hFY1Fi_Qsb9g0FKBhtzHWAzy4tnJxd63QLevIdU2eV44yBWTffJpMbmO3RNTe_rHaiQ01_rcJREJdXjbLKKzsXQ5WcRGBMMSmgeeVl9wtULg/w640-h320/5.%20Profit%20Contribution.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;"><i>Per asset profit contributions for HAA-Balanced (above) and HAA-Simple (below)</i></div>
<p style="text-align: left;">The diagrams below show the allocation percentages to HAA’s defensive universe over more than half a century. Notice in the lower pane the binary all in/out (0/100%) approach of HAA-Simple due to its single risky asset (N1/T1). Because “bad” Top4 assets are replaced by the best safe harbor fund, HAA-Balanced offers more top selection choices (0, 25, 50, 75, and 100%), which at times results in mixed offensive/defensive portfolio allocations (0% < CF < 100%) as the upper pane shows. For reference the middle pane shows the cash fractions based on the canary momentum of TIP only, so without hybrid protection's absolute momentum filter for the offensive universe. </p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgO2OdmYJosHb-Lz-1_1dtvTlkJJQ0w7JN-1xeZIw955ttTr84qn1GfTlVOrqO7HFOy8iSgq7mm9hJbvbtX-1iX_Gms2Z9bUrxLt16EhzWfmysbGgSuIppG1IIajTzn7bT2O0eiXY7kyCdrZHt7qqZy_kqdUr9wsBKRh7oIM7nV-9remG3fOrZoKc2u" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="476" data-original-width="2818" height="108" src="https://blogger.googleusercontent.com/img/a/AVvXsEgO2OdmYJosHb-Lz-1_1dtvTlkJJQ0w7JN-1xeZIw955ttTr84qn1GfTlVOrqO7HFOy8iSgq7mm9hJbvbtX-1iX_Gms2Z9bUrxLt16EhzWfmysbGgSuIppG1IIajTzn7bT2O0eiXY7kyCdrZHt7qqZy_kqdUr9wsBKRh7oIM7nV-9remG3fOrZoKc2u=w640-h108" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiytlvVMMUi4AmFuO8BcsWy3Dwnp1aM_HD0SPZ6w6Qd6tb_Ra8hkRebleg2r6NxT_lXbSeOrBeSOrK1BKJG8edE1uZuwg40M-dWy_F-j7Xa2fAZNg52DLUSVk7gZW_AvOKEvmhCg-D7SKlmtuBo4SFEe5vVtTuxg5fqmtefsOYv9mDxK9tBWj_p5qFc" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="478" data-original-width="2820" height="108" src="https://blogger.googleusercontent.com/img/a/AVvXsEiytlvVMMUi4AmFuO8BcsWy3Dwnp1aM_HD0SPZ6w6Qd6tb_Ra8hkRebleg2r6NxT_lXbSeOrBeSOrK1BKJG8edE1uZuwg40M-dWy_F-j7Xa2fAZNg52DLUSVk7gZW_AvOKEvmhCg-D7SKlmtuBo4SFEe5vVtTuxg5fqmtefsOYv9mDxK9tBWj_p5qFc=w640-h108" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjDdzTPCf9jVonQA1EIUwIAwzsrpX9bsiOmNTQLFgn02dgFOzXxBYE1acvy8iLd4iwGYASrx6a5zawyqvEjEsqxoS-_6704bQb1rHHEinbYSao8ZQOMZhXzvY7GFBQjYNJjEpMrGMgJrqvyveW_IzQ5MGqlLZXlNa9pc7uX4_TVwCpvmp-OH_AsdyXc" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="478" data-original-width="2820" height="108" src="https://blogger.googleusercontent.com/img/a/AVvXsEjDdzTPCf9jVonQA1EIUwIAwzsrpX9bsiOmNTQLFgn02dgFOzXxBYE1acvy8iLd4iwGYASrx6a5zawyqvEjEsqxoS-_6704bQb1rHHEinbYSao8ZQOMZhXzvY7GFBQjYNJjEpMrGMgJrqvyveW_IzQ5MGqlLZXlNa9pc7uX4_TVwCpvmp-OH_AsdyXc=w640-h108" width="640" /></a></div></div></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"><i>Cash Fractions</i></span><i><span style="text-align: left;"> </span>for HAA-Balanced (upper), TIP based (middle), and HAA-Simple (lower)</i></div><div><br /></div><div>The higher rate of diversification (Top4 out of 4 asset classes of each 2 assets, so minimal 2 different asset-classes in each Top4) of the Balanced approach is reflected in the allocation diagram resulting in higher turnover too with on average seven trading months a year while HAA-Simple averages only two months for re-allocations (except for rebalance of the same assets only). Notice the heights of the sky-scraping defensive allocations during times of market turmoil, while the alternation between BIL and IEF reflect the frequent periods with rising respectively falling yields.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhog10FXd4IHdZ5v0_hL3o38qalSvthLWQmFNkiU36j9gswyIeuP9uLWDQrzJcJT6lj2V1YTQNB6fjCD1fqsD2dFMsBXqRyBGR6QNz3ndkdIY0Z7uvkKE1nQO9U0NE8PaEYLjZSuBJaPtjlsHh9fdXaj0y98M4cTpes9i1iwpHhhgOiDhyjrocImcBV/s1400/6.2.%20Manhattan%20Allocation%20Diagram.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="700" data-original-width="1400" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhog10FXd4IHdZ5v0_hL3o38qalSvthLWQmFNkiU36j9gswyIeuP9uLWDQrzJcJT6lj2V1YTQNB6fjCD1fqsD2dFMsBXqRyBGR6QNz3ndkdIY0Z7uvkKE1nQO9U0NE8PaEYLjZSuBJaPtjlsHh9fdXaj0y98M4cTpes9i1iwpHhhgOiDhyjrocImcBV/w640-h320/6.2.%20Manhattan%20Allocation%20Diagram.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigXKy_RLcGXWSk40niB0AZQHbN1x3gZadGFlY_L5PpZmU87ExYC73HKFDIheUSbaeYA05bicnrmj9o0aW1EQWdLvfc8yW1uP3VXUMSCsfH06diHzUTpHlvKMI51lSJVP9a8Feed6lIx-4gh8khwyXcHv5R57x99lIGNKKmArHYPVLsBLSaNwH82HIp/s1400/6.2.%20Manhattan%20Allocation%20Diagram.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="700" data-original-width="1400" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigXKy_RLcGXWSk40niB0AZQHbN1x3gZadGFlY_L5PpZmU87ExYC73HKFDIheUSbaeYA05bicnrmj9o0aW1EQWdLvfc8yW1uP3VXUMSCsfH06diHzUTpHlvKMI51lSJVP9a8Feed6lIx-4gh8khwyXcHv5R57x99lIGNKKmArHYPVLsBLSaNwH82HIp/w640-h320/6.2.%20Manhattan%20Allocation%20Diagram.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"><i>Allocation diagrams</i></span><i><span style="text-align: left;"> </span>for HAA-Balanced (above) and HAA-Simple (below)</i></div><div><b><br /></b></div><div><b>Conclusion</b></div><p>By combining traditional dual momentum with inflation protected canary momentum HAA results in robust performance when applied to diversified investment universes. With a winning month ratio of around 70% especially HAA-Balanced is favorable for sustaining a retail investor’s most important investment ability of all: “the emotional discipline to execute their planned strategy faithfully, come hell, high water, or the apparent end of capitalism as we know it.” (William J. Bernstein, <a href="https://www.amazon.com/Investors-Manifesto-Prosperity-Armageddon-Everything/dp/1118073762/ref=sr_1_1?crid=1AMA0HI14ME73&keywords=The+Investor%27s+Manifesto%3A+Preparing+for+Prosperity%2C+Armageddon%2C+and+Everything+in+Between&qid=1676632443&sprefix=the+investor%27s+manifesto+preparing+for+prosperity%2C+armageddon%2C+and+everything+in+between%2Caps%2C300&sr=8-1" target="_blank">The Investor's Manifesto: Preparing for Prosperity, Armageddon, and Everything in Between</a>). </p><p><b>Strategy signals</b></p><p>A signals table for Hybrid Asset Allocation with the above mentioned setups will be added to the <a href="https://indexswingtrader.blogspot.com/p/strategy-signals.html" target="_blank">Strategy Signals</a> page in due time. Until then, the table is fully functional below. Please take note of the limitations as mentioned on the <a href="https://indexswingtrader.blogspot.com/p/strategy-signals.html" target="_blank">Strategy Signals</a> page.</p><p><span style="color: red;"><b>[Datalink with GoogleFinance appears to be working again, so reversed back to VEA] </b></span></p><p><br />
<iframe height="550" src="https://docs.google.com/spreadsheets/d/e/2PACX-1vRhJ_aPUNgXL9QQkyAfVc3LYi1BHQ9M1_DpLy-fZCZxpJk1zls3zqzdH7msUGZuk7R6JKn2BH8gUAgV/pubhtml?gid=1389397904&single=true&widget=true&headers=false" width="750"></iframe><i>
NB! No guarantee whatsoever is given for the soundness of the strategy nor the proper functioning of the table nor the accuracy of the (time delayed) signals. Please do your own due diligence and use at your peril. The Important Notice in the footer applies as well as the Disclaimer.</i></p><p><b><span style="font-family: inherit;">Endnotes</span></b></p><div style="text-align: left;"><ul style="text-align: left;">
<li><span style="font-family: inherit;">The AmiBroker implementation of HAA supports flexible segmenting to support different portfolio sizes as described in our paper on <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4346906" target="_blank">SSRN</a>.</span></li>
<li><span style="font-family: inherit;"><a href="https://allocatesmartly.com/?aff=220" target="_blank">AllocateSmartly.com</a> has added <a href="https://allocatesmartly.com/members/strategy/keller-and-keunings-hybrid-asset-allocation/?aff=220" target="_blank">HAA</a> to their collection of the industry’s best tactical asset allocation strategies (members area). For a good understanding of HAA be sure to check out their <a href="https://allocatesmartly.com/hybrid-asset-allocation/?aff=220" target="_blank">blog</a> too (public area).</span></li>
<li><span style="font-family: inherit;">All TAA-papers by prof. Keller (lead author) are freely available on <a href="https://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=1935527" target="_blank">SSRN</a>.</span></li></ul></div><p style="text-align: left;">The full AmiBroker code for HAA is available upon <a href="mailto:trendxplorer@gmail.com?Subject=Request%20for%20HAA%20model%20in%20AmiBroker" target="_blank">request</a>. Interested parties are encouraged to support this blog with a donation:</p>
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</div>TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-18759885301527580952020-10-28T16:50:00.004-04:002020-11-08T15:06:02.679-05:00Support message for users of the PAA/GPM spreadsheet<p><span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif" style="caret-color: rgb(34, 34, 34); font-size: 13.199999809265137px;">[Updated] Due to a change in the placement of OHLC price data in Tiingo's feed, version 4.0 of the stand alone Excel spreadsheet should no longer be used! </span><span style="caret-color: rgb(34, 34, 34); font-size: small;">In beta version 5.0 the issue has been fixed by JH. Great job!</span></p><div style="caret-color: rgb(34, 34, 34); font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.199999809265137px;"><br /></div>TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-52133915394595110082018-12-31T06:21:00.004-05:002023-07-29T11:57:23.463-04:00Exploring Smart Leverage: DAA on Steroids<ul>
<li>The constant leverage myth is busted: there is no <strike>spoon</strike> natural decay. </li>
<li>DAA’s fast protective momentum approach successfully detects lower volatility regimes with higher streak potential. </li>
<li>Smart leverage through a clever separation of signals and trades can achieve considerable outperformance even on a risk adjusted basis.</li>
</ul>
<br />
Popular belief that constant leveraging results in decay over time is a myth. Michael Gayed and Charles Bilello busted the myth in their 2016 Dow Award winning paper “<a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2741701" target="_blank">Leverage for the Long Run</a>”. Their research shows that daily re-leveraging is not without risk. At times the act of re-leveraging can even be mathematically destructive. Yet the source of that risk does not come from some inherent form of natural decay. The authors single out high volatility and seesawing action as the (real) enemies of leverage, while low volatility and streaks in performance are its friends.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfKHc17XYRqH8j96-9BvDKZfy_DT06ycza9sv0ET54Axc9KfLBOedPw7F9V5Lb3bgoM9-Wz0WJpyhNlK0jKE4crPKJcWA3nWnYnaLNzthpIluY1HhtroTm2a62LNvtFiwv-n3ESvM-B4c/s1600/blurred+lights+-+123rf.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="565" data-original-width="848" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfKHc17XYRqH8j96-9BvDKZfy_DT06ycza9sv0ET54Axc9KfLBOedPw7F9V5Lb3bgoM9-Wz0WJpyhNlK0jKE4crPKJcWA3nWnYnaLNzthpIluY1HhtroTm2a62LNvtFiwv-n3ESvM-B4c/s400/blurred+lights+-+123rf.jpg" width="400" /></a></div>
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<div class="separator" style="clear: both; text-align: left;">
As stated in the paper daily re-leveraging combined with high volatility creates compounding issues, often referred to as the “constant leverage trap”. A systematic way of identifying lower volatility regimes with higher streak potential is key for achieving outperformance through smart leverage. Expanding on the authors application of moving averages for identifying those conditions, in the following article smart leverage is explored using the DAA framework with its fast 13612W protective momentum approach with a dedicated two-asset canary universe. </div>
<br />
When the stock market is in an uptrend - positive 13612W momentum for all canary assets - favorable conditions for leveraged stock positions are assumed targeting positive streaks in performance. When the stock market is in a downtrend - negative 13612W momentum for one or more of the canary assets - a rise in volatility is expected and a (relatively) safe Treasury bond position is acquired to avoid the constant leverage trap for stocks.<br />
<br />
On top of DAA’s dedicated 13612W protective momentum deployment for detecting favorable conditions for leverage, the smart leverage approach incorporates a clever separation of signals and trades. As proposed by Matthias Koch, a quant from Germany, non-leveraged asset universes are used for signaling momentum based position sizing while universes that hold a limited number of matching leveraged funds are used for actual trading.<br />
<br />
<a name='more'></a>With a modified DAA framework to support the required signal-trade separation, we explore smart leverage based on the diversified G12 ETF portfolio as featured in our DAA-paper: SPY, QQQ, IWM, VGK, EWJ, VWO, GSG, GLD, VNQ, HYG, TLT, and LQD. The demonstration is introduced with the DAA setup as benchmark for the subsequent smart leverage setups.<br />
<br />
For readers unfamiliar with the concepts of breadth momentum and protective momentum, the VAA and DAA posts (see <a href="https://indexswingtrader.blogspot.com/2017/07/breadth-momentum-and-vigilant-asset.html" target="_blank">here</a> and <a href="https://indexswingtrader.blogspot.com/2018/07/announcing-defensive-asset-allocation.html" target="_blank">here</a>) are required reading as these concepts along with the used abbreviations are considered prior knowledge.<br />
<br />
<span style="color: red;"><b>Warning</b></span><b><span style="color: red;">:</span></b> Caution is warranted as leverage involves higher risks to costs and loss.<br />
<br />
<br />
<b>Volatility regimes</b><br />
<br />
The below daily chart for SPY paints a clear picture with respect to the volatility regimes over the last nearly 20 years. The two sub panes show the annualized volatilities measured over the rolling 21-days (1-month) and 252-days (1-year) respectively. Notice the rise in volatility during bear markets and the drop to lower volatility typical for periods when bull markets are picking up steam. Smart leverage targets those lower volatility regimes because of their higher streak potential.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXqYNBTtG7MJmonwQemL00xwniX-XPId9Vx8FYWqgI4dQs1M1i1FIg4ZC5QMnyuGwvsQq2JdA9cdD4rQUAOxzLlU1k_Lcza-beQ4d-s1CG_mWYTu_VR0iYy2KCZtr-IoAUK98yJwr87vI/s1600/%2524SPY+21d+252d+Volatility.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="881" data-original-width="1402" height="402" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXqYNBTtG7MJmonwQemL00xwniX-XPId9Vx8FYWqgI4dQs1M1i1FIg4ZC5QMnyuGwvsQq2JdA9cdD4rQUAOxzLlU1k_Lcza-beQ4d-s1CG_mWYTu_VR0iYy2KCZtr-IoAUK98yJwr87vI/s640/%2524SPY+21d+252d+Volatility.png" width="640" /></a></div>
<br />
The accompanying table with SPY’s key performance indicators offers insight into the regime characteristics for the 2000-2018 time frame. Notice the changes in CAR’s and volatilities. To match the above daily chart, the table metrics are obtained with daily endpoints for higher granularity too.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4A_S3ZGkj2FfB6uq6i6d9vmHb1VL65DJFhdQyef17cPLyQ5dxwGnjGbqK9uua9YJ4GsnbmNGinEUfO4aqw5M9elvaxFwM1A9ewuj_y9YIA2NOpVqjELokE_HSsUJSXlJUef7brThMj0w/s1600/SPY+KPI+table+daily+endpoints.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="351" data-original-width="1600" height="140" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4A_S3ZGkj2FfB6uq6i6d9vmHb1VL65DJFhdQyef17cPLyQ5dxwGnjGbqK9uua9YJ4GsnbmNGinEUfO4aqw5M9elvaxFwM1A9ewuj_y9YIA2NOpVqjELokE_HSsUJSXlJUef7brThMj0w/s640/SPY+KPI+table+daily+endpoints.png" width="640" /></a></div>
<br />
NB! Tables in the remainder of this article are based on monthly endpoints for comparison with previous posts, i.e. on EAA, PAA, VAA, and DAA.<br />
<br />
<br />
<b>Smart Leverage</b><br />
<br />
The smart leverage approach is demonstrated using the DAA framework. To recall, DAA’s key elements are its fast 13612W momentum filter combined with a dedicated protection universe with only two “canary” assets (VWO and BND) whose absolute momentum readings are decisive for capital allocation between “risky”and “safety” assets.<br />
<br />
Smart leverage incorporates a clever separation of signals and trades. Absolute and relative momentum based position sizing is derived from non-leveraged ETF universes, while the actual trading universes may hold matching leveraged ETFs (in bold below).<br />
<br />
To crystalize the concept for the DAA smart leverage framework:<br />
Protection: VWO, BND<br />
Signals: SPY,QQQ,IWM,VGK,EWJ,VWO,GSG,GLD,VNQ,HYG, LQD,TLT + SHY,IEF<br />
Trades: <b>SSO</b>,<b>QLD</b>,<b>UWM</b>,VGK,EWJ,VWO,GSG,GLD,<b>URE</b>,HYG,LQD,<b>UBT</b> + SHY,<b>UST</b><br />
<br />
<br />
<b>Data</b><br />
<br />
For the portfolio ETFs the daily (leveraged) histories are synthetically extended going back to December 31, 1998. For our favorite setup a long-term backtest is shown too, covering smart leverage over 1971-2018. The long-term backtests are based on monthly data going back to December 31, 1969. Both series use October 31, 2018 as end dates. For both the daily and monthly data based series results are reported by using monthly endpoints for comparison reasons.<br />
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<b>Backtests Summary</b><br />
<br />
For both the G4 as well as the G12 universe a comprehensive series of backtests gave the following results. The [updated] <a href="https://drive.google.com/drive/folders/1V0C3IHuPrc6_uUaOdXM9zYJ3iWZFqzfD?usp=sharing" target="_blank">Appendix</a> holds the used universe compositions along with detailed performance results. The Appendix also shows the benefit of using separate universes for signals and trades.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBm6oa6mvBs9NtEglPPYHq2NAKPlK3xoxjT8W0V8HKcLrQ0xOwKHQNJDOf49vgNgqp-3I6KZ_eADj_mJTAy9B6gRfaCrDEKEUqzsePCMpYVQ-JrNsP4dWUiYvCHrXODu73lmr1fO9hztA/s1600/Smart+Leverage+Summary+Table.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="577" data-original-width="1600" height="230" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBm6oa6mvBs9NtEglPPYHq2NAKPlK3xoxjT8W0V8HKcLrQ0xOwKHQNJDOf49vgNgqp-3I6KZ_eADj_mJTAy9B6gRfaCrDEKEUqzsePCMpYVQ-JrNsP4dWUiYvCHrXODu73lmr1fO9hztA/s640/Smart+Leverage+Summary+Table.png" width="640" /></a></div>
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</div>
For the remainder of this post DAA-G12 combined with a limited number of double leveraged assets will be in the spotlights. This is the setup with the highest [long-term] risk adjusted performance as measured by Sharpe, MAR, and K(20%) from the full series (see last table row). Noteworthy, long-term results for the DAA-G4 limited leverage setup are very close to DAA-G12's, while the limited leverage setup of DAA-G4 shows the best results over 2000-2018.<br />
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<br />
<b>DAA-G12: The Non-Leveraged Benchmark</b><br />
<br />
The setups for analyzing the global diversified 12 asset portfolio, adhere to DAA’s novel protective momentum approach as introduced in our DAA paper with (always and only) VWO and BND as canary assets. All non-leveraged and leveraged variations use a T6B1 scenario. With a T6 top size rotation, maximum diversification is reached within the top half of the risky R12 universe during lower volatility regimes with higher streak potential. Additionally, with a binary B1 setting DAA reallocates all capital to the best performing safety (treasury) asset in case one or both canary assets register negative 13612W momentum. Only when both VWO and BND register positive 13612W momentum (and only then), risky assets are under consideration for capital allocation. So the used B1 setting keeps defenses high which is key when leveraged assets are involved.<br />
<br />
Actually the benchmark setup is quite similar to the setup used in the DAA paper, with the exception of a smaller, treasury only, bond universe: SHY and IEF. Furthermore, since no leverage is involved for the benchmark setup, signal-trade discrimination is superfluous at this point, hence the benchmark signals are derived from the trade universe.<br />
<br />
DAA-G12 T6B1 R12 C2 P2 (VWO,BND)<br />
Signals: SPY,QQQ,IWM,VGK,EWJ,VWO,GSG,GLD,VNQ,HYG,TLT,LQD + C2:SHY,IEF<br />
Trades: SPY,QQQ,IWM,VGK,EWJ,VWO,GSG,GLD,VNQ,HYG,TLT,LQD + C2:SHY,IEF<br />
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<span style="font-size: x-small;"><i>NB! All presented results are derived from simulated total return data. Furthermore, trading costs, slippage, and taxes are disregarded. Results are therefore purely hypothetical and no investor could have attained these results. The presented results are no guarantee of future returns.</i></span></div>
<br />
For maximum insight the table shows key performance indicators for 8 distinctive periods with changing market regimes. Our DAA-G12 benchmark achieves both volatility and maximum drawdown readings well below a conservative level of 15%, hence the use of the Keller ratio with a (low) 20% threshold (for more on the Keller ratio see <a href="https://indexswingtrader.blogspot.com/2018/04/presenting-keller-ratio.html" target="_blank">here</a>).<br />
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<br />
<b>DAA-G12: Limited Double Leverage </b><br />
<br />
Next the proposed signal-trade separation is deployed for analyzing smart leverage with mixed leveraged and non-leveraged trade universes. Adding double leverage assets, for the R12 portfolio SPY, QQQ, IWM, VNQ, and TLT are replaced by SSO, QLD, UWM, URE, and UBT respectively, while IEF is exchanged for UST on the bonds side. Furthermore signal-trade separation is deployed to ascertain the discrimination effect of the permanent P2 protection universe. All other settings are kept equal to those of the benchmark setup.<br />
<br />
DAA-G12 T6B1 R12 C3 P2 (VWO,BND)<br />
Signals: SPY,QQQ,IWM,VGK,EWJ,VWO,GSG,GLD,VNQ,HYG, LQD,TLT + C2:SHY,IEF<br />
Trades: SSO,QLD,UWM,VGK,EWJ,VWO,GSG,GLD,URE,HYG,LQD,UBT + C2:SHY,UST<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqaRTKFT_FFMjThI8Y9NGsoelbnWaJDRWWYhMjWZDO8X8BX4v18uNtRDuaZq1kKuxlnlhl-teaCeP9B1_3dd6CrFGCXPeTzJua3uWRQwXi3ybAcby-fqvzuyWYK0AgCdzbrBDO4PulhJA/s1600/Chart+7.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="805" data-original-width="1600" height="322" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqaRTKFT_FFMjThI8Y9NGsoelbnWaJDRWWYhMjWZDO8X8BX4v18uNtRDuaZq1kKuxlnlhl-teaCeP9B1_3dd6CrFGCXPeTzJua3uWRQwXi3ybAcby-fqvzuyWYK0AgCdzbrBDO4PulhJA/s640/Chart+7.png" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0HLluozedCEFiJnT7VKn4MHxSuJqpBOUtL56Rd-vJ1CVyFlZF9z-BjJcxbDKc9eBukHvZnXbfoWzLNSNWy1nrdzjPi1djf1SqTPPrcxgOZ3z4EAbBmGtbTL99l_6u9jrdYq2uO_kjWMY/s1600/Table+7.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="351" data-original-width="1600" height="140" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0HLluozedCEFiJnT7VKn4MHxSuJqpBOUtL56Rd-vJ1CVyFlZF9z-BjJcxbDKc9eBukHvZnXbfoWzLNSNWy1nrdzjPi1djf1SqTPPrcxgOZ3z4EAbBmGtbTL99l_6u9jrdYq2uO_kjWMY/s640/Table+7.png" width="640" /></a></div>
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Referencing the benchmark, the smart leverage setup achieves considerable higher CAR metrics but at the cost of higher volatilities and worse maximum drawdowns. The better K(20%) readings for all but one sub period combined with mostly somewhat lower but still impressive UPI readings demonstrate the robustness of the smart leverage approach on a risk adjusted basis.<br />
<br />
A comparison of the following table with the previous one displays the benefit of using separate signal and trade universes for the DAA-G12 setup with its dedicated P2 protection universe. Omitting the separation between signals and trades results in deteriorated performance on both a raw return and a risk adjusted basis for a multitude of metrics on most sub periods.<br />
<br />
Signals: SSO,QLD,UWM,VGK,EWJ,VWO,GSG,GLD,URE,HYG,LQD,UBT + C2:SHY,UST<br />
Trades: SSO,QLD,UWM,VGK,EWJ,VWO,GSG,GLD,URE,HYG,LQD,UBT + C2:SHY,UST<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtbHqR2dEumK-3brod2aC5EyFzDJhI4E-nUxppavyQ2Fk0inQ4lqdvBKKmyCkO9Izef1SVlV5dJyZkk6I8dA9M0uL98Lb8UV9ekTnIoLyeMHJ2z0UEsfEf110DvhCWDopn_-WR0HisLyM/s1600/Table+7a.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="350" data-original-width="1600" height="138" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtbHqR2dEumK-3brod2aC5EyFzDJhI4E-nUxppavyQ2Fk0inQ4lqdvBKKmyCkO9Izef1SVlV5dJyZkk6I8dA9M0uL98Lb8UV9ekTnIoLyeMHJ2z0UEsfEf110DvhCWDopn_-WR0HisLyM/s640/Table+7a.png" width="640" /></a></div>
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<br />
<b>Long-term Impression: DAA-G12 with Limited Double Leverage</b><br />
<br />
A long-term monthly look from December 31, 1970 (excluding 13612W’s initialization period of 1-year) until October 31, 2018 at the global diversified portfolio concludes the demonstration of the smart leverage approach. The used setup has again a T6B1 rotation scenario for maximum diversification within the G12 portfolio’s top half. The protective B1 setting makes sure that the portfolio rotates 100% into safe treasury assets at the first sign of weakness within the canary assets as measured by their 13612W momentum.<br />
<br />
For the above series of comparisons ETFs were used with synthetically extended daily (leveraged) histories going back to December 31, 1998. Since daily index data going back as far as December 31, 1969 is hard to find, if even available, the below used long-term approximations of leveraged assets are derived from monthly total return data (so with monthly instead of daily resets). Therefore the results of the following backtests are merely an impression how the smart leverage approach might have performed over the last nearly 50 years.<br />
<br />
In familiar fashion first the equity chart of the non-leveraged benchmark portfolio is shown, followed again by the chart of the limited double leveraged portfolio.<br />
<br />
DAA-G12 T6B1 R12 C2 P2 (VWO,BND)<br />
Signals: SPY,QQQ,IWM,VGK,EWJ,VWO,GSG,GLD,VNQ,HYG, LQD,TLT + C2:SHY,IEF<br />
Trades: SPY,QQQ,IWM,VGK,EWJ,VWO,GSG,GLD,VNQ,HYG, LQD,TLT + C2:SHY,IEF<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9ZWQKwgvmgUjKQYVejh_F0W1ZLYfUm_2_fgTdUJiTEXmX9zItr34wJj0VhPdq4-Z7RPAT8-WFUaUeYF8ah7-YLtuiK7U7U9R8bCFQSBgm7jkOQvlN-ssFoIK3OtjFlzzALcPgD79qilo/s1600/LT+G12+T6B1+Benchmark.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="806" data-original-width="1600" height="322" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9ZWQKwgvmgUjKQYVejh_F0W1ZLYfUm_2_fgTdUJiTEXmX9zItr34wJj0VhPdq4-Z7RPAT8-WFUaUeYF8ah7-YLtuiK7U7U9R8bCFQSBgm7jkOQvlN-ssFoIK3OtjFlzzALcPgD79qilo/s640/LT+G12+T6B1+Benchmark.png" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7wGTvVAF5oUWHsBq-1utJf7pGy-HYMdy5kSYov0jVR7u8XFH6BLtSG7-cMN0Fh4ekua75BNKfd1qpKmk8_2PvUVgMB2lXC0K7_M5dbKk-cp1cGFDGWP-5nb5sY4nTeMeq8N6ier1zMyo/s1600/LT+G12+T6B1+Benchmark+-+Statistics+Table.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="356" data-original-width="1600" height="142" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7wGTvVAF5oUWHsBq-1utJf7pGy-HYMdy5kSYov0jVR7u8XFH6BLtSG7-cMN0Fh4ekua75BNKfd1qpKmk8_2PvUVgMB2lXC0K7_M5dbKk-cp1cGFDGWP-5nb5sY4nTeMeq8N6ier1zMyo/s640/LT+G12+T6B1+Benchmark+-+Statistics+Table.png" width="640" /></a></div>
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For the benchmark setup the impact of the 1970s “Oil Shock” is visible in the chart, but due to the highly diversified T6 top size the shock effect is mitigated to a great extent. Furthermore the benchmark using only non-leveraged assets shows impressive performance metrics with an overall CAR of 16.50% combined with very low volatility (8.36%) and maximum drawdown (-8.00%) readings. As a result the overall risk adjusted metrics are nothing less than outstanding.<br />
<br />
Next up is the smart leverage setup with its typical signal-trade separation combined with limited double leveraged universes.<br />
<br />
DAA-G12 T6B1 R12 C2 P2 (VWO,BND)<br />
Signals: SPY,QQQ,IWM,VGK,EWJ,VWO,GSG,GLD,VNQ,HYG, LQD,TLT + C2:SHY,IEF<br />
Trades: SSO,QLD,UWM,VGK,EWJ,VWO,GSG,GLD,URE,HYG,LQD,UBT + C2:SHY,UST<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihDVTpYJw_TZdAcPOYdugkxb0QbsZTKncWdAHqxBMxGiNGzFNt1BUmRPLT8IUZb8Pr8rb5czlkvM7Yc9TX9x7FQRrDepOCiOlphtVHGie4DvjejN9fGxXMDC90ROtr1qGPv-VE4USKLn8/s1600/LT+G12+T6B1+LimDoubleLev.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="807" data-original-width="1600" height="322" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihDVTpYJw_TZdAcPOYdugkxb0QbsZTKncWdAHqxBMxGiNGzFNt1BUmRPLT8IUZb8Pr8rb5czlkvM7Yc9TX9x7FQRrDepOCiOlphtVHGie4DvjejN9fGxXMDC90ROtr1qGPv-VE4USKLn8/s640/LT+G12+T6B1+LimDoubleLev.png" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjZf7aPv6R6UNsdKq4iwnsgFDZRAAow_O2dlaXCr_N4ztolYgFSssI_CRP_pTFm65qgX4yIUE-_EsNJvJDKa-8YKGCIngSk6coxMPdxIZ7MBjWleBMNDLJAaQKfAQF2lWkDsC9J6G5vA8/s1600/LT+G12+T6B1+LimDoubleLev+-+Statistics+Table.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="357" data-original-width="1600" height="142" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjZf7aPv6R6UNsdKq4iwnsgFDZRAAow_O2dlaXCr_N4ztolYgFSssI_CRP_pTFm65qgX4yIUE-_EsNJvJDKa-8YKGCIngSk6coxMPdxIZ7MBjWleBMNDLJAaQKfAQF2lWkDsC9J6G5vA8/s640/LT+G12+T6B1+LimDoubleLev+-+Statistics+Table.png" width="640" /></a></div>
<br />
Referencing the benchmark, over the backtested period of nearly half a century the smart leverage setup achieves a nearly 50% higher CAR reading of 23.78% against 16.50% for the non-leveraged setup. Volatility and maximum drawdown increase by roughly the same ratio. Noteworthy, the maximum drawdown level of 12.54% is still well contained below our 15% mark. The risk adjusted K(20%) metric of the smart leverage setup even beats the one of the benchmark and MAR and UPI readings are only slightly lower. Again, this demonstrates the robustness of the smart leverage approach both on a raw return basis as well as on a risk adjusted basis.<br />
<br />
<br />
<b>Long-term Charts</b><br />
<br />
To conclude our exploration of smart leverage with the the DAA-G12 approach with its protective momentum through dedicated canary assets and signal-trade separation, a couple of extra charts are shown to allow for a detailed impression of its long-term performance.<br />
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Annual returns:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqJtGCsFnzcBYMWUSu2jb0xClGTWD9yKjkMTgCPISzye3IknuFBl9rxRQ73aZqaV4U2dQY5AGRBYgyMXA0yTYkZqKUBwcxmuNEhYq7_Q17aclHBilwQ8nNYWWw6Pbi3oA1URruDhYlf6o/s1600/LT+G12+T6B1+Annual+Returns.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="806" data-original-width="1600" height="322" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqJtGCsFnzcBYMWUSu2jb0xClGTWD9yKjkMTgCPISzye3IknuFBl9rxRQ73aZqaV4U2dQY5AGRBYgyMXA0yTYkZqKUBwcxmuNEhYq7_Q17aclHBilwQ8nNYWWw6Pbi3oA1URruDhYlf6o/s640/LT+G12+T6B1+Annual+Returns.png" width="640" /></a></div>
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Monthly maximum drawdowns:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEird9YrXWl8FqI6Zznxm0UIpujBAMCRfuaSscIY_BTRIXJlCCtrUqHJzi82BZQoBp72t7s-0HbfD__Tuyq18lv2fMgT540GamkT-uQqYN3aJAIkA_ZB7s0Qu3Lzv-lroPh-_qPym1fRVmI/s1600/LT+G12+T6B1+Drawdowns.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="804" data-original-width="1600" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEird9YrXWl8FqI6Zznxm0UIpujBAMCRfuaSscIY_BTRIXJlCCtrUqHJzi82BZQoBp72t7s-0HbfD__Tuyq18lv2fMgT540GamkT-uQqYN3aJAIkA_ZB7s0Qu3Lzv-lroPh-_qPym1fRVmI/s640/LT+G12+T6B1+Drawdowns.png" width="640" /></a></div>
<br />
Profit contribution:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgukA6M8W2zTypfbdJvhSH4TLcuz_cs20QhUlXG0_dc02XS4kFaEoyrBCxGoTEKQaxoek1M6pORkPtZyOCez4ViW9bI7WXaiySlR9ZdWKYLJaclTcEtYjN84DOmnRAJwCvqZTIR1uPiR4g/s1600/LT+G12+T6B1+Profit+Contribution.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="806" data-original-width="1600" height="322" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgukA6M8W2zTypfbdJvhSH4TLcuz_cs20QhUlXG0_dc02XS4kFaEoyrBCxGoTEKQaxoek1M6pORkPtZyOCez4ViW9bI7WXaiySlR9ZdWKYLJaclTcEtYjN84DOmnRAJwCvqZTIR1uPiR4g/s640/LT+G12+T6B1+Profit+Contribution.png" width="640" /></a></div>
<br />
Monthly returns and win-rates:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpKWx9tS2qWEOdjvK1ITXFTW9BXga0vGRSKTJ3zjuyYgFjMpGt7bCmYLybDfgMSxnxVhXa0f4JQZnUNp1s4QNWUJFr-jypTGJk0ugrUy2tAlsBVRcGfl7iuMddlKLEfEv1mlnq3wyc7wQ/s1600/LT+G12+T6B1+Monthly+Returns.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="806" data-original-width="1600" height="322" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpKWx9tS2qWEOdjvK1ITXFTW9BXga0vGRSKTJ3zjuyYgFjMpGt7bCmYLybDfgMSxnxVhXa0f4JQZnUNp1s4QNWUJFr-jypTGJk0ugrUy2tAlsBVRcGfl7iuMddlKLEfEv1mlnq3wyc7wQ/s640/LT+G12+T6B1+Monthly+Returns.png" width="640" /></a></div>
<br />
Rolling 1-year returns:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwqSVzTa8-leFvG8eVizVBimFFaMaNK6sv1FNdE_w8xx5jNt_Ne5h2F1NRK2uIKCE9YgfTCGlyCR8ME_xsFstLDG3oQzJNeKBZ2g-4n5N5CFxiRaiU1qDUtBZ85YEocxrjKZAOdgjdtmk/s1600/LT+G12+T6B1+Rolling+1y+Return.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="804" data-original-width="1600" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwqSVzTa8-leFvG8eVizVBimFFaMaNK6sv1FNdE_w8xx5jNt_Ne5h2F1NRK2uIKCE9YgfTCGlyCR8ME_xsFstLDG3oQzJNeKBZ2g-4n5N5CFxiRaiU1qDUtBZ85YEocxrjKZAOdgjdtmk/s640/LT+G12+T6B1+Rolling+1y+Return.png" width="640" /></a></div>
<br />
<br />
<b>Conclusion</b><br />
<br />
Smart leverage with the demonstrated DAA-G12 setup using signal-trade separation manages to steer clear from the constant leverage trap. Combining smart leverage's clever separation of signals and trades together with DAA's novel canary protection proves successful in detecting lower volatility regimes and banks on its higher streak potential resulting in considerable outperformance for both raw and risk adjusted returns as measured with the conservative K(20%) ratio.<br />
<br />
<br />
<b><span style="font-family: inherit;">Strategy Signals</span></b><br />
<br />
A signals table for the DAA-G12 T6B1 strategy with the above mentioned setup will be added to the <a href="https://indexswingtrader.blogspot.com/p/strategy-signals.html" target="_blank">Strategy Signals</a> page in due time. Until then, the table is fully functional below. Please take note of the limitations as mentioned on the <a href="https://indexswingtrader.blogspot.com/p/strategy-signals.html" target="_blank">Strategy Signals</a> page.<br />
<br />
<iframe height="500" src="https://docs.google.com/spreadsheets/d/e/2PACX-1vQqhL6Sb7_Of9qCVmHvOe1Erg6HQ67k9awNqOz-RTNYjvpcv9eW-tmcdqhzlXgNOdJ5jjOuyUPnX7FQ/pubhtml?gid=1389397904&single=true&widget=true&headers=false" width="750"></iframe><i>
NB! No guarantee whatsoever is given for the soundness of the strategy nor the proper functioning of the table nor for the accuracy of the (time delayed) signals. Please do your own due diligence and use at your peril. The Important Notice in the footer applies as well as the Disclaimer.</i><br />
<br />
<b>Update</b>: By popular demand signals are also maintained for the DAA-SL-G4 T3B1 limited double leverage strategy from the <a href="https://drive.google.com/drive/folders/1V0C3IHuPrc6_uUaOdXM9zYJ3iWZFqzfD?usp=sharing" target="_blank">Appendix</a>. Again, please take note of the limitations as mentioned on the <a href="https://indexswingtrader.blogspot.com/p/strategy-signals.html" target="_blank">Strategy Signals</a> page.<br />
<br />
<center>
<iframe height="500" src="https://docs.google.com/spreadsheets/d/e/2PACX-1vSFFYvKFcT3WHGOn7pZ3km9RBGaWkXgjpLR_HJjHAr07BjA8_sX5IxVzfByOic0At_QnIlstGahDUZS/pubhtml?gid=1389397904&single=true&widget=true&headers=false" width="500"></iframe><br />
</center>
<i>NB! No guarantee whatsoever is given for the soundness of the strategy nor the proper functioning of the table nor for the accuracy of the (time delayed) signals. Please do your own due diligence and use at your peril. The Important Notice in the footer applies as well as the Disclaimer.</i><br />
<br />
<br />
<b>Endnotes and cautions</b><br />
<ul>
<li>All reported results are derived from simulated total return ETF data. Furthermore, trading costs, slippage, and taxes are disregarded. Results are therefore purely hypothetical and no investor could have attained these results. The presented results are <span style="caret-color: rgb(34, 34, 34); color: #222222;"><span style="font-family: inherit;">no guarantee of future returns.</span></span> Especially for synthesizing extended data series of leveraged ETFs expense ratios along with the the impact of historically higher borrowing costs are difficult to estimate.</li>
<li>Liquidity, low trading volumes, and assets-under-management requirements limit the practical application of leveraged assets to avoid high slippage costs. These limitations may cause to be problematic in times of market stress when spreads typically widen. Caveat emptor!</li>
<li>Contrary to the mainly decreasing interest rates environment during the analyzed period, the regime for foreseeable future may be characterized by rising rates. Most likely this will have a negative impact on the reported results.</li>
<li>Recommended further reading: “<a href="https://alphaarchitect.com/2018/12/07/trend-following-on-steroids/" target="_blank">Trend Following on Steroids</a>” by Wouter Keller. Furthermore we have included a leverage example in the latest update of our <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3212862" target="_blank">DAA-paper on SSRN</a> (see section 9, page 22).</li>
</ul>
<br />
The full AmiBroker code for DAA's Smart Leverage framework is available upon <a href="mailto:trendxplorer@gmail.com?Subject=Request%20for%20the%20DAA%20Smart%20Leverage%20model%20in%20AmiBroker" target="_blank">request</a>. Interested parties are encouraged to support this blog with a donation:<br />
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<br />TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-61169864723845374782018-07-12T14:04:00.004-04:002023-07-29T11:58:17.929-04:00Announcing Defensive Asset Allocation (DAA)<ul>
<li>Defensive Asset Allocation (DAA) builds on the framework designed for Vigilant Asset Allocation (VAA)</li>
<li>For DAA the need for crash protection is quantified using a separate “canary” universe instead of the full investment universe as with VAA</li>
<li>DAA leads to lower out-of-market allocations and hence improves the tracking error due to higher in-the-market-rates</li>
</ul>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJ513ATGyYo_yjnoBXPAB_6KZdhDodPEuqeejkNVM6rc0KzJ9QMI-eaL26PDrqp6zBNEpYg_zG2rvRrE5vV0ohoz8WLbGxGBsmK4W7cRuTuN3jzPdsswgui-rpRlP1Q7uDnSaOM-N2_2A/s1600/microphone+on+air+-+123rf.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="784" data-original-width="611" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJ513ATGyYo_yjnoBXPAB_6KZdhDodPEuqeejkNVM6rc0KzJ9QMI-eaL26PDrqp6zBNEpYg_zG2rvRrE5vV0ohoz8WLbGxGBsmK4W7cRuTuN3jzPdsswgui-rpRlP1Q7uDnSaOM-N2_2A/s320/microphone+on+air+-+123rf.jpg" width="249" /></a></div>
<br />
In our brand new <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3212862" target="_blank">SSRN-paper “Breadth Momentum and the Canary Universe: Defensive Asset Allocation (DAA)”</a> we improve on our Vigilant Asset Allocation (VAA, see <a href="https://indexswingtrader.blogspot.com/2017/07/breadth-momentum-and-vigilant-asset.html" target="_blank">post</a>) by the introduction of a separate “canary” universe for signaling the need for crash protection, using the concept of breadth momentum (see VAA). This protective universe functions as an early warning system similar to <a href="https://www.smithsonianmag.com/smart-news/story-real-canary-coal-mine-180961570/" target="_blank">the canary in the coal mine</a> back in the day. For DAA the amount of cash is governed by the number of canary assets with negative momentum. The risky part is still based on relative momentum, just like VAA. The resulting investment strategy is called Defensive Assets Allocation (DAA). The aim of DAA is to lower the average cash (or bond) fraction while keeping nearly the same degree of crash protection as with VAA.<br />
<br />
Using a very simple model from 1925 to 1970 with only the S&P 500 total return index as investment asset, we arrive at a two-asset canary universe (VWO and BND) combined with a protective B2 breadth momentum setting, which defines DAA’s core elements.<br />
<br />
The DAA concept turns out to be quite effective for nearly all four universes examined in our VAA-paper from 1971 to 2018. The average cash fraction of DAA is often less than half that of VAA’s (below 30% instead of nearly 60%), while return and risk are similar and for recent years even better. Deploying a separate “canary” universe for signaling the need for crash protection also improves the tracking error with respect to the passive (buy-and-hold) benchmark due to higher in-the-market-rates than with VAA. The separate “canary” universe also limits turnover. This makes DAA less sensitive for rising cash (or bond) yields, which is key in view of recent low rates.<br />
<br />
To crystallize the DAA concept:<br />
<ol>
<li>When both canary assets VWO and BND register negative <a href="https://indexswingtrader.blogspot.com/2017/07/breadth-momentum-and-vigilant-asset.html" target="_blank">13612W</a> momentum, invest 100% in the single best bond of the cash universe;</li>
<li>When only one of the canary assets VWO or BND registers negative momentum, allocate 50% in the top half of the best risky assets, while applying equal weights, and invest the remaining 50% in the best bond of the cash universe;</li>
<li>When none of canary assets VWO and BND register negative momentum, indicating the risk of a crash is deemed low, invest 100% in the full top risky assets, again applying equal weights. </li>
</ol>
<a name='more'></a>As a first demonstration the performance metrics of DAA-G12 are presented in the table below along with the 1971-2018 equity chart. Notice the key performance indicators in the chart’s title. The demonstrated setup consists of 12 global risky assets (G12): SPY, IWM, QQQ, VGK, EWJ, VWO, VNQ, GSG, GLD, TLT, HYG, and LQD. For out-of-market allocation a three asset cash proxy universe is used: SHY, IEF, and LQD. The (fixed) protection universe for quantifying breadth momentum is populated with (only) the mentioned two “canary” assets: VWO and BND. Using DAA’s protective B2 breadth momentum setting, a one dimensional optimization sweep over a top size T of 1, 2, 3, 4, 5, or 6 assets on the IS 1971-1993 period with K(25%) as target, results in T=6 as being the optimal top size for DAA-G12.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDflsIwzU0j8wovd3TZ6cFznCYBiBtIeBWek9EsFPKdrVhG9oID-yBWY-_kZqEs8YOX7gLYLR3t2wVYv7mphDmVYYiQQQ1jpLzHPmTAPk7QFZoiu6Kr7HuElCLTDGUGI5LBgghjKwifI4/s1600/DAA-G12+FS+T6B2+TC0.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="673" data-original-width="1600" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDflsIwzU0j8wovd3TZ6cFznCYBiBtIeBWek9EsFPKdrVhG9oID-yBWY-_kZqEs8YOX7gLYLR3t2wVYv7mphDmVYYiQQQ1jpLzHPmTAPk7QFZoiu6Kr7HuElCLTDGUGI5LBgghjKwifI4/s640/DAA-G12+FS+T6B2+TC0.png" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS6bthOok4QfLslhWBh-i2SuGCjBNNNUAMdWARK5Z0kgervB1Ep3OMni1CR_zfSPieE3Mt1uwQoff-41MUkWph4u_6LxxTsc3ZGh6vc1Qxab8jYfp9_FRUacytg9rY07H0vQBhm7K0nEQ/s1600/DAA-G12+FS+T6B2+TC0+Table.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="234" data-original-width="942" height="158" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS6bthOok4QfLslhWBh-i2SuGCjBNNNUAMdWARK5Z0kgervB1Ep3OMni1CR_zfSPieE3Mt1uwQoff-41MUkWph4u_6LxxTsc3ZGh6vc1Qxab8jYfp9_FRUacytg9rY07H0vQBhm7K0nEQ/s640/DAA-G12+FS+T6B2+TC0+Table.png" width="640" /></a></div>
<i>NB! Results are derived from simulated monthly total return ETF data. Furthermore, trading costs, slippage, and taxes are disregarded. Results are therefore purely hypothetical. Past performance is no guarantee of future results.</i><br />
<br />
A signals table for the Defensive Asset Allocation strategy with the above mentioned setup will be added to the <a href="https://indexswingtrader.blogspot.com/p/strategy-signals.html" target="_blank">Strategy Signals</a> page in due time. Until then, the table is fully functional below. Please take note of the limitations as mentioned on the <a href="https://indexswingtrader.blogspot.com/p/strategy-signals.html" target="_blank">Strategy Signals</a> page.<br />
<br />
<iframe height="500" src="https://docs.google.com/spreadsheets/d/e/2PACX-1vQBwj2nqncXVyQ4AAswHD82HWjamB5No00Ee8bOi2MSLDDU2As8zGxqCgThAg_E6kBwqLwxEY7REfkO/pubhtml?gid=1389397904&single=true&widget=true&headers=false" width="750"></iframe><i>
NB! No guarantee whatsoever is given for the soundness of the strategy nor the proper functioning of the table nor for the accuracy of the (time delayed) signals. </i><i>Please do your own due diligence and use at your peril. The Important Notice in the footer applies as well as the Disclaimer.</i><br />
<br />
The full AmiBroker code for DAA is available upon <a href="mailto:trendxplorer@gmail.com?Subject=Request%20for%20DAA%20model%20in%20AmiBroker" target="_blank">request</a>. Interested parties are encouraged to support this blog with a donation:<br />
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<br />TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-9691992115348084772018-04-21T15:10:00.000-04:002018-04-28T05:22:53.447-04:00Presenting the Keller Ratio<br />
<ul>
<li>Many traditional return to risk measures are not apt for intuitive interpretation</li>
<li>The Keller ratio is expressed as an adjusted return and therefore easy to interpret</li>
<li>The Keller ratio allows for strategy selection optimally aligned with an investor’s risk appetite</li>
</ul>
<br />
In our <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3002624" target="_blank">VAA-paper</a> we introduced a new metric for assessing a portfolio’s equity line in terms of the reward to risk relationship: return adjusted for drawdown (RAD). We did choose RAD above the usual risk measures like the Sharpe and the MAR ratios (Sharpe: return divided by volatility, MAR: return divided by maximum drawdown), because most retail investors commonly identify true risk with maximum drawdown over volatility. Since RAD is an adjusted return, its interpretation is similar to any return (a simple percentage). For this reason we prefer RAD over MAR, which as such is just a numeric value with little context.<br />
<br />
Frankly, albeit return adjusted for drawdown states exactly what RAD is all about, it is quite a mouthful. Therefore, and not only because RAD is his brainchild, but also to commemorate Wouter Keller’s contributions to the TAA literature (FAA, MAA, CAA, EAA, PAA, and VAA; see <a href="https://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=1935527" target="_blank">SSRN</a>) it only seems fitting to accredit the return adjusted for drawdown indicator with his name. So henceforward RAD is to be named the “Keller ratio”.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6DCXbG_lmHyMt8lgNuhby5r8QbgSAc-y0wsGNoOae_kl8sli-7xXx70n1u6ubVIIcGtAeNlISU9Xjaoj9qXEHoGm0eqrAZmdSZZvqm9nDRt4E0SKTLhF5jKa4H-6ut90xEr50w658i94/s1600/123rf-champagne+bottle.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="692" data-original-width="692" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6DCXbG_lmHyMt8lgNuhby5r8QbgSAc-y0wsGNoOae_kl8sli-7xXx70n1u6ubVIIcGtAeNlISU9Xjaoj9qXEHoGm0eqrAZmdSZZvqm9nDRt4E0SKTLhF5jKa4H-6ut90xEr50w658i94/s400/123rf-champagne+bottle.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Celebrating Wouter Keller's 70th birth year</td></tr>
</tbody></table>
<br />
Every investor with skin in the game acknowledges a large portfolio drawdown as the ultimate investing risk. Large drawdowns are devastating to long term returns. For example, during the 2008 subprime crisis the S&P 500 Total Return index crashed over 50% in approximately 1.5 years from its late 2007 peak, needing 3 years for recovery to breakeven. This left Buy & Hold investors without any positive returns for over nearly five years, not to speak of the excruciating anxiety along the way.<br />
<br />
The following table illustrates how severe drawdowns wreak havoc to portfolio performance. Total loss of principal is the biggest risk of all.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjH-NbgajJuWwdJXdzDL7wDBqLoW-w7O9L2MGTIBD7KY5TIsSbvfCClaAarPXP8Pv9gku1WKsWPsKgAQtVQRmB2dM6LWq1VhozQ2SJ7qXRY5MW9e0kpwjzZBxUIZEnvpdmBLVAskhpTp2E/s1600/Drawdown+Table.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="700" data-original-width="1028" height="434" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjH-NbgajJuWwdJXdzDL7wDBqLoW-w7O9L2MGTIBD7KY5TIsSbvfCClaAarPXP8Pv9gku1WKsWPsKgAQtVQRmB2dM6LWq1VhozQ2SJ7qXRY5MW9e0kpwjzZBxUIZEnvpdmBLVAskhpTp2E/s640/Drawdown+Table.png" width="640" /></a></div>
<br />
<a name='more'></a>Drawdown destroys investment capital, hence the required recovery percentage to get back to breakeven grows exponentially with drawdown. Living through the drawdown quagmire often causes anxiety and can possibly even become a confidence shattering experience. So keeping drawdowns as small as possible is key for ultimate profitability.<br />
<br />
As such, maximum drawdown is a “left tail risk”, because it is located in the outer left part of the statistician’s normal distribution chart. In backtests covering only a limited number of years, maximum drawdown may be a single event occurrence. For any meaningful assessment of drawdown long-term backtests are required, preferably extending over multiple decades and comprised of several bull-bear market cycles with many peak-to-trough declines.<br />
<br />
The Keller ratio adjusts return for drawdown such as to reflect the severity of the observed maximum drawdown. In case maximum drawdown is small, the return adjustment is only limited. But with large maximum drawdown, the impact of the return adjustment is amplified, in similar fashion to the exponentially growing recovery percentages shown in the above table.<br />
<br />
To recall from our <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3002624" target="_blank">VAA-paper</a>, the formula for the Keller ratio (K=RAD) is:<br />
<blockquote class="tr_bq">
<span style="text-align: center;">K = R * ( 1 - D / ( 1 - D ) ), if R >= 0% and D <= 50%, and K = 0% otherwise, </span></blockquote>
where R = CAGR and D = Maximum Drawdown of the portfolio equity line over the chosen backtest period, with D expressed as a positive value, and for our models measured at month’s ends. This K measure is based on the observation that a maximum drawdown of 50% often leads to the liquidation of a hedge fund. In this case the Keller ratio becomes 0%, independent of CAGR.<br />
<br />
The observant reader recognizes the term D / ( 1 - D ) in the Keller formula, which is the algebraic expression of the increase in price necessary for recovery to breakeven at the previous top portfolio capital level after a drawdown of D. At D = 50%, this price gain equals 100%, so the ratio becomes 0%, reflecting the difficulty of getting back to the previous portfolio peak level after a severe drawdown.<br />
<br />
Next, by generalizing the Keller formula an adjustable threshold parameter can be implemented at which the Keller ratio becomes 0%. This allows for a tailored Keller measurement for better reflecting an investor’s risk preference:<br />
<blockquote class="tr_bq">
K( Dmax ) = R * ( 1 - f * D / ( 1 - f * D ) ), </blockquote>
where f = 0.5 / Dmax, with Dmax being D at which K = 0%.<br />
<br />
Accordingly, using 50%, 25%, 20%, and 10% as the respective threshold parameters, the formula for the Keller ratio becomes:<br />
<br />
K(50%) = R * ( 1 - D / ( 1 - D ) ), if R >= 0% and D <= 50%, and K(50%) = 0% otherwise.<br />
K(25%) = R * ( 1 - 2D / ( 1 - 2D ) ), if R >= 0% and D <= 25%, and K(25%) = 0% otherwise.<br />
K(20%) = R * ( 1 - 2.5D / ( 1 - 2.5D ) ), if R >= 0% and D <= 20%, and K(20%) = 0% otherwise.<br />
K(10%) = R * ( 1 - 5D / ( 1 - 5D ) ), if R >= 0% and D <= 10%, and K(10%) = 0% otherwise.<br />
<br />
The following [updated] table crystallizes the effect of the mentioned Keller thresholds for the VAA-G12 strategy covering 1970 - 2017 (mid) as described in our <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3002624" target="_blank">VAA-paper</a> (see also end notes):<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJSAFdr5ngqI1MhEQP7SHPL0yza190quyBV1XEWc6r9VR4bFRFgI2w3y5dgIfqVvPFWUsSmt7ORXtaTcX8N9Xub76L-QxfDSt2_hwtk_5gALGGiegrDM5hFniODtWvn3mkIcF3MJ05w1Q/s1600/VAA-G12+KPIs.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="276" data-original-width="1600" height="110" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJSAFdr5ngqI1MhEQP7SHPL0yza190quyBV1XEWc6r9VR4bFRFgI2w3y5dgIfqVvPFWUsSmt7ORXtaTcX8N9Xub76L-QxfDSt2_hwtk_5gALGGiegrDM5hFniODtWvn3mkIcF3MJ05w1Q/s640/VAA-G12+KPIs.png" width="640" /></a></div>
<br />
<i>NB! Results are derived from simulated monthly total return data. Furthermore, trading costs, slippage, and taxes are disregarded. Results are therefore purely hypothetical. Past performance is no guarantee of future results.</i><br />
<br />
Using the Keller threshold as the allowed maximum portfolio drawdown, the Keller ratio allows the investor to select the strategy scenario optimally aligned with his risk appetite. An investor with an offensive risk profile might still feel comfortable with high drawdowns, therefore using K(50%) as scenario selector resulting in the T1/B4 setting. An investor with a moderate risk tolerance can select K(25%) as threshold value, leading to preference for the T5/B4 setting. In this particular instance the same diversified T5/B4 scenario happens to be selected too with the threshold lowered to K(20%) or K(10%) respectively. Other TAA strategies may offer broader ranges of choice for risk targeting through heightening or lowering the Keller threshold.<br />
<br />
Point to note: with K(20%), by design the indicator value for the T1/B4 scenario becomes 0%, because the registered maximum portfolio drawdown of the T1/B4 scenario (D = 21.13%) exceeds the chosen K(20%) threshold (Dmax = 20%). The same is true for the T1/B4, T2/B4, and T3/B4 scenarios with the K(10%) threshold deployed.<br />
<br />
To elaborate our preference for the Keller ratio over the usual ones like the Sharpe and MAR ratio, let’s revisit the reasoning in our <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3002624" target="_blank">VAA-paper</a>. The Sharpe ratio is defined as the annual return R (often in excess over a target return like the risk-free rate) divided by the annual volatility V of the returns. The MAR ratio (similar to the Calmar ratio) is simply annual return R divided by maximum drawdown D (expressed as D >= 0%). Both measures assume that you can apply leverage to arrive at higher R, V and D combinations with the same Sharpe and MAR ratio. But, as we know from leveraged ETFs, this only holds for constant growth (combined with a lending rate equal to the risk-free rate). However, in practice the resulting Sharpe ratio will be much less after leverage. Furthermore, not all investors - especially not retail investors - have access to cheap leverage at (near) risk-free rates. Therefore, when optimizing TAA-models using Sharpe or MAR ratios as target, one might get stuck at relative low returns R with low risk, especially when using a low (near) risk-free or zero target return for the Sharpe threshold.<br />
<br />
As an alternative for the Keller ratio the Ulcer Performance Index (UPI) or “Martin Ratio” springs to mind. UPI is return divided by the Ulcer index (UI), where the Ulcer Index measures the depth and duration of percentage drawdowns in price from earlier highs. The greater a drawdown in value, and the longer it takes to recover to earlier highs, the higher the UI. Technically, UI is the square root of the mean of the squared percentage drawdowns in value. The squaring effect penalizes large drawdowns proportionately more than small drawdowns. (From Peter G. Martin’s explanation at <a href="http://www.tangotools.com/ui/ui.htm" target="_blank">tangotools.com</a>). UPI takes the entire drawdown record into account, which is statistically preferable. However, using UPI as target frequently results in lower optimal returns and broad top selections, because in general those diversified tops coincide with smaller drawdowns.<br />
<br />
In our current research the Keller ratio is preferred, especially because of its risk targeting through lowering or heightening of the drawdown threshold. However, without the multi decade In-Sample optimization / Out-of-Sample (IS/OS) validation approach, as adhered to in our research, where IS/OS each cover several market cycles, optimizing for the Keller ratio bears the risk of data snooping because maximum drawdown is just a single data point, prone to overfitting.<br />
<br />
<b>End notes</b><br />
<ul>
<li>The VAA-strategy is explained is this post: <a href="https://indexswingtrader.blogspot.com/2017/07/breadth-momentum-and-vigilant-asset.html" target="_blank">Breadth Momentum and Vigilant Asset Allocation</a>.</li>
<li><a href="https://allocatesmartly.com/?aff=220" target="_blank">AllocateSmartly</a> will begin tracking VAA-G12 T2/B4 "in the near future".</li>
<li>Detailed views at the performance of VAA-G12 for the T2/B4, T3/B4, T4/B4, and T5/B4 scenarios are available in the <a href="https://drive.google.com/open?id=0BwovO-kzwAfgclcxU3lXMlc2WkU" target="_blank">charts suites</a> (zooming required).</li>
<li>The signals for VAA-G12 with T2/B4 and T5/B4 are available on the <a href="https://indexswingtrader.blogspot.com/p/strategy-signals.html" target="_blank">Strategy Signals</a> page (with T4/B4 being discontinued shortly).</li>
<li>This post is simultaneously published on <a href="https://seekingalpha.com/article/4166894-presenting-keller-ratio" target="_blank">SeekingAlpha</a>.</li>
<li>Expanded example for calculating the Keller Ratio in Excel is available on the Google drive folder attached to this post (<a href="https://drive.google.com/open?id=1XN3B4AqLBL3lVX0VGALIpNtGEUXrfnbo" target="_blank">click to open folder</a>).</li>
</ul>
TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-57351624350130590382017-11-11T10:36:00.004-05:002023-07-30T07:30:11.213-04:00Matrix Iterations for Adaptive Asset Allocation<br />
<ul>
<li>Adaptive Asset Allocation (AAA) is based on the Nobel Prize winning portfolio theory of Markowitz (1952)</li>
<li>AAA combines asset’s momentum, volatilities, and cross-correlations for building diversified investment portfolios</li>
<li>In a tactical application AAA exploits momentum for crash detection and results in consistent returns at mitigated risk levels</li>
</ul>
<br />
Actually, their encounter was coincidental. The fortuitous conversation between a stockbroker and a young mathematician in the early 1950’s proved to be seminal. After the stockbroker learned about the mathematician’s expertise, linear programming and utility maximization, and its real-life applications, he suggested to apply the math to financial portfolios. Fast-forwarding four decades, in 1990 Harry Markowitz shared the Nobel Prize in Economics for his pioneering work on Modern Portfolio Theory (MPT).<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwor56ZhvIipCBnUijJxEsAvj7iZYUnwlHX1rs058QJNlkvy6Z_v30kbcdQ7X8hpg9sFNYuFX2-2qRM6AxNXWfe-p8H2tAL-0AkaMqRNYMM8qJXEvofaNTVUeo-iMkLXMtEHgHP-seYJ0/s1600/matrix-blog.gif" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwor56ZhvIipCBnUijJxEsAvj7iZYUnwlHX1rs058QJNlkvy6Z_v30kbcdQ7X8hpg9sFNYuFX2-2qRM6AxNXWfe-p8H2tAL-0AkaMqRNYMM8qJXEvofaNTVUeo-iMkLXMtEHgHP-seYJ0/s400/matrix-blog.gif" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><div style="text-align: center;">
Matrix rain animation courtesy <a href="http://thecodeplayer.com/experiment/matrix-rain-animation-html5-canvas-javascript/1" target="_blank">TheCodePlayer</a>.</div>
<div style="text-align: center;">
AniGif created with <a href="http://gifbrewery.com/" target="_blank">Gif Brewery</a>.</div>
</td></tr>
</tbody></table>
<br />
The mathematical framework of MPT combines asset’s expected returns, volatilities, and cross-correlations for assembling well-balanced and diversified portfolios while maximizing the expected return for a given level of risk. Its key proposition: for a multi asset portfolio returns can be maximized for a given level of risk. Likewise, risk can be minimized for a desired level of return. With the efficient frontier as its famous graphical depiction (see graph below), Markowitz’ MPT is also known as “mean-variance analysis” since the “mean” or expected return is maximized given a certain level of risk, defined as the portfolio variance (which is volatility squared).<br />
<br />
<br />
<b>Efficient Frontier</b><br />
<br />
MPT proposes a mathematical framework how investors can reduce overall risk while maximizing return by holding a diversified portfolio of non-correlated asset classes. Instead of looking at the risk-return characteristics of each single asset class, MPT assesses risk and return as cumulative factors for the portfolio as a whole. The Markowitz Efficient Frontier is the graphical depiction of the collection of portfolios that offer the lowest risk for a given level of return. In an excellent <a href="https://www.youtube.com/watch?v=yx3n692K3Pw" target="_blank">video</a> Arif Irfanullah explains in merely 3 minutes how the efficient frontier represents the set of portfolios that will give the highest return at each level of risk or the lowest risk for each level of return (highly recommended).<br />
<br />
To illustrate key elements of MPT, let’s bring to bear the top selection from a diversified investment universe SPY, EWJ, VGK, EEM, and DBC (both the full universe population as well as the selection methodology are explained in the next section).<br />
<br />
The portfolio concept under consideration for this contribution is the <i>long only minimum variance portfolio</i> without leverage, located at the magenta dot on the outer left side of the purple portfolio cloud (see statistics in bold font in the table below the following graph). For this special case portfolio risk is minimized for all feasible long only combinations. To localize this particular portfolio an Adaptive Asset Allocation (AAA) approach is applied. Please note the <span style="color: purple;"><b>purple</b></span> long only portfolio cloud is only a subset of the full unconstrained long/short portfolio space demarcated by the <b><span style="color: blue;">blue</span></b> portfolio envelop hyperbola.<br />
<br />
Speed readers may jump to the next section, others please bear with me while painting the full picture.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheFOELm1pfIp6lkSTJ2kyQ2zYQPdIYeGJxKLWHoAQzlBstH_yqTW-cDA8CRvZG7Cm6fk4HVmUZTrXh5iPRmKKeB2ELVDM2Tal6NVtZD2E8up63YJ9sDWtu5IYsTCdxebNm1YJOZ5TLT_c/s1600/AAA+Global+Portfolio+Space.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="992" data-original-width="1600" height="396" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheFOELm1pfIp6lkSTJ2kyQ2zYQPdIYeGJxKLWHoAQzlBstH_yqTW-cDA8CRvZG7Cm6fk4HVmUZTrXh5iPRmKKeB2ELVDM2Tal6NVtZD2E8up63YJ9sDWtu5IYsTCdxebNm1YJOZ5TLT_c/s640/AAA+Global+Portfolio+Space.png" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoovG9ljgdlFkDxeyVtq86DmncycGYFiGH-HH1Z-LrsYOgrWYpf3dFo0kcKM6BwC8vJ0EpenXItXfx7jwxCcZTqElgzYRuKPI91LtJU54NoR1AzrzcOvvRxaRz3yTGCLXC23LplcBB9-U/s1600/Portfolios+Stats.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="398" data-original-width="1326" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoovG9ljgdlFkDxeyVtq86DmncycGYFiGH-HH1Z-LrsYOgrWYpf3dFo0kcKM6BwC8vJ0EpenXItXfx7jwxCcZTqElgzYRuKPI91LtJU54NoR1AzrzcOvvRxaRz3yTGCLXC23LplcBB9-U/s640/Portfolios+Stats.png" width="640" /></a></div>
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In the above risk-return graph the portfolio space is plotted for every unconstrained long/short portfolio of 5 ETFs: SPY, EWJ, VGK, EEM, and DBC, with portfolio weights summed to 100%. All feasible long/short combinations are contained by the <b><span style="color: blue;">blue</span></b> portfolio envelop hyperbola, with the <i>efficient frontier</i> being the solid upper boundary and the <i>inefficient frontier</i> the dashed lower one. The grey dots represent 10,000 random unconstrained long/short portfolios. The well-known <i>minimum variance portfolio</i> (MVP) is located at the green cross-mark, being the portfolio with the lowest risk; every single other portfolio combination will result in higher risk. The so-called <i>tangency portfolio </i>(TP) is situated at the red tangent point where the capital allocation line (also in red; basis: 1% risk free rate) touches to the efficient frontier. The TP is suggested to be the mathematical optimal non-leveraged portfolio under the mean variance framework (in the continuation of the <a href="https://www.youtube.com/watch?v=yx3n692K3Pw" target="_blank">video</a> Arif Irfanullah discusses the TP too). On the same capital allocation line, but outside the portfolio envelop, are two particular portfolios depicted. This are two portfolio combinations of the five mentioned ETFs along with a separate risk-free asset: the green dot showing the portfolio with reserved or saved capital and the purple dot the one with borrowed capital (leverage), with target volatilities of 6% and 12%, respectively.<br />
<br />
With the long only constraint imposed, each of the orange diamonds depicts a 100% holding in one of the five ETFs, and the purple hurricane shaped cloud represents 5,151 long only portfolios consisting of SPY, EWJ, and DBC (with 1% sized steps). As stated, the <i>long only minimum variance portfolio</i> is to be found at the magenta dot on the outer left side of the <b><span style="color: purple;">purple</span></b> portfolio cloud. Under the long only constraint, the weights for VGK and EEM are fixed at 0% in order to reach minimal risk (shorting is prohibited). Hence the 3 asset purple portfolio cloud. In the remainder of this contribution the localization and characteristics of this special case portfolio will be assessed.<br />
<br />
<br />
<b>Adaptive Asset Allocation</b><br />
<br />
As stated, the MPT framework relies on estimates for returns, volatilities, and correlations. Since these estimates are notoriously difficult to predict, especially with regard to the future, a tactical timeframe is adopted for the necessary calculations using a heuristically composed diversified investment universe like the one proposed by the <a href="http://www.investresolve.com/" target="_blank">InvestReSolve</a> team (formerly <a href="http://www.gestaltu.com/" target="_blank">Gestaltu</a>) in their <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2328254" target="_blank">AAA-primer</a>: SPY, VGK, EWJ, EEM, VNQ, RWX, DBC, GLD, TLT, and IEF (see also end notes below).<br />
<br />
For starters, each month the best 5 out of 10 ETFs are selected based on their 126-day momentum. Next the minimum variance portfolio is determined as the optimal mix of these five ETFs for obtaining the lowest possible risk (=volatility), using the following steps.<br />
<br />
First, for this top half a “weighted” covariance matrix ∑(i,j) is calculated by combining 126-day correlations ρ(i,j) with 20-day volatilities σ(i) and σ(j):<br />
<blockquote class="tr_bq">
∑(i,j) = ρ(i,j) * σ(i) * σ(j),</blockquote>
where i,j refers to the top 5 ETFs<span style="font-family: inherit;">. <span style="background-color: white; color: #222222;">Finally, the minimum variance portfolio is obtained by minimizing the </span><span style="background-color: white; color: #222222;">following matrix formula</span>:</span><br />
<blockquote class="tr_bq">
σ<sup>2</sup> = w'∑w, </blockquote>
where w is the weights vector with sum equal to 100% and w(i) ≥ 0 and ∑ equals the covariance matrix.<br />
<br />
To establish the weight combination that satisfies the minimum variance σ<sup>2</sup> objective, a Cyclical Coordinate Descent algorithm is deployed (see end notes for sources). For a preset number of cycles, the CCD algo iterates through the weight combinations, approaching closer to the minimum variance objective with each cycle. In the following graph the red zigzag line paints these iterations going from right to left, minimizing portfolio volatility σ.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWhNa8X1pMdMqfW8yLAEZttFMfcXTB4Cs4Dh10Drix5F0pOc1Mu_sYVlOA75552iZ7rCpT99dRewPXicD7q2jKNcM15MmbMJ0XgmpOVIMtlipA5EXxsPFXOYkD4mJAxjgWOf-4iQwkxR4/s1600/CCD+graph.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="905" data-original-width="1600" height="362" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWhNa8X1pMdMqfW8yLAEZttFMfcXTB4Cs4Dh10Drix5F0pOc1Mu_sYVlOA75552iZ7rCpT99dRewPXicD7q2jKNcM15MmbMJ0XgmpOVIMtlipA5EXxsPFXOYkD4mJAxjgWOf-4iQwkxR4/s640/CCD+graph.png" width="640" /></a></div>
<br />
<br />
<b>Native crash protection</b><br />
<br />
By selecting only the best 5 out of 10 assets, AAA is capable of detecting momentum based trend changes. In up-trending markets capital is allocated into offensive assets, like stocks, REITs, and commodities, while during market sell-offs especially intermediate US-treasuries are in vogue. The following diagram shows the allocation transformations during the bear-bull cycles since the turn of the millennium. Notice the waxing of IEF in periods of market stress (shown for the native InvestResolve universe).<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8wGCYaK937txZ41Fm4RejJKm22MPRhyphenhyphen-OjCYjb_LZd4ElcgrchySkMjpnSlYNCWYE3DyzQkfSoN1EJjVuQc_t424l6a9UeB0xRNeIotH2uENC7JopTvzAsxQYHH1aJUYZ_4Egqj2PCu8/s1600/AAA_N10_T5_2000-2017_MAD.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="669" data-original-width="1600" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8wGCYaK937txZ41Fm4RejJKm22MPRhyphenhyphen-OjCYjb_LZd4ElcgrchySkMjpnSlYNCWYE3DyzQkfSoN1EJjVuQc_t424l6a9UeB0xRNeIotH2uENC7JopTvzAsxQYHH1aJUYZ_4Egqj2PCu8/s640/AAA_N10_T5_2000-2017_MAD.png" width="640" /></a></div>
<br />
<br />
<b>Backtesting AAA</b><br />
<br />
The following charts provide a detailed view on AAA’s end-of-month performance using <a href="http://www.amibroker.com/" target="_blank">AmiBroker</a> as backtest platform. For this demonstration an alternative investment universe is deployed: SPY, QQQ, IWM, EFA, EEM, VNQ, RWX, DBC, TLT, and IEF.<br />
<br />
By substituting VGK, EWJ, and GLD with QQQ, IWM, and EFA the universe at hand is tilted toward domestic US assets, while at the same time demonstrating GLD is not per se required to reach sufficient diversification.<br />
<br />
Equity chart with key performance indicators:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjghU0Z4_YCnFC6adwF2Hw8LB4SOW4OgOiZDksEdEFbOTH29rguDJ2eLI-O6Dr-yD-U-7d_PcNOiaDgeorhkdY4dEbbFFmfjThshn8p8qbpIVPgbW2f4poa6ayHaLTi0UVDyest6KocEKs/s1600/AAA+ALT10+Equity.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="671" data-original-width="1600" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjghU0Z4_YCnFC6adwF2Hw8LB4SOW4OgOiZDksEdEFbOTH29rguDJ2eLI-O6Dr-yD-U-7d_PcNOiaDgeorhkdY4dEbbFFmfjThshn8p8qbpIVPgbW2f4poa6ayHaLTi0UVDyest6KocEKs/s640/AAA+ALT10+Equity.png" width="640" /></a></div>
<blockquote class="tr_bq">
<i>NB! Results are derived from simulated daily total return data. Furthermore, trading costs, slippage, and taxes are disregarded. Results are therefore purely hypothetical. Past performance is no guarantee of future results.</i></blockquote>
Drawdown chart:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheq3IuA7pinSZmiiw8D6yhyphenhyphenjk4s5zOe44KsxdbmgKJ07EJAZLCqMQWSes60WlrJLy7HFUgi_9-d5nl4YfVrAFThTNU7mCDZ3pk1D_d8rqcM6Z9Z84NJ0AgKk7MGRNX72Ekb82clkFK55w/s1600/AAA+ALT10+Drawdown.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="670" data-original-width="1600" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheq3IuA7pinSZmiiw8D6yhyphenhyphenjk4s5zOe44KsxdbmgKJ07EJAZLCqMQWSes60WlrJLy7HFUgi_9-d5nl4YfVrAFThTNU7mCDZ3pk1D_d8rqcM6Z9Z84NJ0AgKk7MGRNX72Ekb82clkFK55w/s640/AAA+ALT10+Drawdown.png" width="640" /></a></div>
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Annual returns:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-ml71B1YrmfOFhHxDhH7wPfaeNHec7U3jacCWvt1mtlU4yYt4cTk5Rptp8P7PxJbNNizhtjYd4KhMvfxcuJdzG7EJGjYOuBkCZSCvtyFptoyHl4vQvvKoL6V0s2wcj_4t_vROkvDkY4E/s1600/AAA+ALT10+Annual+Returns.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="670" data-original-width="1600" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-ml71B1YrmfOFhHxDhH7wPfaeNHec7U3jacCWvt1mtlU4yYt4cTk5Rptp8P7PxJbNNizhtjYd4KhMvfxcuJdzG7EJGjYOuBkCZSCvtyFptoyHl4vQvvKoL6V0s2wcj_4t_vROkvDkY4E/s640/AAA+ALT10+Annual+Returns.png" width="640" /></a></div>
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Monthly returns:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6HTzrp9aWCLJsDYwsv9lJk5UekTEeW0qE8dN-RCu5riYe-0Wv3LLoGgV3yLv0hoPPeOEkJqdcs956W19gtwAcTD_y4uQ1wMwneFkjHGnuQ_SVPyiS2tM5QvZPppoJpuuZ3X7xQqboZ70/s1600/AAA+ALT10+Monthly+Return+Distribution.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="671" data-original-width="1600" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6HTzrp9aWCLJsDYwsv9lJk5UekTEeW0qE8dN-RCu5riYe-0Wv3LLoGgV3yLv0hoPPeOEkJqdcs956W19gtwAcTD_y4uQ1wMwneFkjHGnuQ_SVPyiS2tM5QvZPppoJpuuZ3X7xQqboZ70/s640/AAA+ALT10+Monthly+Return+Distribution.png" width="640" /></a></div>
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Histogram of monthly returns:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVfV4isdnzVSW7re99semMo3fg1H-GWwR9knt6dY6xmWVXNlH1l2H9HZ99d_954WIZ-25Oq3FhUsQKs2xPOIwdmVPk4-sCyQPXL7SI5JzPkHQf-zbUxhRCwlqg4lIhh1RwU_9rdawEx9s/s1600/AAA+ALT10+Histogram.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="671" data-original-width="1600" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVfV4isdnzVSW7re99semMo3fg1H-GWwR9knt6dY6xmWVXNlH1l2H9HZ99d_954WIZ-25Oq3FhUsQKs2xPOIwdmVPk4-sCyQPXL7SI5JzPkHQf-zbUxhRCwlqg4lIhh1RwU_9rdawEx9s/s640/AAA+ALT10+Histogram.png" width="640" /></a></div>
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Rolling 3-year returns:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJgoN11Hd3rPk4GDijsoR2D5UbrYfrv9VMP9IxOWLggWC0oZz1nnWsF1cCqAHjdH772HTWmadxmGLKsxYmlLXGzvRaLHlnOmywVM9o15X-TaFraufoCFFTVieRGvybbv-47GF47DRLfFE/s1600/AAA+ALT10+Rolling+3y+Return.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="671" data-original-width="1600" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJgoN11Hd3rPk4GDijsoR2D5UbrYfrv9VMP9IxOWLggWC0oZz1nnWsF1cCqAHjdH772HTWmadxmGLKsxYmlLXGzvRaLHlnOmywVM9o15X-TaFraufoCFFTVieRGvybbv-47GF47DRLfFE/s640/AAA+ALT10+Rolling+3y+Return.png" width="640" /></a></div>
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Profit contribution:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_3Uzqb-mLKvXSBZpYWPN9B_xdRaPqs1vFsws49WdInt25K3XKKkaJxGGl_-lydzgf-KzEDCreJf0IZq7OUAtkuGmFI6NxAbaI8WQhp87GXuYE4Frv82IkYbYbpHp5l6-rJsV6pLXIqbo/s1600/AAA+ALT10+Profit+Contribution.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="670" data-original-width="1600" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_3Uzqb-mLKvXSBZpYWPN9B_xdRaPqs1vFsws49WdInt25K3XKKkaJxGGl_-lydzgf-KzEDCreJf0IZq7OUAtkuGmFI6NxAbaI8WQhp87GXuYE4Frv82IkYbYbpHp5l6-rJsV6pLXIqbo/s640/AAA+ALT10+Profit+Contribution.png" width="640" /></a></div>
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Average allocation:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi08ZSF6aJGbOQ0cizryf7RLkkSRn8vdJFEa_8o1EJ-jSGIIqphXkdg44DqgNrrzDA2lxemnt0aCKE2TrKo_qBYenchAr1WGwo0vZ_vtn6WpUgRaXEmPLz5xbso4HCAikA2Ajlh-V6jGus/s1600/AAA+ALT10+Allocation+Time.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="670" data-original-width="1600" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi08ZSF6aJGbOQ0cizryf7RLkkSRn8vdJFEa_8o1EJ-jSGIIqphXkdg44DqgNrrzDA2lxemnt0aCKE2TrKo_qBYenchAr1WGwo0vZ_vtn6WpUgRaXEmPLz5xbso4HCAikA2Ajlh-V6jGus/s640/AAA+ALT10+Allocation+Time.png" width="640" /></a></div>
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Allocation table:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMj3OsjzC3n9FJ_2gPQxebf87DnQ506atdGAHYTzoGsIvERsvLpOQS3D2um7bJzray_m9PxMcWFHIpKNmZCqUcXaaG8gX8kLKpPeeu5C59EjgYFJ-aJwnpzeOrz9nRuWFTXXm_vhzIQvE/s1600/AAA+ALT10+Allocation+Table.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="228" data-original-width="1600" height="90" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMj3OsjzC3n9FJ_2gPQxebf87DnQ506atdGAHYTzoGsIvERsvLpOQS3D2um7bJzray_m9PxMcWFHIpKNmZCqUcXaaG8gX8kLKpPeeu5C59EjgYFJ-aJwnpzeOrz9nRuWFTXXm_vhzIQvE/s640/AAA+ALT10+Allocation+Table.png" width="640" /></a></div>
<br />
Allocation diagram<br />
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<br />
<br />
<b>Strategy Signals</b><div><b><br /></b></div><div>In case no signals are shown, try to open the google sheet in a separate tab/window (right-click table).</div><div>Alternatively <a href="mailto:trendxplorer@gmail.com?Subject=Request%20for%20AAA%20Google%20Sheet" target="_blank">request</a> for a personal copy of the stand alone version of the AAA google sheet.<br />
<br />
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<blockquote class="tr_bq">
<span style="font-family: inherit;"><i style="color: #222222; text-align: -webkit-center;">NB! No guarantee whatsoever is given for the soundness of the strategy nor the proper functioning of the table nor for the accuracy of the signals. </i><i>Data may be delayed. </i><i style="color: #222222; text-align: -webkit-center;">Please do your own due diligence and use at your peril. The <b style="color: red;">Important Notice</b> in the footer applies as well as the <a href="http://indexswingtrader.blogspot.com/p/disclaimer.html" style="color: #888888; text-decoration: none;" target="_blank">Disclaimer</a>.</i></span></blockquote>
<br />
<b>End notes</b><br />
<ul>
<li>The native InvestResolve universe is tracked by <a href="https://allocatesmartly.com/?aff=220" target="_blank">AllocateSmartly</a>. Their <a href="https://allocatesmartly.com/adam-butler-gestaltu-adaptive-asset-allocation/?aff=220" target="_blank">AAA-post</a> offers additional information along with an extended backtest.</li>
<li>The <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2328254" target="_blank">AAA-primer</a> by the InvestResolve team and their <a href="https://www.amazon.com/Adaptive-Asset-Allocation-Dynamic-Portfolios/dp/1119220351" target="_blank">AAA-book</a> are recommended readings.</li>
<li>The implementation of the CCD-algorithm as used in the Google Sheet is developed by Roman Rubsamen, a French <a href="http://www.lequant40.com/" target="_blank">quant</a>. Modified for AmiBroker, this implementation is also the core element of the AAA-code used for this contribution. On his <a href="https://github.com/lequant40/portfolio_allocation_js" target="_blank">GitHub repository</a> Roman shares an expanding JavaScript library with portfolio allocation routines.</li>
<li>Mathematically inclined readers may find the treatise interesting on the CCD algorithm in appendix A.2 of this <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2595051" target="_blank">Smart Beta paper</a> by two other French quants, Jean-Charles Richard and Thierry Roncalli.</li>
<li>The AAA strategy is published on <a href="https://seekingalpha.com/article/4125438-adaptive-asset-allocation-minimum-variance-investing" target="_blank">Seeking Alpha</a> too, featuring the native InvestReSolve / AllocateSmartly investment universe with 10 global asset classes.</li>
</ul>
<br />
The full AmiBroker code for AAA is available upon <a href="mailto:trendxplorer@gmail.com?Subject=Request%20for%20AAA%20model%20in%20AmiBroker" target="_blank">request</a>. Interested parties are encouraged to support this blog with a donation: <br />
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<br /></div>TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-66976531974947328732017-08-27T06:07:00.001-04:002023-07-29T12:00:33.336-04:00Update For Global Equities Momentum Excel VBABy popular demand a new beta update is available for the Global Equities Momentum Excel VBA spreadsheet. The new edition sources data from Tiingo's. Following the same work flow as <a href="http://indexswingtrader.blogspot.com/2016/12/ho-ho-ho-excel-vba-for-global-equities.html" target="_blank">before</a>, the spreadsheet allows to backtest <a href="http://www.dualmomentum.net/" target="_blank">Gary Antonacci's</a> popular GEM strategy (<a href="http://indexswingtrader.blogspot.com/2016/10/prospecting-dual-momentum-with-gem.html" target="_blank">see post</a>).
<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcMbd9PDb7ae3j3d1pPeB86aG1DGgjNXdS2dmJhEX9-tMPbVftfgM_uljPV1oI0whVVmgl81FtN8dHgMilZcY2aIkM_fyPyW6ca7ae167OV7SB6-iaDcQ6r5nJiEZWz4grPr7a9kXJ8BE/s1600/GEM+VBA+Stats+Charts.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: inherit;"><img border="0" data-original-height="1292" data-original-width="1152" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcMbd9PDb7ae3j3d1pPeB86aG1DGgjNXdS2dmJhEX9-tMPbVftfgM_uljPV1oI0whVVmgl81FtN8dHgMilZcY2aIkM_fyPyW6ca7ae167OV7SB6-iaDcQ6r5nJiEZWz4grPr7a9kXJ8BE/s640/GEM+VBA+Stats+Charts.png" width="570" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: inherit; font-size: small;">GEM with mutual funds for longer historical backtest</span></td></tr>
</tbody></table>
<blockquote class="tr_bq">
<i>
NB! Backtested results do not reflect actual trading. Furthermore, trading costs, slippage, and taxes are disregarded. Results are therefore purely hypothetical. Terms and conditions apply.</i></blockquote>
Next to some bug fixes a new pie chart and an annual returns table have been added to the spreadsheet. The pie chart shows the average allocations over the test periode. And the annual returns table specifies GEM's annual returns along with those of the underlying components and the classical 60/40 benchmark.<br />
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<b><br /></b>
<b>Tiingo Freemium Account</b><br />
<br />
The new version downloads the ETF/MF data from Tiingo's. Tiingo offers two tailored subscription plans: a free Basic account or a $10/m Power account. A registration/subscription to one of these plans is a prerequisite, because the spreadsheet requires your unique Tiingo token for accessing Tiingo's data server (see instructions in the spreadsheet). To register at Tiingo's: go to <a href="https://www.tiingo.com/welcome" target="_blank">Tiingo's welcome page</a>.<br />
<b>NB!</b> After signing up, your personal token is listed on <a href="https://api.tiingo.com/docs/tiingo/daily" target="_blank">Tiingo's API</a> page (new login required).<br />
<br />
<span style="background-color: white; color: #222222;"><span style="font-family: inherit;"><b>Acknowledgements</b></span></span><br />
<br />
The current spreadsheet is a modified version of the Excel batch data downloader originally designed by <a _blank="" href="http://investexcel.net/%20target=">InvestExcel</a> and adapted for GEM by Denis Bergemann. Like the previous version, the spreadsheet only works with Excel for Windows. The VBA coding changes related to downloading data from Tiingo, as well as the addition of the allocation pie chart and the annual returns table, were done by William (Will) Johnson, <a _blank="" href="http://www.geeks4hireinc.com/%20target=">www.Geeks4HireInc.com</a><br />
<br />
<b>Disclaimer</b><br />
<br />
Apart from being a subscriber, no affiliation with Tiingo's at the time of publication.<br />
<br />
<br />
The Excel sheet for GEM is available upon <a href="mailto:trendxplorer@gmail.com?Subject=Request%20for%20GEM%20spreadsheet" target="_blank">request</a>. Interested parties are encouraged to support this blog with a donation.
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<br />TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-85589585958490654742017-07-29T04:56:00.000-04:002017-11-18T05:59:53.607-05:00Strategy Signals Powered By Tiingo'sAs the new kid on the block, Tiingo is shaking up the data community. Tiingo offers Freemium access to high quality data for an extensive collection covering the full historical record. Starting today historical dividend adjusted data for the <a href="http://indexswingtrader.blogspot.com/p/strategy-signals.html" target="_blank">Strategy Signals page</a> is sourced from Tiingo's, with delayed current day's NYSE data grabbed "real time" from Google Finance.<br />
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<br />
For improved performance a newly designed dedicated backend caches updates from Tiingo's data servers, and operates as on-demand feed for the various Strategy Signal tables.<br />
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Tiingo's Freemium service consists of two tailored plans: a free basic service and a power service for $10/m. For details see Tiingo's <a href="https://www.tiingo.com/pricing" target="_blank">Pricing</a> page.<br />
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<br /></div>
TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-62448410977555127062017-07-14T14:09:00.002-04:002023-07-29T12:01:22.510-04:00Breadth Momentum and Vigilant Asset Allocation (VAA)<br />
<ul>
<li>Breadth momentum extends traditional absolute momentum approaches for crash protection.</li>
<li>Breadth momentum quantifies risk at the universe level by the number of assets with non-positive momentum relative to a breadth protection threshold.</li>
<li>Vigilant Asset Allocation matches breadth momentum with a responsive momentum filter for targeting offensive annual returns with defensive crash protection.</li>
</ul>
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<br /></div>
Vigilant Asset Allocation (VAA) is a dual-momentum based investment strategy with a vigorous crash protection and a fast momentum filter. Dual momentum combines absolute (trend following) and relative (cross-sectional) momentum. Contrary to the traditional dual momentum approaches with crash protection through trend following on the asset level, in VAA risk is quantified at the universe level. For superior protection the VAA cash fraction equals the number of assets with non-positive momentum relative to a breadth protection threshold. The combination of breadth momentum with a responsive filter for measuring dual momentum results in a granular crash indicator that allows for targeting offensive annual returns while offering defensive tail risk protection. The VAA methodology is comprehensively explained in our paper published on <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3002624" target="_blank">SSRN</a>.
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</div>
<br />
<b>The VAA recipe</b>
<br />
<ol>
<li>Given a top selection T and a breadth protection threshold B, for each month:</li>
<li>Compute 13612W momentum for each asset</li>
<li>Pick the best performing assets in the “risk-on” universe as top T</li>
<li>Pick the best asset in the “risk-off” universe as safety asset for “cash”</li>
<li>Compute the number of assets with non-positive momentum in the “risk-on” universe (b)</li>
<li>Compute b/B and round down to multiples of 1/T as “cash fraction” CF for “easy trading”</li>
<li>Replace CF of top T by “cash” asset as selected in step 3</li>
</ol>
<br />
<b>13612W momentum filter</b><br />
<b><br /></b>
In the dual momentum frame work cross-sectional or relative strength momentum is applied for picking the best performing assets for top selection while absolute momentum is utilized to establish whether or not an asset is an uptrend or downtrend (trend following). Different momentum filters are in vogue, like Antonacci’s 12-month return (RET12) for <a href="http://indexswingtrader.blogspot.com/2016/10/prospecting-dual-momentum-with-gem.html" target="_blank">GEM</a>, Keller’s price relative to its 12-month simple moving average (SMA12) for <a href="http://indexswingtrader.blogspot.nl/2016/04/introducing-protective-asset-allocation.html" target="_blank">PAA</a>, or Faber’s averaged momentum over the past 1, 3, 6, and 12 months (13612) for <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=962461" target="_blank">GTAA</a>. For VAA we developed a new momentum filter: a variant of the 13612 filter, but now with an even faster response curve by using the average annualized returns over the past 1, 3, 6, and 12 months (13612W). Our 13612W filter has the following composition:<br />
<blockquote class="tr_bq">
13612W = ( 12 * r1 + 4 * r3 + 2 * r6 + 1 * r12 ) / 4, with rt = p0/pt - 1 where pt equals price p with a t-month lag </blockquote>
This results in monthly return weights for p0/p1, p1/p2, …, p11/p12 of 19, 7, 7, 3, 3, 3, 1, 1, 1, 1, 1, 1, respectively. Notice that our responsive 13612W filter gives a weight of 40% (19/48) to the return over the most recent month as compared to 8% (RET12), 15% (SMA12), and 18% (13612). The following graphic crystallizes the various weighting schemes for the mentioned momentum filters.
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3bvKZ5vxyOdo77muMUOd9LNN-Us1aSySnVs323Fz9ZaV2-vHZ3NRKgxPKdD3pyXHNgCJqXggWVZNMl5BwlM6u1LZTzYOzx5ri_rzY8npwjMw2MNjvRZS5_BY23VJKn0uQ1CGEFTZ9-Xs/s1600/MonthlyReturnWeights.png" imageanchor="1"><img border="0" height="379" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3bvKZ5vxyOdo77muMUOd9LNN-Us1aSySnVs323Fz9ZaV2-vHZ3NRKgxPKdD3pyXHNgCJqXggWVZNMl5BwlM6u1LZTzYOzx5ri_rzY8npwjMw2MNjvRZS5_BY23VJKn0uQ1CGEFTZ9-Xs/s640/MonthlyReturnWeights.png" width="640" /></a></div>
<br />
Within the VAA frame work our 13612W filter is applied for both relative and absolute momentum.
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<br />
<a name='more'></a><br />
<b>Quantifying breadth momentum for defensive crash protection</b>
<br />
<b><br /></b>
Expanding on the crash protection routine laid down in our <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2759734" target="_blank">PAA-paper</a>, our breadth protection threshold (B) adds granularity and allows for swift allocation adjustments when trend changes occur. Like for PAA, assets are tested on absolute momentum, but now using the responsive 13612W filter, resulting in a number of assets with positive and non-positive momentum respectively (the so-called “bad” and “good” assets). Thus, absolute momentum is applied for establishing a universe’s breadth momentum. Next, our new breadth protection threshold B is defined as the minimum number of “bad” assets (b) for which the strategy is 100% invested in a “risk-off” asset (“cash”). For an N-sized “risk-on” universe, a portfolio’s cash fraction (CF) is determined by the ratio b/B. In formula:
<br />
<blockquote class="tr_bq">
CF=b/B with 0<=CF<=1 limits, where b=0,1,..,N and B<=N.</blockquote>
For more explanation please refer to our paper, or post a question in the comment section.
<br />
<br />
<br />
<b>Easy trading</b>
<br />
<b><br /></b>
In the traditional dual momentum approaches (only) top assets are tested on absolute momentum and as a result, the top asset fractions equal the cash fractions. Hence every top asset is replaced by an equal share of cash in case it fails to pass absolute momentum testing. This results in “easy trading” with capital sizes of 1/T: every “bad” asset is simply replaced by “cash”.
<br />
<br />
Like with PAA, the universe based breadth approach for cash protection is prone to awkward capital sizes which leads to more trading for rebalancing open or initiating new positions. To facilitate “easy trading” (ET) for VAA too, the fractions b/B need to be mapped to a multiple of the top asset fractions 1/T, and the corresponding worst asset(s) from the top T are to be replaced by the found cash fraction CF (the worst assets are those with the lowest 13612W momentum in the top T). Rounding down the raw fractions b/B to multiples of 1/T renders the desired result. In general, the formula for CF with ET through rounding becomes:
<br />
<blockquote class="tr_bq">
CF=(1/T) * floor(b*T/B) with 0<=CF<=1 limits</blockquote>
<br />
<b>VAA-G4 with T=1/B=1 & Top=2/B=1 compared to GEM</b>
<br />
<b><br /></b>
Focusing on concentrated portfolios, the Global 4 (G4) universe from our VAA-paper universes is inspired by Antonacci’s GEM (<a href="http://indexswingtrader.blogspot.com/2016/10/prospecting-dual-momentum-with-gem.html" target="_blank">see post</a>). The ETFs for GEM are VOO (US-stocks) or VEU (global market stocks ex US) and BND (US aggregate bonds) as safety net. To accommodate for sufficient breadth VEU is separated into VEA (developed international market stocks) and VWO (emerging market stocks). Furthermore, BND is added, which leads to an excess return approximation: to be eligible for capital allocation, the stock ETFs have to outperform BND. The “cash” universe is populated with SHY (US short-term treasuries), IEF (US mid-term treasuries), and LQD (US investment grade corporate bonds) to prospect “<a href="https://blog.thinknewfound.com/2015/05/search-crisis-alpha-weathering-storm-using-relative-momentum/" target="_blank">crisis alpha</a>”.
<br />
<br />
The chart below compares the equity curves and drawdown profiles for two VAA-G4 strategies against GEM over the backtested period: Dec. 1970 – June 2017. VAA-G4 in blue with T=1/B=1 and T=2/B=1 in black. GEM is depicted in red.
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkDhtBOioMmF9aDjpDnJttP6dZ46zKiLWmqiLFVegmCHBr8jGpM9RIlVZ8mXurBeyV9zMfKOrlnS2NwlXZg_Gi_VJR4X1FwIcpz7_-i_9ExQ4d1d_JLSkM2u9S6ZlL0C6VbZNr2-VhbAY/s1600/VAA-Statistics.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="62" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkDhtBOioMmF9aDjpDnJttP6dZ46zKiLWmqiLFVegmCHBr8jGpM9RIlVZ8mXurBeyV9zMfKOrlnS2NwlXZg_Gi_VJR4X1FwIcpz7_-i_9ExQ4d1d_JLSkM2u9S6ZlL0C6VbZNr2-VhbAY/s640/VAA-Statistics.png" width="640" /></a>
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<blockquote class="tr_bq">
<i>NB! Results are derived from simulated monthly total return data based on indices corrected for tracking errors. Furthermore, trading costs, slippage, and taxes are disregarded. Results are therefore purely hypothetical.</i></blockquote>
As the above table with the key performance indicators illustrates, both VAA-G4 strategies clearly show outperformance over GEM, not only on “raw” returns, but especially in risk-adjusted terms. Notice the considerable lower drawdowns D and high win-rates for VAA-G4.
<br />
<br />
To be fair, the flip-side of VAA-G4’s outperformance (and its responsive 13612W momentum filter) is substantial asset re-allocation as is shown in the following diagrams with VAA-G4 with T=1/B=1 on the upper chart and GEM on the lower one.
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvP57PhQxVUIyORaikaL4Yt4HA63bKg377WhejoOWuh1qKjZ28HZkWQsJbf2LU6zstrsQ4nisrTUj7KLj_syF2OfUpL_XutFJyKo9uNFX03y4NeobAyKLejoMnJ-HB1yCK104ZZMV8WCg/s1600/VAA-G4T1B1-MAD.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="272" data-original-width="1600" height="108" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvP57PhQxVUIyORaikaL4Yt4HA63bKg377WhejoOWuh1qKjZ28HZkWQsJbf2LU6zstrsQ4nisrTUj7KLj_syF2OfUpL_XutFJyKo9uNFX03y4NeobAyKLejoMnJ-HB1yCK104ZZMV8WCg/s640/VAA-G4T1B1-MAD.png" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjk6AopvlrLTAQAySk5CNzNttIW2vC32BW45hPsQgmuZ29EUT73fWoK3Z_ekwXe5nqW1WpjqYi7PYEPmVieliD_n52hQVh6D9mKR-ShxC-uBFhHBZPjBCf0ejff8AJ3zgdoiaZf2UYZE0k/s1600/GEM-MAD.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="272" data-original-width="1600" height="108" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjk6AopvlrLTAQAySk5CNzNttIW2vC32BW45hPsQgmuZ29EUT73fWoK3Z_ekwXe5nqW1WpjqYi7PYEPmVieliD_n52hQVh6D9mKR-ShxC-uBFhHBZPjBCf0ejff8AJ3zgdoiaZf2UYZE0k/s640/GEM-MAD.png" width="640" /></a></div>
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<br />
<b>Charts for VAA-G4 with T=2/B=1</b>
<br />
<b><br /></b>
The following charts provide a detailed view on VAA-G4’s performance with T=2/B=1, being the strategy with the best risk-adjusted performance (see also <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3002624" target="_blank">VAA-paper</a>, note 15).<br />
<br />
To summarize: with T=2/B=1, capital is allocated 50:50 into the best two assets out of VOO, VEA, VWO, or BND, provided none of these four assets register non-positive 13612W momentum. However, if any single asset out of these four assets becomes “bad”, all capital is re-allocated to the best asset in the “cash” universe: SHY, IEF, or LQD.
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Equity chart with key performance indicators:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIRgwH8VwrtgRs9ghZz8lU7Y41cBmH7lLE906ykeNQtKR3nleHz7X_tF6wDniArtSOgNv9fX-DVk0ehrLLiSliRDn_gS2JHL3lQTe6mMuBSBlGc_RDDOAldLNh62352fWeZJdajaj73So/s1600/VAA-G4T2B1-Equity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIRgwH8VwrtgRs9ghZz8lU7Y41cBmH7lLE906ykeNQtKR3nleHz7X_tF6wDniArtSOgNv9fX-DVk0ehrLLiSliRDn_gS2JHL3lQTe6mMuBSBlGc_RDDOAldLNh62352fWeZJdajaj73So/s640/VAA-G4T2B1-Equity.png" width="640" /></a>
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Drawdown chart:
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjil1XY5ttCV-lzg4WYLZJX6QNQekkVTSwJXCERIonPFJvYQkiqh7O600gSa6fTlKUfJ56kpE0qb3tizz0rqr0K3wfdX23-k9rAHQmmNcS4jO9F8GFTGqgB332asN6BhYNXXUN2h9iSn5Q/s1600/VAA-G4T2B1-Drawdown.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjil1XY5ttCV-lzg4WYLZJX6QNQekkVTSwJXCERIonPFJvYQkiqh7O600gSa6fTlKUfJ56kpE0qb3tizz0rqr0K3wfdX23-k9rAHQmmNcS4jO9F8GFTGqgB332asN6BhYNXXUN2h9iSn5Q/s640/VAA-G4T2B1-Drawdown.png" width="640" /></a>
</div>
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Annual returns:
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHHGNz7tJyLglEo4ypHqWmqtcV1Vm9tlEM92HJF-X89ntQd2AjaVscObVVuBdMqi6ug9vcWnIucuVOu8n5o58S2BD5k1BxTEznAr69qC52JoSBlm90a7714n_VBX9XQBlTxsUJCnmu8Bs/s1600/VAA-G4T2B1-AnnualReturns.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHHGNz7tJyLglEo4ypHqWmqtcV1Vm9tlEM92HJF-X89ntQd2AjaVscObVVuBdMqi6ug9vcWnIucuVOu8n5o58S2BD5k1BxTEznAr69qC52JoSBlm90a7714n_VBX9XQBlTxsUJCnmu8Bs/s640/VAA-G4T2B1-AnnualReturns.png" width="640" /></a>
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<br />
Monthly returns:
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjX1r5YcUiPuhkRFibLq-WBr1NdMujd0P_m22sYVagLHTE2tSn4LfJKUXml9GGGsozJwiGNKI9bY-gNLQ69kxYs9Cu_-exK5xQ9tUAQi-brehm8MRNpaips68wSn5-oKRxPVaJPTHfdJoE/s1600/VAA-G4T2B1-MonthlyReturns.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjX1r5YcUiPuhkRFibLq-WBr1NdMujd0P_m22sYVagLHTE2tSn4LfJKUXml9GGGsozJwiGNKI9bY-gNLQ69kxYs9Cu_-exK5xQ9tUAQi-brehm8MRNpaips68wSn5-oKRxPVaJPTHfdJoE/s640/VAA-G4T2B1-MonthlyReturns.png" width="640" /></a>
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Rolling 3-year returns:
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwkRSZ4OTT6dg3GY6J-64HnTodi58QVZCNOM-oyRwT59HAjtjQUCe-UJ5D3DrunIXZ2psg13JUSpJ_g0IaugEzrBETmqo5vwci4Lk5IwM2vqZjPdG25lPLwiaM0BNej8vi0OHQIKZzqIM/s1600/VAA-G4T2B1-3yRR.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwkRSZ4OTT6dg3GY6J-64HnTodi58QVZCNOM-oyRwT59HAjtjQUCe-UJ5D3DrunIXZ2psg13JUSpJ_g0IaugEzrBETmqo5vwci4Lk5IwM2vqZjPdG25lPLwiaM0BNej8vi0OHQIKZzqIM/s640/VAA-G4T2B1-3yRR.png" width="640" /></a>
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Allocation pie chart:
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiras20TA9rAKyclSIQHsmakbSiNlRvgeF9_RfEEq-8cV9CXF564J4DNB7g4rvDKXX818NDg9HJaVcq3wW3ucF0jTToelJyZwjnOS0NjzcIafEL6VKBz6b7EOiH32VHccf-B73fBxOvDNE/s1600/VAA-G4T2B1-AllocationPercentages.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiras20TA9rAKyclSIQHsmakbSiNlRvgeF9_RfEEq-8cV9CXF564J4DNB7g4rvDKXX818NDg9HJaVcq3wW3ucF0jTToelJyZwjnOS0NjzcIafEL6VKBz6b7EOiH32VHccf-B73fBxOvDNE/s640/VAA-G4T2B1-AllocationPercentages.png" width="640" /></a></div>
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Profit contribution:
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1g-QEiIpVpkZxmw-V3ED7HSnaJRIt6pTyKooODlngfrOW4_Hes676rbjTnPviyp1veeYr8ga4Y-__nJMmaUinpmCbfGGeuv-2U-cDXGu1b1ltrc7igSHcFxeqUqflKrdlzTRUUG6fYbE/s1600/VAA-G4T2B1-ProfitContribution.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1g-QEiIpVpkZxmw-V3ED7HSnaJRIt6pTyKooODlngfrOW4_Hes676rbjTnPviyp1veeYr8ga4Y-__nJMmaUinpmCbfGGeuv-2U-cDXGu1b1ltrc7igSHcFxeqUqflKrdlzTRUUG6fYbE/s640/VAA-G4T2B1-ProfitContribution.png" width="640" /></a></div>
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Allocation diagram:
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuS6z-OnfUoP05QHB89LMQo9xAwYca4PoNy9DG-5MYyB0Y6CrRan8TCTuzw1WhMDQkYliER1adMx8gtxST8wN7DRDeQYNtLYciF0Dztboz5WTwfevtChp_11MJ3ybIc4RLAvSSHUXM61s/s1600/VAA-G4T2B1-MAD.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuS6z-OnfUoP05QHB89LMQo9xAwYca4PoNy9DG-5MYyB0Y6CrRan8TCTuzw1WhMDQkYliER1adMx8gtxST8wN7DRDeQYNtLYciF0Dztboz5WTwfevtChp_11MJ3ybIc4RLAvSSHUXM61s/s640/VAA-G4T2B1-MAD.png" width="640" /></a></div>
<br />
<br />
<b>Strategy Signals</b><br />
<b><br /></b>
The signals for VAA-G4 are available on the <a href="http://indexswingtrader.blogspot.com/p/strategy-signals.html" target="_blank">Strategy Signals page</a>.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNPjKJFi5Sn1U40ugX1FSOM7x7sXJABujj-tbkp6PuPQHj2Wpl-oEtybQXadqcxV_OcCNAEmwP98zbE2eD1PDv6pS2j0N4YBFQe9dJk0IKA7c0g734K8Fmcyv76t1-OScJ58AFMbzSzt4/s1600/Signals+VAA-G4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="810" data-original-width="1218" height="424" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNPjKJFi5Sn1U40ugX1FSOM7x7sXJABujj-tbkp6PuPQHj2Wpl-oEtybQXadqcxV_OcCNAEmwP98zbE2eD1PDv6pS2j0N4YBFQe9dJk0IKA7c0g734K8Fmcyv76t1-OScJ58AFMbzSzt4/s640/Signals+VAA-G4.png" width="640" /></a></div>
<br />
<br />
<b>End notes</b>
<br />
<ul>
<li><a href="https://allocatesmartly.com/?aff=220" target="_blank">AllocateSmartly</a> has added VAA-G4 with T=1/B=1 to their collection of tactical asset allocation strategies.</li>
<li>The mentioned GEM, PAA, and GTAA strategies are "real time" monitored by <a href="https://allocatesmartly.com/?aff=220" target="_blank">AllocateSmartly</a>.</li>
<li>The full charts suite for VAA-G4 with T/B=1/1 is available for <a href="https://drive.google.com/open?id=0BwovO-kzwAfgclcxU3lXMlc2WkU" target="_blank">download</a> (zooming required).</li>
<li>Investors seeking more diversification might consider VAA-G12 with settings of T=2/B=4, T=3/B=4, T=4/B=4, or T=5/B=4 (<a href="https://drive.google.com/open?id=0BwovO-kzwAfgclcxU3lXMlc2WkU" target="_blank">see charts suites</a>, zooming required).</li>
<li>This post has been simultaneously published on <a href="https://seekingalpha.com/article/4087925-breadth-momentum-vigilant-asset-allocation" target="_blank">SeekingAlpha</a>.</li>
</ul>
<br />
The full AmiBroker code for VAA is available upon <a href="mailto:trendxplorer@gmail.com?Subject=Request%20for%20VAA%20model%20in%20AmiBroker" target="_blank">request</a>. Interested parties are encouraged to support this blog with a donation.<br />
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<br />TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-9321696080212877362017-05-31T15:57:00.000-04:002017-07-29T04:02:41.635-04:00On The Lookout For Better Data[Revised: Originally this post was about sourcing data from Quandl's premium QuoteMedia EOD service ($$$). Due to the migration to <a href="http://www.tiingo.com/" target="_blank">Tiingo's</a> as preferred data supplier for the <a href="http://indexswingtrader.blogspot.com/p/strategy-signals.html">Strategy Signals</a> the contents have become obsolete. This entry is now solely maintained as anchor for the contributions in the comment section below.]
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TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-73814572290315728232017-05-18T14:55:00.000-04:002017-05-18T15:28:42.020-04:00Yahoo Finance API Ceased WorkingUnfortunately this week the Yahoo Finance team changed the functionality of their financial data service. Apart from modifying the construction of the download link, the order and contents of the supported data fields have been altered too. As of writing support of total return data has been suspended.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_U5awXkkgIWu60amoifYT8rMmeMlWxW-QtTFIWNVg5HsYMGFAplgMSUboxh4nXtb8_6VFsvw4NDu3V5TI1F9qQa-VsJH8JISLMZa3pl-hQN1JJ9Nx0NHQmVJ_eSsCqpCikH389v2-rPA/s1600/maze.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_U5awXkkgIWu60amoifYT8rMmeMlWxW-QtTFIWNVg5HsYMGFAplgMSUboxh4nXtb8_6VFsvw4NDu3V5TI1F9qQa-VsJH8JISLMZa3pl-hQN1JJ9Nx0NHQmVJ_eSsCqpCikH389v2-rPA/s320/maze.jpg" width="320" /></a></div>
<br />
Regretfully, as a result both the Excel VBA spreadsheets and the Google Sheets on the Strategy Signals page have stopped functioning. Until further notice I have no other choice but to discontinue these services from the blog.<br />
<br />
Thank you for your understanding and please share your thoughts in the comment section below on fixes or alternative download sources.<br />
<br />
For more information see the <a href="https://forums.yahoo.net/t5/Yahoo-Finance-help/Is-Yahoo-Finance-API-broken/td-p/250503/page/3" target="_blank">Yahoo Help Community</a>.TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-58474040262410017802017-03-09T15:50:00.002-05:002017-03-11T09:51:24.023-05:00Index Mapping For ETF ProxiesIn order to present results as realistic as possible in our <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2759734" target="_blank">PAA-paper</a>, we constructed long-term end-of-month data series for popular ETF proxies, like SPY, GLD and TLT (see paper appendix on <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2759734" target="_blank">SSRN</a>). All data series start December 1969. For the pre-inception history, the proxies are derived from suitable indices. As part of a complete revision of the long-term data set, we recently improved the construction of the data series by mapping the underlying index through a linear formula to arrive at the best fit over the life span of the ETF to be replicated. The construction process is demonstrated below for <a href="https://www.ishares.com/us/products/239623/" target="_blank">EFA</a>. The link to an example spreadsheet with all the necessary calculations is published at the end of this post.<br />
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<a href="https://www.ishares.com/us/products/239623/" target="_blank">EFA</a> seeks to track the investment results of the MSCI EAFE index which is composed of large- and mid-capitalization developed market equities, excluding the U.S. and Canada. The index data is available as free download from the <a href="https://www.msci.com/end-of-day-data-regional" target="_blank">MSCI website</a>. Comparing EFA’s <a href="https://www.ishares.com/us/239623/fund-download.dl" target="_blank">historical data record</a> against the various index levels supported by MSCI like Price, Gross, Net, reveals the MSCI EAFE <b>Net</b> index as underlying index. Historical dividend adjusted data for EFA itself is offered by <a href="https://finance.yahoo.com/quote/EFA" target="_blank">Yahoo Finance</a>, also for free. For constructing a long-term EFA proxy the data from both sources is required.<br />
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With the data readily available in Excel, the next step is to derive the data for the ETF-proxy from the underlying index for the In-Sample (IS) period. The goal is to map the underlying to arrive at the best fit over the life span (=IS) of the ETF through a linear formula: r+ = b * r + a, where “r” is the return of the index and “r+” is the return for the proxy. The values for the coefficients “a” and “b” are determined through Excel’s Solver add-in by minimizing the unexplained sum of squared deviations for the return series of EFA and the ETF-proxy.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuPhNIkh-to1VlNcM8yy_GhM9S86bCL9EFj2E3bVE2VxEKFhJUU3jweMjP3Ua6NmomfOTHGVTvnCyZnE5_XMSQ6wccYxtQjPwPCMEI4K2NqK_4YYqlQN57T0PnAoKrnD6HUjPV9NlLz70/s1600/Mapping+Settings.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuPhNIkh-to1VlNcM8yy_GhM9S86bCL9EFj2E3bVE2VxEKFhJUU3jweMjP3Ua6NmomfOTHGVTvnCyZnE5_XMSQ6wccYxtQjPwPCMEI4K2NqK_4YYqlQN57T0PnAoKrnD6HUjPV9NlLz70/s400/Mapping+Settings.png" width="341" /></a></div>
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After Solver finishes the calculation cycles, the found coefficients result in high R-Squared and correlation readings.<br />
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Visual inspection of the resulting curves shows a high degree of fit with minimal distortions.<br />
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The found mapping formula can be checked by plotting the return series of MSCI EAFE and EFA as scatter graph with the linear regression line overlaid. The coefficients of the regression line match with the ones derived by Solver. Hence the scatter graph approach offers a handy shortcut, making the Solver approach essentially superfluous.<br />
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Furthermore the results may be double-checked by a regression analysis through Excel’s Analysis Toolpak add-in. The low <i>Significance F</i> reading (below 0.05) shows the found coefficients are reliable (statistically significant).<br />
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Having found statistically significant coefficients for the IS period (2001-2015), EFA's history can now be extended for the Out-of-Sample period, back to the inception date of the MSCI EAFE index: December 1969. The final result is a proxy for EFA covering 1969 - 2015: "EFA+"<br />
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After following the same workflow for other ETF’s, the final result is a collection of data series in Excel like the below sample (DummyData.xlsx):<br />
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To export the data from Excel and save each ETF-proxy in its separate csv-file, the following [updated] <a href="https://cran.r-project.org/index.html" target="_blank">R-code</a> comes in handy. The code adds a $-prefix to each ETF’s name for distinction.<br />
<script class="brush: js" type="syntaxhighlighter"><![CDATA[
# --- load libraries ---
require( quantmod )
require( PerformanceAnalytics )
require( openxlsx )
# --- select data source ---
excelfile <- "DummyData.xlsx"
# --- read data from spreadsheet ---
# prices <- read.xlsx2( excelfile, sheet = "Prices" )
prices <- read.xlsx( excelfile, sheet = 1 )
# --- replace excel's numeric date format ---
dates <- prices[,1]
dates <- as.character( dates )
dates <- as.numeric( dates )
# --- synch with start of data set: "1969-12-31" ---
dates <- dates - 25568
dates <- as.Date( dates, origin = "1969-12-31" )
# --- update date column ---
prices[,1] <- dates
# --- create xts object from prices with dates as index ---
data <- xts( x = prices[,-1], order.by = prices[,1])
# --- do housekeeping on column names ---
colnames( data ) <- gsub( "\\.[A-z]*", "", colnames( data ) )
# --- save data for each asset in a separate csv ---
symbolnames <- colnames( data )
for( i in 1:length( symbolnames ) )
{
name <- symbolnames[i]
dat <- data[,i]
dat <- as.data.frame( dat )
dat <- cbind( Date = rownames( dat ), dat )
write.table( dat, file = paste( '$', name, '.csv', sep = '', na = '' ), append = FALSE,
quote = FALSE, sep = ",", eol = "\n", na = "NA", dec = ".", row.names = FALSE,
col.names = FALSE, qmethod = c("escape", "double"), fileEncoding = "")
}
# --- end of code ---
]]></script>
[Update:] Hat tips to <a href="http://www.investresolve.com/ca/who-we-are/" target="_blank">Adam Butler</a> and <a href="https://twitter.com/Carlos_Espeleta" target="_blank">Carlos Espeleta</a> for pointing at the <a href="https://cran.r-project.org/web/packages/openxlsx/index.html" target="_blank">openxlsx package</a> for R, which removes the Java dependent package previously used.<br />
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The output of the R-code is a collection of csv-files with dates and closes, ready for import in your charting program.<br />
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Sources of interest:<br />
-<span class="Apple-tab-span" style="white-space: pre;"> </span><a href="https://finance.yahoo.com/" target="_blank">Yahoo Finance</a><br />
-<span class="Apple-tab-span" style="white-space: pre;"> </span><a href="https://www.msci.com/end-of-day-data-search" target="_blank">MSCI</a><br />
-<span class="Apple-tab-span" style="white-space: pre;"> </span><a href="https://www.reit.com/data-research/reit-indexes/ftse-nareit-us-real-estate-index-historical-values-returns" target="_blank">NAREIT</a><br />
-<span class="Apple-tab-span" style="white-space: pre;"> </span><a href="http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html" target="_blank">Fama/French</a><br />
-<span class="Apple-tab-span" style="white-space: pre;"> </span><a href="https://index.db.com/" target="_blank">Deutsche Bank IQ</a><br />
-<span class="Apple-tab-span" style="white-space: pre;"> </span><a href="https://www.quandl.com/collections/markets" target="_blank">Quandl</a><br />
-<span class="Apple-tab-span" style="white-space: pre;"> </span><a href="http://news.morningstar.com/index/indexReturn.html" target="_blank">Morningstar</a><br />
-<span class="Apple-tab-span" style="white-space: pre;"> </span><a href="https://www.barchart.com/stocks/indices" target="_blank">Barchart</a><br />
-<span class="Apple-tab-span" style="white-space: pre;"> </span><a href="https://www.premiumdata.net/products/premiumdata/worldindices.php" target="_blank">Norgate Data</a><br />
-<span class="Apple-tab-span" style="white-space: pre;"> </span><a href="http://www.mikemiddleton.com/Excel-Exponential-Curve-Fit-2010.pdf" target="_blank">Mike Middleton</a><br />
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The example spreadsheet along with the R-code and the DummyData.xlsx files are available on the <a href="https://drive.google.com/drive/folders/0BwovO-kzwAfgLVpPdTgteDFYSDg?usp=sharing" target="_blank">Google Drive folder</a> connected to this post.<br />
<br />TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-65433753030071702322016-12-24T11:33:00.002-05:002023-07-29T12:11:35.873-04:00Ho, Ho, Ho: Excel VBA For Global Equities MomentumJust in time for Santa! Based again on a foundation by <a href="http://investexcel.net/" target="_blank">InvestExcel</a>, Denis Bergemann collaborated with me on another Excel VBA project covering Gary Antonacci's popular Global Equities Momentum (GEM).<br />
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The VBA driven Excel spreadsheet follows the official rules for GEM (see <a href="http://indexswingtrader.blogspot.com/2016/10/prospecting-dual-momentum-with-gem.html" target="_blank">here</a>) and allows you to select your preferred US and International stocks fund. This applies also for the out-of-market bond fund and for the proxy fund for observing the risk free rate. The lookback parameter for both relative and absolute momentum is user adjustable.<br />
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[Update] In the latest edition of the spreadsheet [v3], the widely used 60/40 benchmark is depicted as a reference point. The 60/40 portfolio <span style="background-color: white; color: #424242; font-family: inherit;">holds 60% equities and 40% bonds with monthly rebalancing. In the spreadsheet the 60/40 mix is composed of the US stocks fund and the out-of-market bond fund.</span><br />
<span style="background-color: white; color: #424242; font-family: inherit;"><br /></span>
Results for both the GEM and 60/40 portfolios as well as the separate components are presented in tabular and graphical format.<br />
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<a name='more'></a>The [updated] work flow is pretty much identical to the one for the PAA / GPM VBA (see <a href="http://indexswingtrader.blogspot.com/2016/10/flexing-vba-for-quants-and-everyone-else.html" target="_blank">here</a>):<br />
<ul>
<li>Currently, the sheet only works with Excel for Windows</li>
<li>Run the backtest after Yahoo Finance has published the closing data for the month</li>
<li>Enter the [two] required stock funds in the dedicated column of the sheet</li>
<li>Repeat for the out-of-market bond fund and the proxy fund resembling the risk-free rate</li>
<li>Set start and end dates<br />(NB! Observe an initialization period for the fund with the shortest history equal to the chosen lookback range)</li>
<li>Click the button [Download Data] and wait until downloading has finished (graphs and tables will disappear)</li>
<li>Finally click the button [Allocation] and wait for the VBA to crunch the numbers (graphs and tables are reprocessed).</li>
</ul>
The VBA-code embedded in the Excel sheet takes care of downloading the data as well as all the necessary calculations and permutations.<br />
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Please observe the required number of [four] assets (no more, no less!) as indicated in the spreadsheet.<br />
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Running the spreadsheet at the end of the month, after Yahoo Finance has published the closing data for the month, will give the allocation for the upcoming month. End of month data is usually available a couple of hours after the NYSE market session has ended on the last trading day of the month. Since GEM deploys an all-in approach, the allocation percentage is 100% of dedicated capital.<br />
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Merry Xmas!<br />
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The Excel sheet for GEM is available upon <a href="mailto:trendxplorer@gmail.com?Subject=Request%20for%20GEM%20spreadsheet" target="_blank">request</a>. Interested parties are encouraged to support this blog with a donation.
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<br />TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-64075315812081344372016-10-23T09:08:00.003-04:002023-07-29T12:12:12.690-04:00Flexing VBA For Quants (And Everyone Else)<div><b><span style="color: red;">Update</span></b>: </div><div><span style="color: red;"><b>Due to a change in the placement of OHLC price data in Tiingo's feed, version 4.0 of the stand alone Excel spreadsheet should no longer be used! In the meantime JH has fixed the issue, which is available as beta version 5.0. Thanks JH, great job!</b></span></div><div><br /></div><div><br /></div>Would it not be great to have the models for <a href="http://indexswingtrader.blogspot.com/2016/04/introducing-protective-asset-allocation.html" target="_blank">Protective Asset Allocation</a> (PAA) and <a href="http://indexswingtrader.blogspot.com/2016/06/deciphering-correlation-hedged-momentum.html" target="_blank">Global Protective Momentum</a> (GPM) in Excel, so you can run your own backtests without <a href="http://www.amibroker.com/" target="_blank">AmiBroker</a>? And not being limited to a pre-defined universe? Actually, now you can.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5lVQg18U8Hj8Di9zeSwG-sEH8G4pWeXpy6Zn7i4KJLyVPHeuN2bKvZL1xHRSehTYqmINH7uv070YT2h237swYlXXn40a2KCxS5f8MPdYqCdkj97GFp9XlQ155u4o1VQ02sttDHqBRUKY/s1600/excel-vba-logo.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5lVQg18U8Hj8Di9zeSwG-sEH8G4pWeXpy6Zn7i4KJLyVPHeuN2bKvZL1xHRSehTYqmINH7uv070YT2h237swYlXXn40a2KCxS5f8MPdYqCdkj97GFp9XlQ155u4o1VQ02sttDHqBRUKY/s1600/excel-vba-logo.png" /></a></div>
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Based on a foundation by <a href="http://investexcel.net/multiple-stock-quote-downloader-for-excel/" target="_blank">InvestExel</a>, Denis Bergemann from Germany collaborated with me in developing an Excel spreadsheet that allows you to select your preferred risk-on and risk-off assets, set backtest parameters to your liking and review results by their statistics as well as in graphical format.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgd0mxrKxg00EqddlQzimm94AacItvrGr4fLbhyLt3MEgx547AdBGoAhFzIPeAoxC4e8w11k2yqck8tEY8N_vBC4_51KguC4jbY7XGmY9rOxer35nSbZEiwtJncdeCh5XjxPzZ_YMjp1ZU/s1600/VBA+Graphs.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="586" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgd0mxrKxg00EqddlQzimm94AacItvrGr4fLbhyLt3MEgx547AdBGoAhFzIPeAoxC4e8w11k2yqck8tEY8N_vBC4_51KguC4jbY7XGmY9rOxer35nSbZEiwtJncdeCh5XjxPzZ_YMjp1ZU/s640/VBA+Graphs.png" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjphJ5Ye4SkXdZQ1n6G5DKC26QvEsjmPYEyiMREOvdwZe_hkph7x3R-K1Ke3VBlBll98nibg5JfjrATgBlgFCGlsGCpLp1ckT-De88iqRo-lWcLg_piGH-k38OQr9V_piZ_5GH_zAXI0tU/s1600/VBA+Statistics.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="110" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjphJ5Ye4SkXdZQ1n6G5DKC26QvEsjmPYEyiMREOvdwZe_hkph7x3R-K1Ke3VBlBll98nibg5JfjrATgBlgFCGlsGCpLp1ckT-De88iqRo-lWcLg_piGH-k38OQr9V_piZ_5GH_zAXI0tU/s640/VBA+Statistics.png" width="640" /></a></div>
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<a name='more'></a>The work flow goes like this:<br />
<ul>
<li>Run the backtest after Yahoo has published the closing data for the month</li>
<li>Enter the risk-on and risk-off assets in the two dedicated columns of the sheet</li>
<li>Set start and end dates<br />(NB! Observe a 1-year initialization period for the ETF with the shortest history)</li>
<li>Keep frequency at m (=monthly quotes)</li>
<li>Adjust protection level* (default = 2: high protection)</li>
<li>Select number of top assets</li>
<li>Click the button [Download Data] and wait until downloading has finished (graphs and tables will disappear)</li>
<li>Finally click the button [Calculate Systems] and wait for the VBA magic to finalize (graphs and tables are reprocessed).</li>
</ul>
The VBA-code embedded in the Excel sheet takes care of downloading the data as well as all the necessary calculations and permutations.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8BeFU1bsjO3rHli0ZtxsZ2HMLzashoM2SogrfjumfACze858w-H_v1ELMYqLtcsijbvvdku8-FXIgSdZeEmnYvt5jS8RYtFnufZWx0gGqu-1RuYN7Grcl-IogtHvVCmZ4HiBsAOG3qQs/s1600/VBA_Control.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="392" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8BeFU1bsjO3rHli0ZtxsZ2HMLzashoM2SogrfjumfACze858w-H_v1ELMYqLtcsijbvvdku8-FXIgSdZeEmnYvt5jS8RYtFnufZWx0gGqu-1RuYN7Grcl-IogtHvVCmZ4HiBsAOG3qQs/s400/VBA_Control.png" width="400" /></a></div>
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The sheet allows for adjusting the protection level or the top selection without a new download, but changing the backtest range or altering the asset lists requires to start with a fresh data download.<br />
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Please note the number of risk-on or risk-off assets is not restricted to 12 and 2, just select the ETFs and/or mutual funds you prefer.<br />
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The sheet also shows the allocation percentages for the upcoming month after Yahoo has published the monthly closing data, usually available a couple of hours after the NYSE market session has ended on the last trading day of the month.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtW3LLihyphenhyphenK5CiPoUOWOcx1QJh-4E3s8bVMwPfaX1EoGGdzkFDnGP2djJrUIjeQm6hKERMnt17S21o37vRhHPHJ0UiacEyetBPVucXgEJGuL_CgrMjiobJrXXdI3bSPfka3D_xtLHiEvms/s1600/VBA+Allocations.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="142" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtW3LLihyphenhyphenK5CiPoUOWOcx1QJh-4E3s8bVMwPfaX1EoGGdzkFDnGP2djJrUIjeQm6hKERMnt17S21o37vRhHPHJ0UiacEyetBPVucXgEJGuL_CgrMjiobJrXXdI3bSPfka3D_xtLHiEvms/s640/VBA+Allocations.png" width="640" /></a></div>
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<b>End notes</b><br />
<ul>
<li>The sheet only works with Windows.</li>
<li>The protection level is simplified to ( p * ∑ [ri <= 0] ) / N, so p = 0 turns the protection logic off. With p = 2, the protection level equals high protection as used in the presentation of PAA and GPM.</li>
</ul>
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The Excel sheet for PAA / GPM is available upon <a href="mailto:trendxplorer@gmail.com?Subject=Request%20for%20Excel%20VBA%20spreadsheet" target="_blank">request</a>. Interested parties are encouraged to support this blog with a donation.
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<br />TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-8325178762650827172016-10-04T14:22:00.004-04:002023-07-29T12:13:13.443-04:00Prospecting Dual Momentum With GEM<ul>
<li>Gary Antonacci popularized dual momentum with an effective and simple approach for dynamic asset allocation: Global Equities Momentum (GEM).</li>
<li>Using simulated ETF data series, GEM’s performance over past market conditions can be approximated.</li>
<li>For longer investment horizons GEM’s implementation with ETFs obtained positive returns with high consistency.</li>
</ul>
After winning first place in 2012 in the <a href="http://www.naaim.org/programs/wagner-award-papers/" target="_blank">NAAIM Wagner competition</a>, Gary Antonacci popularized his momentum investing approach in the award winning book “Dual Momentum Investing”.<br />
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<a href="https://www.amazon.com/Dual-Momentum-Investing-Innovative-Strategy/dp/0071849440" target="_blank"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZ9fFpsmfBObbdwZ2j4w9tUKmS4L3ydZnc-BspzUgYREmIXu5ySQM4c7cPv2ncWh_CCsmvOixZvprhe6WGLAzf3X7UPhBwKxC7eOAcxuPs1_SdnM5_61GPmxTjinlKzUDAT2X3EfLCAlQ/s320/dualmomentumbook.jpg" width="212" /></a>
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In his book Antonacci makes a strong case for combining relative strength price momentum with trend following absolute momentum. The first 90 pages are a comprehensive overview, introducing the “premier market anomaly”, describing the history of momentum research and its early practitioners, behavioristics and lots of other interesting themes. Frankly, these pages alone make the book a must read, not least due to the conversational, at times even playful tone of Antonacci’s light pen.<br />
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At the center of the book lies the chapter covering Global Equities Momentum (GEM), where Antonacci explains the mechanics of the dual momentum approach for dynamic asset allocation. GEM is quite brilliant in its simplicity: a 12-month lookback for both absolute and relative momentum combined with just three asset classes, are all of GEM’s components. <br />
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Both in his book and on his <a href="http://www.optimalmomentum.com/index.html" target="_blank">website</a>, Antonacci presents the Global Equities Momentum (GEM) approach with non-tradable total return index data. Going back as far as the seventies has the benefit of incorporating a rising yields decade too. Therefore, to get insight into GEM’s long-term performance with today’s ETFs, index based simulated total return proxies are required. By applying GEM’s dynamic asset allocation to such simulated ETFs, the practitioner may get a good impression (nothing more) of GEM’s “real” performance during past market conditions. Before doing so, first GEM’s performance with index data will be replicated to validate the accuracy of the presentation in this contribution.<br />
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Noteworthy, the rules often shared for GEM, derived from the flow chart on page 101, are <b>not</b> the official GEM rules. Actually the flow chart along with the corresponding instructions on page 112 is only a simplified way to determine GEM’s allocations for those using a website like <a href="http://stockcharts.com/freecharts/perf.php?IVV,BIL,VEU" target="_blank">PerfCharts</a> to get their signals. However, when doing calculations with a charting program like <a href="http://www.amibroker.com/" target="_blank">AmiBroker</a>, the instructions on page 98 are to be adhered instead. <br />
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<a name='more'></a>In contrast to common practice, GEM’s official rules administer absolute momentum before the application of relative strength momentum. According to recently confirmed <a href="http://www.kof.ethz.ch/en/news-and-events/news/kof-bulletin/kof-bulletin/2016/09/international-stock-return-predictability.html" target="_blank">academic research</a> the U.S. stock market tends to lead the rest of the world especially during recessions, hence the trend of stocks is determined first using just the S&P 500 index. Only when an uptrend (positive excess return) in the S&P 500 is identified by comparing its 12-month total return against that of the 3-month U.S. T-Bill, relative strength momentum is applied to select the best performing stock index for allocation: the S&P 500 index or the All Countries World Index ex U.S. Otherwise the U.S. Aggregate Bond index is selected for capital preservation. For more about GEM’s mechanics and the strong case Antonacci builds for dual momentum investing see his highly recommended book and the <a href="http://www.optimalmomentum.com/faq.html" target="_blank">FAQ</a> on his website.<br />
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In the following chart both the official version (INDEX98 in black) and the simplified version (INDEX101 in gray) are painted along with GEM’s three index components. The upper subpane shows the monthly allocations according to GEM’s official rules. The lower subpane has the allocations following the simplified logic. <br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPFetSC3oWvTyvT-1avjPCrD8zn3PWDxSlRmBa24ZUQHiJDGwpMhcWfJ5OwYNvOVb3RVbXwwCfsqjqIAmUrmZAZCNuXoTEfj2bTpnbmbWmayWBMn4WMuEwXcl1a41Ql4HPXiJsPHM8eDQ/s1600/GEM-Index-Comparison.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="446" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPFetSC3oWvTyvT-1avjPCrD8zn3PWDxSlRmBa24ZUQHiJDGwpMhcWfJ5OwYNvOVb3RVbXwwCfsqjqIAmUrmZAZCNuXoTEfj2bTpnbmbWmayWBMn4WMuEwXcl1a41Ql4HPXiJsPHM8eDQ/s640/GEM-Index-Comparison.png" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4bcNQ_zOFUiQ3oVEaeHMYnFQ4VRXsvbF_JMOwwBleKOBuNBNj4uMg63RKfw1BsuALypADcXMm-m0jtEve_kLe1Pw3TWGYrh2KKc2Z3YQSxSHEN0NSfYXAIPKtBjJ7EwbGlnxIwJ6YUko/s1600/GEM-Index-Statistics.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="74" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4bcNQ_zOFUiQ3oVEaeHMYnFQ4VRXsvbF_JMOwwBleKOBuNBNj4uMg63RKfw1BsuALypADcXMm-m0jtEve_kLe1Pw3TWGYrh2KKc2Z3YQSxSHEN0NSfYXAIPKtBjJ7EwbGlnxIwJ6YUko/s640/GEM-Index-Statistics.png" width="640" /></a></div>
<i>NB! Results are derived from non-tradable monthly total return indexes and are therefore purely hypothetical.</i><br />
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Close inspection of the two allocation panes reveals how the official set of rules has GEM switching to bonds earlier than the simplified approach, but comes along with slightly more whipsaw too. The earlier switch to risk-off results in higher absolute return as well as better risk-adjusted performance as shown in the statistics table. For the remainder of this contribution the official GEM logic is observed. <br />
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Validating the monthly selections against GEM’s published <a href="http://www.optimalmomentum.com/gem_allocation.html" target="_blank">allocations</a> gives a match for all but 3 out of 540 months (1971-2015). The 3 observed differences are due to the application of the 30-day T-Bill total return series instead of the 3-month T-Bill.<br />
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Now let’s apply GEM to the markets with today’s ETFs: IVV, BND and VEU (per Antonacci’s <a href="http://www.optimalmomentum.com/faq.html" target="_blank">FAQ</a>). For the following simulation the data histories are back extended with the underlying total return index and corrected for the observed tracking error between the ETF and the underlying total return index. <br />
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The next chart shows the simulated ETF performance for GEM (black) with BIL as risk free proxy against the index performance (dashed) and the 3 ETFs eligible for allocation. Again, the subpane has the monthly allocations confirming the low turnover of the approach, while also showing the inevitable periods with some whipsaw.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrBM8PtHK0YZAHDEoqDsJO46uV4qjHgwm0dzxM-6KIVsHzmpSGLAG_97r7vrDyQROPnOkjRQhnL_y-FVYEeoMECqv-0hTFKoTYSYPc1XwRFvq0M8WlQ4NYCUqNRAkosuRbNkTsKMJtq1o/s1600/GEM-ETF98-BH.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="446" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrBM8PtHK0YZAHDEoqDsJO46uV4qjHgwm0dzxM-6KIVsHzmpSGLAG_97r7vrDyQROPnOkjRQhnL_y-FVYEeoMECqv-0hTFKoTYSYPc1XwRFvq0M8WlQ4NYCUqNRAkosuRbNkTsKMJtq1o/s640/GEM-ETF98-BH.png" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEin4tSNBXckbZ7wS2vsXegawXxO1cElA6QUVw6NadG4pzecPDuhN3_rm1FOK5CxkB5z0UoRhWBBzIHHkFjegRhaVnwkfuGv4whN47RHadfi7_JW4FdE8rcPgWGxDlX0TBqRYR4p49tb18Y/s1600/GEM-ETF-Statistics.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="74" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEin4tSNBXckbZ7wS2vsXegawXxO1cElA6QUVw6NadG4pzecPDuhN3_rm1FOK5CxkB5z0UoRhWBBzIHHkFjegRhaVnwkfuGv4whN47RHadfi7_JW4FdE8rcPgWGxDlX0TBqRYR4p49tb18Y/s640/GEM-ETF-Statistics.png" width="640" /></a></div>
<i>NB! Results are derived from simulated monthly total return data based on indices corrected for tracking errors. Furthermore trading costs, slippage and taxes are disregarded. Results are therefore purely hypothetical.</i><br />
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As the charts shows, the ETF implementation tracks a near perfect footprint. Remarkably, the risk-adjusted performance of the ETF implementation even exceeds that of the original index version as shown in the statistics table. Notable is the 3-year positive win rate of more than 99%. <br />
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Due to GEM’s drawdown profile as charted below for the ETF implementation, the investor needs to have a longer investment horizon for being able recover. Point to note: for a lot of sensible investors a drawdown close to 20% is a deal breaker because a netted 25% recovery is required only to get back to break-even again. However, in the longer run GEM proves to be quite resilient as the chart ahead will show.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitOZSFjuRwVekgrxPbwwcX9kc6z_nHPOOjs8FlTIfvl2kQ64srb62Vv5VkNWnCW4KnlKiOMExENrdLfzTo7Y-MAmFY47qN2G16OgFKi_1VYi2bMCkYkfudnu0PJj8A7S8tCEQSvyIeNg0/s1600/GEM-ETF-Drawdown.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="284" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitOZSFjuRwVekgrxPbwwcX9kc6z_nHPOOjs8FlTIfvl2kQ64srb62Vv5VkNWnCW4KnlKiOMExENrdLfzTo7Y-MAmFY47qN2G16OgFKi_1VYi2bMCkYkfudnu0PJj8A7S8tCEQSvyIeNg0/s640/GEM-ETF-Drawdown.png" width="640" /></a></div>
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For the long term investor GEM’s tendency to recover is shown on the following chart The chart depicts the rolling 3-year return for GEM (red) and SPY (blue). In contrast to SPY’s prolonged sub-zero periods, notice GEM hardly ever dips down the 0% water mark. This is indicative for GEM’s high consistency in registering positive returns on investment for nearly all 3-year periods during 1974-2015.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAg2BoZmMqfXHHaN_oAQCKg4fky5-IX7ewgBYK7Fa8BmAv44ae5y-GPWvbBW9lUWiFtdL8hNuxTlqjL4eVErPtxeYBuUo6VYDqY8UHToxII1xuMFh7wf3vxfQ0Rrli3AFtXKpxTASrQno/s1600/GEM-SPY-ETF-Rolling3y.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="222" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAg2BoZmMqfXHHaN_oAQCKg4fky5-IX7ewgBYK7Fa8BmAv44ae5y-GPWvbBW9lUWiFtdL8hNuxTlqjL4eVErPtxeYBuUo6VYDqY8UHToxII1xuMFh7wf3vxfQ0Rrli3AFtXKpxTASrQno/s640/GEM-SPY-ETF-Rolling3y.png" width="640" /></a></div>
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The dual momentum approach identifies the overall market direction – are stocks globally expected to go up or down? – by putting U.S. stocks to the absolute momentum test. To pass the absolute momentum threshold U.S. stocks, in the ETF approach represented by IVV, need to outperform an (assumed) risk free investment like in 30-day or 3-month U.S. T-Bills. The following chart compares GEM’s application with 4 different absolute momentum proxies: BIL (blue), SHV (magenta), SHY (green) and a 0% cash holding (red). The original (non-tradable) index performance is again added for reference (dashed black). For “live” application BIL or SHV appear to be the best choices, confirming Antonacci’s <a href="http://www.optimalmomentum.com/faq.html" target="_blank">FAQ</a>.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiplGW4dDO94AfCdf3VM1-m1Hj9E3HMtPmwB3l8WaJWGMuf3PBfzJRyH_k3XhPGtSgDdKzo_qWHZHl03h1gFxd3cWW_Krtx6JLdpMC7oexH-2aBiOkgmojjV8wmQFqnfN6uwAYyiliH3os/s1600/GEM-RiskFree-Comparison.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="446" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiplGW4dDO94AfCdf3VM1-m1Hj9E3HMtPmwB3l8WaJWGMuf3PBfzJRyH_k3XhPGtSgDdKzo_qWHZHl03h1gFxd3cWW_Krtx6JLdpMC7oexH-2aBiOkgmojjV8wmQFqnfN6uwAYyiliH3os/s640/GEM-RiskFree-Comparison.png" width="640" /></a></div>
<i>NB! Results are derived from simulated monthly total return data based on indices corrected for tracking errors. Furthermore trading costs, slippage and taxes are disregarded. Results are therefore purely hypothetical.</i><br />
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<b>Strategy signals</b><br />
<br />
The monthly asset selection for GEM is shown in the signal table below. For interpretation of the signals please refer to the explanation on the <a href="http://indexswingtrader.blogspot.com/p/strategy-signals.html">Strategy Signals page</a>.
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<center>
<iframe height="480" src="https://docs.google.com/spreadsheets/d/1GBbs5Unv9rkcXAnBUAB3c0qgIqcQ7LHVr9QFh07o0hw/pubhtml?gid=65999399&single=true&widget=true&headers=false" width="480"></iframe>
<br /><br />
<table style="width: 480px;"><tbody>
<tr><td><center>
<i>NB! No guarantee whatsoever is given for the soundness of the strategy nor the proper functioning of the table nor for the accuracy of the signals. </i><i style="text-align: left;">Data may be delayed. </i><i style="text-align: left;">Please do your own due diligence and use at your peril. The <b style="color: red;">Important Notice</b> in the footer applies as well as the <a href="http://indexswingtrader.blogspot.com/p/disclaimer.html" style="text-decoration: none;" target="_blank">Disclaimer</a>.</i></center>
</td></tr>
</tbody></table>
</center>
<br />
<b>Endnotes</b><br />
<ul>
<li>Different from the book, the statistics tables show CAGR readings and conservatively CAGR-based Sharpe ratios.</li>
<li>The author has no affiliation with Gary Antonacci nor AmiBroker and receives no compensation from anyone of them.</li>
<li>This contribution is simultaneously published on <a href="http://seekingalpha.com/article/4010394-prospecting-dual-momentum-gem" target="_blank">SeekingAlpha</a>.</li>
<li><span style="font-size: small;"><span style="font-family: inherit;">GEM is also featured on <a href="https://allocatesmartly.com/?aff=220" target="_blank">AllocateSmartly.com</a>. By signing up through this <a href="https://allocatesmartly.com/?aff=220" target="_blank">link</a>, you support my work.</span></span> </li>
<li><span style="font-family: inherit;">View an <a href="https://vimeo.com/164047189?autoplay=1" target="_blank">online presentation</a> of Dual Momentum Investing by Gary Antonacci.</span></li>
<li><span style="font-family: inherit;">Listen to the <a href="http://mebfaber.com/2017/03/29/episode-45-gary-antonacci-get-synergy-happens-use-dual-momentum/" target="_blank">podcast</a> by <a href="http://mebfaber.com/" target="_blank">Meb Faber</a> and <a href="http://www.dualmomentum.net/" target="_blank">Gary Antonacci</a> talking Dual Momentum Investing.</span></li>
<li><span style="font-family: inherit;"><span style="background-color: white; color: #222222;">Request a copy of the Global Equities Momentum Excel VBA spreadsheet <a href="http://indexswingtrader.blogspot.com/2017/08/update-for-global-equities-momentum.html" target="_blank">here</a>.</span></span></li>
</ul>
<br />
<b>Disclosure</b>: The author has no positions in any stocks mentioned, but may initiate a long position in IVV, VEU, BND over the next 72 hours.<br />
<br />
The full AmiBroker code for GEM is available upon <a href="mailto:trendxplorer@gmail.com?Subject=Request%20for%20GEM%20model%20in%20AmiBroker" target="_blank">request</a>. Interested parties are encouraged to support this blog with a donation.<br />
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<br />TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-36840326004611240682016-09-03T09:40:00.005-04:002016-11-14T10:38:07.610-05:00AllocateSmartly<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
Launched only recently, <a href="https://allocatesmartly.com/?aff=220" target="_blank">AllocateSmartly.com</a> tracks the industry’s best tactical asset
allocation strategies with thorough, up-to-date backtests. As of writing 16 (sub) strategies are tracked and benchmarked on near real-time basis. All of the tracked strategies are both quantitative and
systematic, meaning well-defined mathematical rules govern exactly when
and what to trade. Among the featured strategies are GEM, GTAA, EAA and PAA. Take the platform for a test drive with a <a href="https://allocatesmartly.com/pricing/?aff=220" target="_blank">free limited membership</a> or sign up for <a href="https://allocatesmartly.com/pricing/?aff=220" target="_blank">full membership</a> to access all the neat features.<br />
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<b>Disclaimer</b>: Signing up to <a href="https://allocatesmartly.com/?aff=220" target="_blank">AllocateSmartly.com</a> through my blog provides support for my work. <br />
<br />TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-36651214608540956592016-07-23T05:09:00.001-04:002016-07-23T05:09:08.436-04:00Summer reading<center>
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<a href="https://www.amazon.com/DIY-Financial-Advisor-Solution-Protect/dp/111907150X" target="_blank"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3sGkrjRPiAD7ph3Xd13IR3i5q5JuZZpAUk7znyPVK0NL8VZEknN1J7nodvO-8ST3xeAqyj3gDV5rQDlzz6JkPzFpMwt6x8NSkRUh-p65BaMDqO-3xf-wub15TVhJAHtCzxV17trD_fFk/s320/DIY-Financial-Advisor.jpg" width="214" /></a>
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TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-40732352252345233692016-06-29T12:34:00.002-04:002023-07-29T12:13:57.356-04:00Deciphering Correlation Hedged MomentumIn a new <a href="http://seekingalpha.com/article/3985525-generalized-protective-momentum" target="_blank">SeekingAlpha contribution</a> we combine PAA’s protective multi-market breadth approach with a generalized momentum metric based on correlation hedged returns. The resulting model is called Generalized Protective Momentum (GPM). In this blogpost the correlation hedge is deciphered.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQ2RWMGgUgZ1br-UnABwAm9Wdll7ZCO0Jhu1JjWHLlPm8zA2cAxIRv8nxH8CMFlvulcZfIZfJ2ob8rFgr9kQOf1IQgUxylKTCtYpyesKxIAKdmA8wOebjLrw_DUjxVIrF8V_9VU-DGOy4/s1600/yay-floating_numbers.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQ2RWMGgUgZ1br-UnABwAm9Wdll7ZCO0Jhu1JjWHLlPm8zA2cAxIRv8nxH8CMFlvulcZfIZfJ2ob8rFgr9kQOf1IQgUxylKTCtYpyesKxIAKdmA8wOebjLrw_DUjxVIrF8V_9VU-DGOy4/s400/yay-floating_numbers.jpg" width="400" /></a></div>
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The correlation hedge is a simplified version of Keller and Butler’s EAA-formula (see <a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2543979" target="_blank">paper</a> or <a href="http://indexswingtrader.blogspot.com/2015/01/a-primer-on-elastic-asset-allocation.html" target="_blank">primer</a>). For GPM we only use return and correlation information as momentum metric. We do so with two variations:<br />
<ul>
<li>GPM<span style="background-color: yellow;"><b>x</b></span>M: the correlation multiplied return metric <b>ri * ( 1 – ci )</b></li>
<li>GPM<span style="background-color: yellow;"><b>x</b></span>F: the correlation fractioned return metric <b>ri / ( 1 + ci )</b> </li>
</ul>
where <span style="background-color: yellow;"><b>x</b></span> is the degree of crash protection, <b>ri</b> is the average return of asset i over 1, 3, 6 and 12 months, and <b>ci</b> the 12-month correlation of asset i with the equal weighted “risky” investment universe. The correlation multiplier <b>( 1 – ci )</b> is based on the EAA-model, the correlation fraction <b>1 / ( 1 + ci )</b> was recently suggested by Wouter Keller. For the mechanics of the crash protection algorithm, see the <a href="http://indexswingtrader.blogspot.com/2016/04/introducing-protective-asset-allocation.html" target="_blank">PAA-post</a>.<br />
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In the graph below, the two correlation hedge variations are painted.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQV23UqQtUKWb8-oHGFJxh1Asb8z7tuIsrPRlhhSiSocDLxRl9HFswaZbNlTgzUzP8xoJYWgFk64nAT2TtU1kfM-k8Dq6sGuDE8daMj05RN2XoMbSPsZBFwQOzQuafW2qn76z5xpjGr6c/s1600/CorrelationHedge.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="378" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQV23UqQtUKWb8-oHGFJxh1Asb8z7tuIsrPRlhhSiSocDLxRl9HFswaZbNlTgzUzP8xoJYWgFk64nAT2TtU1kfM-k8Dq6sGuDE8daMj05RN2XoMbSPsZBFwQOzQuafW2qn76z5xpjGr6c/s640/CorrelationHedge.png" width="640" /></a></div>
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<a name='more'></a>Notice how<b> ri</b> is downplayed by the multiplier variation <b>( 1 – ci )</b> (blue curve) for assets with positive correlations more and more (the hedge multiplier approaches 0 when <b>ci</b> approaches 1), while <b>ri</b> is amplified in a near linear fashion for assets with negative correlations (the hedge multiplier increases to a maximum value of 2 when <b>ci</b> approaches -1).
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For the fraction variation <b>1 / ( 1 + ci )</b> (red curve) the hedge effect is inverted: for assets with positive correlations ri is downplayed by half (the maximum hedge fraction is 2 when <b>ci</b> approaches 1), while <b>ri</b> is increasingly amplified for assets with negative correlations (the hedge fraction approaches 0 when <b>ci</b> approaches -1).
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We will illustrate the two hedge variations for the “risky” N12 globally diversified universe as demonstrated in our <a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2759734" target="_blank">PAA-paper</a> (SPY, QQQ, IWM, EEM, VGK, EWJ, IYR, GSG, GLD, TLT, HYG and LQD). As safety asset we deploy the best out of two treasury ETFs: SHY and IEF, using the same correlation hedged momentum measure for selection. Each month 3 out of 12 assets with the highest correlation hedged return readings are eligible for capital allocation next to the safety asset's allocation. The backtests cover the 45+ year period December 1970 until May 2016.
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<br />
Contrary to our <a href="http://seekingalpha.com/article/3985525-generalized-protective-momentum" target="_blank">SA-contribution</a> where high protection is applied, we will now backtest GPM with low protection. Quick re-cap: with low protection (so x = pf = 0, see <a href="http://indexswingtrader.blogspot.com/2016/04/introducing-protective-asset-allocation.html" target="_blank">PAA-post</a>) for each “risky” asset with non-positive momentum a capital fraction of 1/N is allocated to the safety asset. With low protection GPM leaves more room to the “risky” assets for harvesting risk premia. This also allows for a good look at the absolute and relative changes in average capital allocation for the risky assets.
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The table below holds some key performance indicators for three variations of GPM:<br />
<ul>
<li>GPM0R: unhedged “raw” 1/3/6/12m return and low protection (green)</li>
<li>GPM0M: correlation multiplied return and low protection (blue)</li>
<li>GPM0F: correlation fractioned return and low protection (red)</li>
</ul>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4vBQ77n7wH7OADXlcAbPGWk8Epb0orn8DMFX-lmhHWp0RUxR2UQJ0SebDWB0eqsZQ3VChTB-TddFXISazMWlSGNGY0vA45-zSHZ-tDk11mdwIrt8SaGarEyVPipUWZmg-DcqUR5GGFfA/s1600/GPM0_StatsTable.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="62" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4vBQ77n7wH7OADXlcAbPGWk8Epb0orn8DMFX-lmhHWp0RUxR2UQJ0SebDWB0eqsZQ3VChTB-TddFXISazMWlSGNGY0vA45-zSHZ-tDk11mdwIrt8SaGarEyVPipUWZmg-DcqUR5GGFfA/s640/GPM0_StatsTable.png" width="640" /></a></div>
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<i>NB! All results in this post are derived from synthetic monthly total return data constructed by us based on indices net of costs. Furthermore trading costs, slippage and taxes are disregarded. Results are therefore purely hypothetical.</i>
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None of the low protection scenarios of GPM meet our positive performance requirements: rolling 1-year return win rates of above 95% and 99%, but the mark is barely missed (with medium or high protection enabled GPM does satisfy the requirements for both correlation hedge variations. See our <a href="http://seekingalpha.com/article/3985525-generalized-protective-momentum" target="_blank">SA-contribution</a>). Regarding risk-adjusted performance, both hedged correlation variations beat GPM’s unhedged “raw” return baseline scenario, see for example the lower drawdown (D), the higher Sharpe (SR) and MAR ratios.
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The table below shows the effect of the correlation hedge on the average capital allocation for both the hedge multiplier and the hedge fraction compared to the unhedged “raw” averaged return version of GMP, all with the PAA-like capital protection set to “low” (0). The capital allocations for the safety assets SHY and IEF are excluded from the table.
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZoIfFCrKCofotaLQRCQiMVUIoedqtk7PT3e8xQn-rSUY5MSCY4N1OveLXOeBuct1cDgXlUqOOasC47Q4lSurQia8bXAbtTnr_ZmhVQ_5KUyaAMX5xa4UahbT-r9AEzpy__nLAtTJj1D8/s1600/GPM0_AverageCapitalAllocation.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="92" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZoIfFCrKCofotaLQRCQiMVUIoedqtk7PT3e8xQn-rSUY5MSCY4N1OveLXOeBuct1cDgXlUqOOasC47Q4lSurQia8bXAbtTnr_ZmhVQ_5KUyaAMX5xa4UahbT-r9AEzpy__nLAtTJj1D8/s640/GPM0_AverageCapitalAllocation.png" width="640" /></a></div>
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Notice that for <b>ri * ( 1 – ci )</b> compared to <b>ri</b> emphasize is added to EWJ, GSG, GLD, TLT, HYG and LQD, while SPY, QQQ, IWM, EEM, VGK and IYR are de-emphasized.
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Compared to <b>ri</b>, for <b>ri / ( 1 + ci )</b> the capital allocations for SPY, QQQ, IWM, EEM and VGK are downplayed again, but less strongly than with <b>ri * ( 1 – ci )</b>, EWJ and IYR both get about the same allocations, while GSG, GLD, TLT, HYG and LQD are again emphasized, but to a lesser extent.
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The table below holds the relative changes in average capital allocations for each asset compared to the ones for <b>ri</b>.
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgq0q8L3n1KLSiI-fkvnw_iFJodDNPRu83LOkBPdeRKvO1Qsy-r_W74253vJdPAOkHAdZb8rziC4GH6O44Ltj4bmdWFAk8BLT36Tu6HfWfHFa1ix_-rjYndQG5fFdpFLvwKoTsFUAc2BZc/s1600/GPM0_ChangeAverageCapitalAllocation.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="92" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgq0q8L3n1KLSiI-fkvnw_iFJodDNPRu83LOkBPdeRKvO1Qsy-r_W74253vJdPAOkHAdZb8rziC4GH6O44Ltj4bmdWFAk8BLT36Tu6HfWfHFa1ix_-rjYndQG5fFdpFLvwKoTsFUAc2BZc/s640/GPM0_ChangeAverageCapitalAllocation.png" width="640" /></a></div>
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Especially the change for SPY stands out: compared to the unhedged ri baseline the correlation hedged multiplier <b>ri * ( 1 – ci ) </b>causes a reduction in capital allocation of 85% (5.5% to 0.8%) On the opposite end of the spectrum LQD is to be found with an amplification from 2.5% to 7.2%, a gain of nearly 290%, followed by TLT and HYG with a gain of 255% and 229% respectively.
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The impact on average capital allocation demonstrates the provident characteristic of the hedge multiplier <b>( 1 – ci )</b> through the strong emphasis foremost on bonds and secondly on “physical” assets to the detriment of stocks. The hedge fraction <b>1 / ( 1 + ci )</b> shows a similar, but less distinct effect, leaving more room for stocks to prospect risk premia.
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The effect of the correlation hedge is noticeable on the following two screenshots of monthly rankings for a 3 out of 12 asset selection. Based on “raw” return ri, the top three assets are: IYR, QQQ, EWJ. However, due to the correlation multiplied hedge <b>ri * ( 1 – ci )</b> the generalized momentum top three becomes: EWJ (3), GLD (7), VGK (5). Because of its negative correlation reading, GLD climbs from 7th to 2nd place. The opposite happens for IYR: as a result of its high correlation IYR drops from 1st to 4th place, out of reach for capital allocation. This occurs also for QQQ, which drops from 2nd to 6th place.
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwBQ2g-BjCRoNv58FL7-bi-C-0hpcsLHSgpdP2NdaywCJ2P5zJ1GBZ4zbu_We-IQsJRNGHPZhVHDpGI7J8nzzRWmQZqs66TDbvCpzKfGZ_04XRFr6g9fJtNhm3bBGbiC5JDVX_zcxQZ5c/s1600/GPM2M_Exploration.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="306" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwBQ2g-BjCRoNv58FL7-bi-C-0hpcsLHSgpdP2NdaywCJ2P5zJ1GBZ4zbu_We-IQsJRNGHPZhVHDpGI7J8nzzRWmQZqs66TDbvCpzKfGZ_04XRFr6g9fJtNhm3bBGbiC5JDVX_zcxQZ5c/s640/GPM2M_Exploration.png" width="640" /></a></div>
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The second screenshot shows the monthly rankings for the correlation fractioned hedge <b>ri / ( 1 + ci )</b>. Due to the strong amplication of its negative correlation reading, GLD (7) even climbs to 1st place, followed by IYR (1) and EWJ (3, so unchanged). High/positive correlations are downplayed too, but to a lesser extrent. IYR declines from 1st to 2nd place, still eligible for capital allocation. QQQ drops from 2nd to 5ft place and gets no capital allocated.
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhInZ-EesqWkn6LEjrFtNdmcqJK1QPPqdgd58epZ4xpVj7bWHgcSLG0EiHmV6N-LO0lBJPs7jtKXs3Y9weDzwd7Md6VC4GoNoug52woWut69jLGLP68aQ02nUqhN4Tcoks9nR0ajVjmXgs/s1600/GPM2F_Exploration.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="306" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhInZ-EesqWkn6LEjrFtNdmcqJK1QPPqdgd58epZ4xpVj7bWHgcSLG0EiHmV6N-LO0lBJPs7jtKXs3Y9weDzwd7Md6VC4GoNoug52woWut69jLGLP68aQ02nUqhN4Tcoks9nR0ajVjmXgs/s640/GPM2F_Exploration.png" width="640" /></a></div>
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The observed characteristics of the two hedge approaches present themselves in the following cumulative profit contribution table too.
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiONB1PssfqBtgpoQVcTDOjjelMtwkXQCn6lT8Y4eEV2cV-83kl4LlltbOd4BvBlWcReZigl3iOSm6mxt7vHztjYfoWWzf_jn6X18sBlZ2Ec3ZXzZ6SwBhh5A_ZJ631HiQGYBZU2vu8CNs/s1600/GPM0_CumulativeProfitContribution.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="90" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiONB1PssfqBtgpoQVcTDOjjelMtwkXQCn6lT8Y4eEV2cV-83kl4LlltbOd4BvBlWcReZigl3iOSm6mxt7vHztjYfoWWzf_jn6X18sBlZ2Ec3ZXzZ6SwBhh5A_ZJ631HiQGYBZU2vu8CNs/s640/GPM0_CumulativeProfitContribution.png" width="640" /></a></div>
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The difference in hedge effect are most clear when we review the relative changes in cumulative profit contributions as shown in the table below.
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDxWAHrp-_equk0O4jegWIPBRy3SvGhxGDBKH0_nJhgyS9L7ejMZ9K1-7h0x0HnHHDIcuJNHv9I26U-N7YWvyscgW_wq2woX0GTiEPeWFFkkCl4faPfnY7FSGNuSAHpzr7BjwQiFBQz1g/s1600/GPM0_ChangeCumulativeProfitContribution.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="92" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDxWAHrp-_equk0O4jegWIPBRy3SvGhxGDBKH0_nJhgyS9L7ejMZ9K1-7h0x0HnHHDIcuJNHv9I26U-N7YWvyscgW_wq2woX0GTiEPeWFFkkCl4faPfnY7FSGNuSAHpzr7BjwQiFBQz1g/s640/GPM0_ChangeCumulativeProfitContribution.png" width="640" /></a></div>
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For the hedge multiplier <b>( 1 – ci )</b>, EEM (18%), IWM (32%) and SPY (35%) form the lower-end extremes, while LQD (439%) and GSG (527%) are the higher-end extremes.
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The impact of the hedge is controlled by the (non-stationary) correlations of the respective “risky” assets. To illustrate the differences in correlations and their non-stationary nature, the following chart has in the upper price pane the equity curve of the monthly rebalanced risky N12 equal weighted (1/N per asset) portfolio (black) as well as the equity curves of three buy-and-hold investments: for SPY (blue), TLT (green) and GLD (orange “gold”) respectively. In the three subpanes the 12-month correlation coverage is plotted for the equal weighted N12 with SPY, TLT and GLD respectively.
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZ0FfAkKa6zXDUWvpKe989WLed105fIEvlGpaY3iZ6J5W1dEs7mu2S6sVD0VbEO-g7Bm3cS_fKaTOmWlP0Ssv8yY81oZxVzXbZv8SwyKr0az2DLd1qjU9nlPVLAcpJB_dQaJ7bbRE13H4/s1600/Correlation_EW-SPY-TLT-GLD.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="420" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZ0FfAkKa6zXDUWvpKe989WLed105fIEvlGpaY3iZ6J5W1dEs7mu2S6sVD0VbEO-g7Bm3cS_fKaTOmWlP0Ssv8yY81oZxVzXbZv8SwyKr0az2DLd1qjU9nlPVLAcpJB_dQaJ7bbRE13H4/s640/Correlation_EW-SPY-TLT-GLD.png" width="640" /></a></div>
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The chart above shows that an asset like SPY, which on average reflects a high correlation with the N12 risky universe (see the correlation graph in blue), generally will be substantially downplayed through the correlation hedge term. Hence SPY has a slim chance on selection for capital allocation. On the other hand, assets like TLT and GLD benefit especially during the periods when their correlations are negative, resulting in a hedge induced boost of their momentum rankings and thereby fatter chances on capital allocations.
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To wrap-up: Highly correlated assets are downplayed most pronounced by the correlation multiplier hedge <b>( 1 – ci )</b> and to a lesser extent by the correlation fraction hedge <b>1 / ( 1 + ci )</b>. For low correlated assets the effect is inverted. Both correlation hedges have about the same impact for assets with correlations in the -0.25 until +0.25 range. Joining the generalized momentum measure based on correlations and returns together with our multi-market breadth crash protection algorithm, leads to conservative capital allocations resulting in higher risk-adjusted performance.
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Special thanks to <a href="http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=1935527" target="_blank">Wouter Keller</a> for his support and contributions to this post.<br />
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The monthly asset selections for GPM's correlation multiplied momentum approach <b>ri * ( 1 - ci )</b> with high protection are shown below. For interpretation of the signals please refer to the explanation on the <a href="http://indexswingtrader.blogspot.com/p/strategy-signals.html" target="_blank">Strategy Signals page</a>. GPM can be tracked through <a href="https://allocatesmartly.com/keuning-kellers-generalized-protective-momentum/?aff=220" target="_blank">AllocateSmartly</a> too (affiliation).<br />
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<center>
<iframe height="450" src="https://docs.google.com/spreadsheets/d/1grBn8yZJqwFc8PF-wn1Plkb48qhYbnOwrikGVM6rZ9g/pubhtml?gid=1389397904&single=true&widget=true&headers=false" width="750"></iframe>
</center>
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<div style="text-align: center;">
<span style="font-family: inherit;"><i><span style="background-color: white;">NB! No guarantee whatsoever is given for the soundness of the strategy nor the proper functioning of the table nor for the accuracy of the signals. </span></i></span><i style="text-align: left;">Data may be delayed. </i><i style="font-family: inherit;"><span style="background-color: white;">Please do your own due diligence and use at your peril. The </span><b style="color: red;">Important Notice</b><span style="background-color: white;"> in the footer applies as well as the </span><a href="http://indexswingtrader.blogspot.com/p/disclaimer.html" style="text-decoration: none;" target="_blank">Disclaimer</a><span style="background-color: white;">.</span></i></div>
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<b>Disclosure</b>: long GLD, IYR, IEF.
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The full AmiBroker code for GPM is available upon <a href="mailto:trendxplorer@gmail.com?Subject=Request%20for%20GPM%20model%20in%20AmiBroker" target="_blank">request</a>. Interested parties are encouraged to support this blog with a donation.<br />
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<br />TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-14669730897833933892016-04-08T15:27:00.002-04:002023-07-29T12:14:49.123-04:00Introducing Protective Asset AllocationProtective Asset Allocation (PAA) is a new provident long only tactical investment strategy that combines a dual momentum approach with a vigorous capital preservation routine. The key elements of PAA are:<br />
<ul>
<li>dual momentum based timing and selection mechanism </li>
<li>innovative c(r)ash protection routine through protective momentum</li>
<li>support for separate “risk-on” and “risk-off" universes </li>
</ul>
Each of these building blocks will be explained quite comprehensively followed by a detailed comparative backtest covering 45 years (Dec. 1970 – Dec. 2015). But first be ready for a truckload of conceptual particularities ;-)<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmyyKGylZL1vEkvTku70LkbVBMlQSOS8wd85eTk0abVWldZ9TQ2BLLpqSU7rIOv6hp4ev-k89iAUenMfUsa0H92HN_QuuQLL2JL2G0BKpy5GjCyYf4oKiQ_wwpLkBBZ6iuW6Nodib_dqo/s1600/yay-world-with-lifebuoy.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="309" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmyyKGylZL1vEkvTku70LkbVBMlQSOS8wd85eTk0abVWldZ9TQ2BLLpqSU7rIOv6hp4ev-k89iAUenMfUsa0H92HN_QuuQLL2JL2G0BKpy5GjCyYf4oKiQ_wwpLkBBZ6iuW6Nodib_dqo/s320/yay-world-with-lifebuoy.jpg" width="320" /></a></div>
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In our quest for a yield neutral <i>absolute return performance</i> strategy Wouter Keller and I developed PAA (long only) with its innovative protective momentum approach for capital preservation in times of market turmoil. The interested reader might consider reading our <a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2759734" target="_blank">PAA-paper on SSRN</a> too. <br />
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PAA exploits the well-defined momentum phenomenon: the empirically observed tendency for asset prices to keep moving in the same direction. By applying PAA to a broad diversified global universe of sufficiently uncorrelated ETFs, PAA will auto-detect bull trends that emerge. Meanwhile protective momentum keeps guard over global market-breadth to adjust the “equity” : “cash” spread of the portfolio. And when trends shift, PAA catches the change and adapts, be it bullish or bearish. In doing so PAA is purely mechanical, so there is no need second guessing market conditions nor predicting trends. PAA is capable of delivering <i>absolute return performance</i> with 1-year-rolling-return win rates of more than 95% (R1yWin>0%) and 99% (R1yWin>-5%).<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibWpQC8weRc7iC0fonqwabYfIFLOJM_7Fwq79I20WwqC1Zs_qqp8HolXv_pTemsUAnw3-Gb9nMrSTx5Wzlbz7O2bgO1Fr02pNGTe9zSRBhtjU7mUm3Q7y2g92xCUjMAvVbCOGx-uhU9oc/s1600/PAA2T6_EquityKPI.png" style="margin-left: auto; margin-right: auto;"><img border="0" height="284" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibWpQC8weRc7iC0fonqwabYfIFLOJM_7Fwq79I20WwqC1Zs_qqp8HolXv_pTemsUAnw3-Gb9nMrSTx5Wzlbz7O2bgO1Fr02pNGTe9zSRBhtjU7mUm3Q7y2g92xCUjMAvVbCOGx-uhU9oc/s640/PAA2T6_EquityKPI.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Equity chart of the PAA strategy demonstrating high return/risk performance</td></tr>
</tbody></table>
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<a name='more'></a><br />
<b>PAA setup and recipe</b><br />
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Before clarifying the model’s principle ingredients, PAA is defined by the following mechanics:<br />
<ul>
<li>populate a diversified global “risk-on” equity universe with preferably 10 or more ETFs for harvesting risk premia</li>
<li>populate another universe consisting of “risk-off” treasury ETFs suitable as safe harbor for weathering market turmoil</li>
<li>sort both ETF universes on their peer performance (relative momentum)</li>
<li>assign capital proportional to the number of “risky” ETFs with non-positive momentum to the (best) safe harbor treasury ETF</li>
<li>assign remaining capital equally to the “risky” ETFs with positive momentum in the top selection</li>
<li>apply monthly portfolio reforms</li>
</ul>
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<b>SMA based filtering and selection</b><br />
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For weeding out downtrending assets an SMA based absolute momentum filter is applied while concurrently assets are scored by the very same SMA based momentum metric for selecting the top performers for capital allocation. So absolute and relative momentum are derived from one and the same momentum metric:<br />
<blockquote class="tr_bq">
<i><span style="font-family: "times" , "times new roman" , serif;"><span style="font-size: large;">MOM(L) =</span></span> </i>
<span style="font-size: large;">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow>
<mfrac>
<mrow>
<mi mathvariant="italic">p0</mi>
</mrow>
<mrow>
<mi mathvariant="italic">SMA(L)</mi>
</mrow>
</mfrac>
</mrow>
</semantics></math>
</span><span style="font-size: large;">
<i> - <span style="font-family: "times" , "times new roman" , serif;">1</span></i></span>
</blockquote>
For staying close to the customary vocabulary by expressing momentum as a function of time, eg. Antonacci’s 12 month momentum model (p0/p12-1), an extra price point needs to be added to the SMA formula to comprise the same return collection. Hence for MOM(12) the data range of the SMA becomes 12+1 which covers a full year of monthly return data, just like the 12 month rate of change approach.<br />
<br />
Point to note: in our formula the notation between SMA(L) and RET(L) with lookback (L) is harmonized, to such extent that i.e. SMA10 = SMA(9). Notice also risk-free return is not accounted for with regard to timing and selection. <br />
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<b>Protective Momentum</b><br />
<br />
The rationale behind PAA’s capital preservation routine is the global contagion effect of market crises. When turmoil hits the equities markets, risky assets tend to become highly correlated and start tanking in tandem. PAA assesses the risk of a market crisis by measuring multi-market breadth: the relative number of downtrending risky assets (MOM(L) ≤ 0). The more assets in distress, the higher the capital fraction that seeks shelter in a “safety asset”: a short- or mid-term treasury ETF. For this assessment PAA has three protection levels: low, medium and high. These c(r)ash protection levels are controlled through a “protection factor” (pf), which is an adjustable parameter in our Bond Fraction (BF) formula for an N-size “risk-on” universe:<br />
<blockquote class="tr_bq">
<span style="font-family: "times" , "times new roman" , serif; font-size: large;"><i>BF =</i></span>
<span style="font-size: large;">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow>
<mfrac>
<mrow>
<munderover>
<mo>∑</mo>
<!--<mo> </mo>-->
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>N</mn>
</mrow>
</munderover>
<msub>
<mi mathvariant="italic">MOM(L)</mi>
<mn>i</mn>
</msub>
<mo> </mo>
<mo>≤</mo>
<mo> </mo>
<mi mathvariant="italic">0</mi>
</mrow>
<mrow>
<mi mathvariant="italic">N</mi>
<mo> </mo>
<mo>-</mo>
<mo> </mo>
<mi mathvariant="italic">pf</mi>
<mo>·</mo>
<mfrac>
<mrow>
<mi mathvariant="italic">N</mi>
</mrow>
<mrow>
<mi mathvariant="italic">4</mi>
</mrow>
</mfrac>
</mrow>
</mfrac>
</mrow>
</semantics>
</math>
</span>
<span style="font-family: "times" , "times new roman" , serif; font-size: large;"><i>, with 0% ≤ BF% ≤ 100%
</i></span>
</blockquote>
At low protection level the protection factor pf is set at 0. The full “risk-on” universe is monitored for non-positive momentum. For each and every risky asset with non-positive momentum, an equal part (1/N) is allocated to the “safe” treasury fund, which allocation equals the fraction of assets with non-positive momentum relative to the full size of the “risk-on” universe (with pf=0, the denominator of the BF formula reads: N). The capital fraction for the “safe” treasury fund reaches 100% when none of the risky assets has positive momentum.<br />
<br />
With the protection level set to medium the protection factor is increased to 1: like before, all risky assets are under scrutiny, but full capital allocation to the safe haven is reached earlier: the “safe” treasury allocation equals the fraction of assets with non-positive momentum relative to three-quarters of the universe size (with pf=1, the denominator of the BF formula reads: <span style="font-size: small;">¾</span>N). Put differently, in case the number of risky assets with positive momentum becomes 25% or less, total capital goes to the “safety asset”. <br />
<br />
At high protection level all assets in the risky universe are examined for non-positive momentum, but the pace of the c(r)ash protection build up is quite vigorous: the allocation to the “safe” treasury asset equals the fraction of assets with non-positive momentum relative to half of the size of the risky universe. This is achieved by a protection factor of 2, so the denominator of the BF formula reads <span style="font-size: small;">½</span>N.<br />
<br />
To crystallize PAA’s c(r)ash protection routine, for each protection level the below table shows the fraction of capital allocated to the “safe” harbor treasury applied for a universe with 12 risky assets.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYlaDpoMUM00IISE9k3xk1Dk316D1jBbS2yHGQI3hQkTWBCHoqyfj0NRelZe8kUU9Np6Zr6WZ649x9RYDnIlIPjlqTcscc-H0sH059EMmp3MPsaP8yfkVIqQ5VOCKL87OdM6xw4TPy-Pg/s1600/N12+Protection+Factor+Table.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="73" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYlaDpoMUM00IISE9k3xk1Dk316D1jBbS2yHGQI3hQkTWBCHoqyfj0NRelZe8kUU9Np6Zr6WZ649x9RYDnIlIPjlqTcscc-H0sH059EMmp3MPsaP8yfkVIqQ5VOCKL87OdM6xw4TPy-Pg/s640/N12+Protection+Factor+Table.png" width="640" /></a></div>
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<b>Dual universe support</b><br />
<br />
Commonly in absolute momentum strategies a single “safety asset” like SHY, TLT or AGG is used for storm sheltering when the absolute momentum filter kicks in. However, a bet on long-term treasuries might prove itself hazardous when the proverbial tide goes out for global equities in a rising rate environment. On the other hand, the deployment of short-term treasuries might prohibit capturing capital gains on longer maturity T-Notes or T-Bonds as rates fall. Hence PAA supports multi treasury universes too, like the SHY/IEF combination, as the “safety asset” for mitigating yield risk while at the same time prospecting improved risk adjusted performance as well as attaining <i>absolute return performance</i> (explained below). With multiple treasury funds to choose from, capital is allocated to the treasury asset with the highest relative momentum score irrespective of the sign. <br />
<br />
<br />
<b>Backtests</b><br />
<br />
As stated in our PAA paper the mechanics of the model are inspired by the work of both <a href="http://mebfaber.com/timing-model/" target="_blank">Faber</a> and <a href="http://www.dualmomentum.net/" target="_blank">Antonacci</a>. Hence our choice for an SMA (Faber) based momentum formula with a lookback of 12 months (Antonacci) that is used for calculating both absolute momentum (timing) as well as relative momentum (selection).<br />
<br />
The PAA model will be backtested from Dec 1970 – Dec 2015 (45 years) on monthly total return data (see <a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2759734" target="_blank">paper</a> for data construction). The universe of choice is a global diversified multi-asset universe consisting of proxies for 12 so called “risky” ETFs: SPY, QQQ, IWM (US equities: S&P500, Nasdaq100 and Russell2000 Small Cap), VGK, EWJ (Developed International Market equities: Europe and Japan), EEM (Emerging Market equities), IYR, GSG, GLD (Alternatives: REIT, Commodities, Gold), HYG, LQD and TLT (US High Yield bonds, US Investment Grade Corporate bonds and Long Term US Treasuries). The broadness of the universe makes it suitable for harvesting risk premia during different economical regimes. <br />
<br />
<b>NB!</b> <i>Results in this post are derived from synthetic data, do not reflect trading costs, slippage nor taxes and are purely hypothetical. The Disclaimer applies.</i><br />
<br />
<br />
<b>GTAA* performance</b><br />
<br />
For the purpose of a reference point the concept of Meb Faber’s famous Global Tactical Asset Allocation model (GTAA) is used (see his 2013 updated <a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=962461" target="_blank">Quantitative Approach paper</a>): allocate capital in equal portions to all assets or to the top selection of a universe that are above their long-term SMA and invest the remainder in a safe haven treasury fund like SHY with monthly portfolio reforms. <br />
<br />
(*) For this replication – and different from Faber’s approach- our MOM(12) formula is deployed both for absolute and relative momentum (hence the term “Dual” in our paper). The performance metrics of our take on GTAA are summarized in the below table. <br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjltQHcECqZDdI8dGqS6kxHyq-SGks9kjYOP7X0xnZOE0LhiDBpqHxyZ9_9aB8pLCpVosW9zogsljPJ4tNtRoLXKrCb7fMvQ-prbEMwhx-kouDIjrb6i39MLPQUWKivd9vODWpHDyIAybk/s1600/GTAA_34612.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="80" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjltQHcECqZDdI8dGqS6kxHyq-SGks9kjYOP7X0xnZOE0LhiDBpqHxyZ9_9aB8pLCpVosW9zogsljPJ4tNtRoLXKrCb7fMvQ-prbEMwhx-kouDIjrb6i39MLPQUWKivd9vODWpHDyIAybk/s640/GTAA_34612.png" width="640" /></a></div>
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With Top=12 capital may be divided in equal portions over all assets in the universe provided each assets latest price resides above its long term SMA. As such with N=Top=12 capital allocation is only governed by timing. The capital fraction assigned to the safe harbor fund (here: SHY) is equal to the number of assets below their SMAs relative to the total number of assets in the universe. <br />
<br />
With Top=6, 4, 3 next to timing (trend filtering) selection (relative strength) features too, assigning capital exclusively to the top performing “risky” assets, while top assets get capital assigned in equal portions, but only if they are above their long-term SMA, otherwise that portion of the portfolio is moved to a “safety asset” (here again: SHY). <br />
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The table demonstrates the effect of lower to higher concentrated portfolios: the high density Top=3 portfolios yields higher return R than the lowest density portfolio Top=12, but at the cost of higher volatility V, worse drawdown D and lower Sharpe SR (R/V) and MAR (R/D) ratios. <br />
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<i><b>Absolute return performance</b></i><br />
<br />
Despite the Top=12 scenario is getting really close, none of the GTAA scenarios attains <i>absolute return performance</i> as defined in our paper: a 95% win rate of all rolling 1-year returns above 0% (R1yWin>0%) combined with a 99% win rate of all rolling 1-year returns above -5% (R1yWin>-5%). To clarify the metric: the rolling 1-year return reflects the cumulative portfolio return over a period of 12 months, where the observation “window” moves month-by-month as time passes. Since our data set contains monthly total return closing prices, our 45 year backtest period holds (45-1)x12+1=529 rolling 1-year observation points (44 instead of 45 because of the initial year). So to satisfy our <i>absolute return performance</i> condition the rolling 1-year return must be above 0% for at least 95% of all 529 (=503) monthly observations while at the same time the rolling 1-year return needs to stay above the -5% watermark for a minimum of 99% of all a monthly observations, so for 524 or more months. <br />
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The below chart of the rolling 1-year return for the GTAA’s Top=3 scenario illustrates the application of the combined rolling 1-year-return requirement. The <i>absolute return performance</i> levels are the horizontal lines at 0% (solid black) and -5% (dotted red) with the metrics denoted by the two R1yWin values on the right side of the chart’s title section. Note the required win rates are not satisfied for this scenario.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsIpYZrz9ST9Xf7a3vn2BQnxn1Z9N0dolzkFdQbhUNCinrlOKHf5q3jS9sRtoHVKJ-MoRBJkStHooiTOrNBYQhlmQup1KKn4hT-inNJY9ipl-Algvj7nB9zDJ8weem0wQqLupOw3ZpDdo/s1600/GTAA3_RR.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="322" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsIpYZrz9ST9Xf7a3vn2BQnxn1Z9N0dolzkFdQbhUNCinrlOKHf5q3jS9sRtoHVKJ-MoRBJkStHooiTOrNBYQhlmQup1KKn4hT-inNJY9ipl-Algvj7nB9zDJ8weem0wQqLupOw3ZpDdo/s640/GTAA3_RR.PNG" width="640" /></a></div>
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<br />
<b>PAA performance</b><br />
<br />
Contrary to the GTAA safe harbor capital assignment, which is dependent on the number of Top assets not above their long-term SMAs, instead PAA with its multi-market breadth driven c(r)ash protection routine allocates capital to the safe harbor asset based on market-breadth for the full universe, so independently from the Top size (see again the capital fraction table earlier in this post). <br />
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The following table shows the impact of protective momentum for PAA with the protection level set to low (pf=0, denoted PAA0) for the same model scenarios GTAA was backtested for above.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWH4SHEZmnRC-MZZNOZ7_8PCwip_pzC0W-PFTqirBpCctneyfivy56ZJ-2SukUpAkLd82jrZuoTRttAEGWFXoFG2pls-yVvikP13DLOQqST_MkNXdgIKmI_5wVyAupvi8ccN5go9UO6vY/s1600/PAA0_34612.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="72" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWH4SHEZmnRC-MZZNOZ7_8PCwip_pzC0W-PFTqirBpCctneyfivy56ZJ-2SukUpAkLd82jrZuoTRttAEGWFXoFG2pls-yVvikP13DLOQqST_MkNXdgIKmI_5wVyAupvi8ccN5go9UO6vY/s640/PAA0_34612.png" width="640" /></a></div>
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Note that PAA0’s Top=12 scenario at low protection level is equal to GTAA with Top=12, so the reported results are equal. As stated, for the Top=6, 4, 3 scenarios the difference lies in the safe harbor capital allocation. While GTAA only checks timing for its top assets, PAA0 does so for its full universe. Albeit for every top scenario PAA0 realizes lower return R than GTAA (each roughly 1% lower), PAA0 reduces volatility V and drawdown D considerably. This holds true for risk adjusted return too (see SR and MAR). However, despite the improved risk adjusted returns, for none of the scenarios with PAA at low protection <i>absolute return performance</i> is reached. The R1yWin rates falter just below the required 95% and 99% levels.<br />
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As the below table shows, when the protection level is increased to high (pf=2, denoted PAA2), PAA2 does attain <i>absolute return performance</i> for three of the four scenarios (Win rates noted bold): Top=12, 6, 3 with scenario Top=4 barely missing its mark.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCNaPBOPR6TsXsvq6vQw4Z7JIUcwo0FbOV7S60PVD8-mdGGdT7T99XJgY2UvdGq6fo9SAhXt6iklFRrAa3feuHkX9F87PBL3_wWJ7UZ7n9jb6FW8rIiwqwiIG5-ycVzyLlTJNZTS0sqrg/s1600/PAA2_34612.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="72" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCNaPBOPR6TsXsvq6vQw4Z7JIUcwo0FbOV7S60PVD8-mdGGdT7T99XJgY2UvdGq6fo9SAhXt6iklFRrAa3feuHkX9F87PBL3_wWJ7UZ7n9jb6FW8rIiwqwiIG5-ycVzyLlTJNZTS0sqrg/s640/PAA2_34612.png" width="640" /></a></div>
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Compared to PAA0 risk adjusted performance is improved with PAA2, but once again at the cost of return R (0.8%-1.6%). With regard to optimal risk adjusted performance the Top=6 scenario looks appealing considering it achieves the highest MAR and R1yWin>-5% (tie) and second best Sharpe and R1yWin>0% readings. <br />
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<b>“Crisis alpha”</b><br />
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For the N12 universe at hand, with high protection enabled PAA invests on average over 50% in “cash” (see sub-pane of equity chart below). Although capital is well preserved with a short-term treasury asset like SHY, this also constitutes a drag on portfolio performance. However, swapping SHY for i.e. TLT introduces higher duration risk and goes along with more volatility and drawdown. Instead, the intermediate treasury fund IEF appears to be the trade-off as a replacement for cash. Still, the deployment of an alternating “safety asset” proved to be the best choice in risk adjusted terms. Thus PAA is less vulnerable to rate hikes, while at the same time the prospect to increase crisis alpha – higher risk adjusted performance during market crises - is not forfeited. With multiple safe harbors for sheltering on alert, capital is allocated to the treasury asset with the highest relative momentum score irrespective of the sign. For more on “crisis alpha” check Nathan Faber's winning NAAIM Wagner Award paper <a href="https://blog.thinknewfound.com/2015/05/search-crisis-alpha-weathering-storm-using-relative-momentum/" target="_blank"><i>The Search for Crisis Alpha: Weathering the Storm Using Relative Momentum</i></a>.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCdZcJeuh00ddmljH-8qPHuie6MxhWRKtw7xYidFZ0uLqTciRCXX7wE_qRhn9FxNC49NGEv3T4wGISFgEHAqRUqSL7r7cCMl4v4ULOb6kczspnP6DfsCGyLJuiaSV5ddiGhRXbARZ_Wr0/s1600/PAA2T6_DUAL.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="116" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCdZcJeuh00ddmljH-8qPHuie6MxhWRKtw7xYidFZ0uLqTciRCXX7wE_qRhn9FxNC49NGEv3T4wGISFgEHAqRUqSL7r7cCMl4v4ULOb6kczspnP6DfsCGyLJuiaSV5ddiGhRXbARZ_Wr0/s640/PAA2T6_DUAL.png" width="640" /></a></div>
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The above table shows the performance break down of PAA2 with Top=6 sorted on R1yWin(>0%). Regarding <i>absolute return performance</i> the SHY/IEF pair manages to combine the highest Win rates with near top R, second best SR plus MAR and third best V and D. Noteworthy is the impressive risk adjusted performance registered by both the single IEF and the single SHY scenarios too. <br />
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(*) For demonstration purposes three scenarios with TLT are listed too. Deployment of TLT as a storm shelter implies TLT features both in the “risk-on” universe as well as the “risk-off” universe. Notice the high drawdowns for each of these combinations along with elevated volatility levels, proving the point that TLT nor its combinations may regarded favorable for storm sheltering. Furthermore the return of IEF and its combinations is equally good or better along with lower volatility and left tail risk. <br />
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<b>Comparison line up</b><br />
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To conclude this introduction of protective momentum first PAA2 with Top=6 is compared to three other strategies: <br />
<ul>
<li>EW (1/N for N12 equities universe, monthly rebalancing), </li>
<li>SPY (buy and hold), </li>
<li>60/40 (SPY/IEF, monthly rebalancing). </li>
</ul>
The PAA2 results are for the N12 universe with SHY/IEF to pick as “safety asset”. Next some detailed charts for the PAA2 scenario at hand are presented.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvXLqrn-2tk-Alh96F6u47trd5IiXx9X2tOaifzgmO5X1u6Zrgc4olKMo8e8Z7J0jUg9AkynvsCuzcgDbyRon-PZU5tdr4jX7Ju0_CM5OK1QQMWZvlcPFN4x3HAFtQabJOjUbQ3LTt-Oc/s1600/N12_EquityComparison.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="448" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvXLqrn-2tk-Alh96F6u47trd5IiXx9X2tOaifzgmO5X1u6Zrgc4olKMo8e8Z7J0jUg9AkynvsCuzcgDbyRon-PZU5tdr4jX7Ju0_CM5OK1QQMWZvlcPFN4x3HAFtQabJOjUbQ3LTt-Oc/s640/N12_EquityComparison.png" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjLGzmTEOJawEhg3-QS_7iEIpplYfW7Sex4XAFAnn-b5r5d1kfEXzF_aI1ZlKTPHxiWpihWGGjZLh92brNMPaHABjm3OQ2zlQYNgiKZ_AbRkD3FMXBIv95k24NPNVwxw91rmQMEW3N-ck/s1600/N12_Comparison.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="88" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjLGzmTEOJawEhg3-QS_7iEIpplYfW7Sex4XAFAnn-b5r5d1kfEXzF_aI1ZlKTPHxiWpihWGGjZLh92brNMPaHABjm3OQ2zlQYNgiKZ_AbRkD3FMXBIv95k24NPNVwxw91rmQMEW3N-ck/s640/N12_Comparison.png" width="640" /></a></div>
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The chart depicts (in semi-log scale) the equity curves of the four strategies in “wet paint” fashion to emphasize depth and duration of drawdowns. For PAA2 the chart’s subpane shows the capital allocation for the safety asset: SHY or IEF. The table holds the performance metrics of the four charted strategies.<br />
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PAA2 paints a smooth curve with shallow and constrained drawdown periods. Actually, time spend in drawdown is only 48.70% with a longest drawdown period of 19 months against SPY’s 68.52% and 74 months. Return is higher not only in risk adjusted terms, but also in absolute terms thanks to low volatility and drawdown readings. This demonstrates the key benefit of protective momentum: the low-risk profile keeps drawdowns in check during times of market turmoil. <br />
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Over recent years the performance of PAA2 lags the 60/40 benchmark as well as SPY. The lower return reflects the “insurance premium” due for PAA2’s market-breadth capital protection which typically leads to outperformance during bear markets and underperformance in prolonged bull. <br />
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<b>Performance charts</b><br />
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To conclude this introduction of PAA some detailed charts offer more perspective into PAA2’s performance with Top=6 selection.<br />
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Annual returns:<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJ4GyvSlwZbiI0AQj29tKvPhKSz4QVIuSWSkucYfcIsva2Tvv5zH0sI4IWhbB0aYw0UU_mQy8o_g6KJV32TEqQnrCec_IuTEo2fSAD0oauKbLN7DePjISkPZkGXF9kl8mfalu-hQocZ5Y/s1600/PAA2T6_YearlyReturns.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="284" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJ4GyvSlwZbiI0AQj29tKvPhKSz4QVIuSWSkucYfcIsva2Tvv5zH0sI4IWhbB0aYw0UU_mQy8o_g6KJV32TEqQnrCec_IuTEo2fSAD0oauKbLN7DePjISkPZkGXF9kl8mfalu-hQocZ5Y/s640/PAA2T6_YearlyReturns.png" width="640" /></a></div>
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Profit contribution:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2Qofbj6dld3hRYPU4md0puX2VBOr-OqMIl_As5QTsn0Ggs6U41Mb75Drue-7ZXq37lQ-ibOHabLYcbH7V0_Sm1LvKpj5wB-cCPsNDw0ok6O0J8xQG07yXsOb3PwlDvEO5W22Z57bK5ac/s1600/PAA2T6_ProfitContribution.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="284" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2Qofbj6dld3hRYPU4md0puX2VBOr-OqMIl_As5QTsn0Ggs6U41Mb75Drue-7ZXq37lQ-ibOHabLYcbH7V0_Sm1LvKpj5wB-cCPsNDw0ok6O0J8xQG07yXsOb3PwlDvEO5W22Z57bK5ac/s640/PAA2T6_ProfitContribution.png" width="640" /></a></div>
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Capital allocation:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbP1F0lT0GnU64TCL-PdG6rhw35nwKPh5YCBu-aXsp1CdwHzIu6UuI_mZrWNQpBCH-Nr4O6HpEZ0tYowd6JQm1Kp5GF714mle4ejBBlqJQLBDuG4DetZBvsxsUObz4YGaJdQAsF63YqiE/s1600/PAA2T6_CapitalAllocation.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="284" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbP1F0lT0GnU64TCL-PdG6rhw35nwKPh5YCBu-aXsp1CdwHzIu6UuI_mZrWNQpBCH-Nr4O6HpEZ0tYowd6JQm1Kp5GF714mle4ejBBlqJQLBDuG4DetZBvsxsUObz4YGaJdQAsF63YqiE/s640/PAA2T6_CapitalAllocation.png" width="640" /></a></div>
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Drawdown:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipqhZB17f2LUDp8Q1XIfG7kd8E0TxVxWVtq9DWiYynFW90KozLIlGgDvw_MHgLHfGxBQKdQt7E-pZzzgEXG9p_RYCgtp1qKPOicHDb06KdYOn-iHq-H56xzCRKdtJEH4qqKoqSpX5Z49Q/s1600/PAA2T6_DrawDown.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="284" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipqhZB17f2LUDp8Q1XIfG7kd8E0TxVxWVtq9DWiYynFW90KozLIlGgDvw_MHgLHfGxBQKdQt7E-pZzzgEXG9p_RYCgtp1qKPOicHDb06KdYOn-iHq-H56xzCRKdtJEH4qqKoqSpX5Z49Q/s640/PAA2T6_DrawDown.png" width="640" /></a></div>
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Monthly return distribution:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrZZnQj2JQFINM0NEFDdoOKTMjpTK3OKiUtHQaLC5b9HYmI-ZlEO5k5phZlezdeIgipRoDVpOR4Ifnm4O5aC34YlMAxKKiFdE_XRlvXXy4Q4A7lAHr6n-3RvPqNNhov7G4isjDT1VA-Jw/s1600/PAA2T6_MonthlyReturns.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="284" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrZZnQj2JQFINM0NEFDdoOKTMjpTK3OKiUtHQaLC5b9HYmI-ZlEO5k5phZlezdeIgipRoDVpOR4Ifnm4O5aC34YlMAxKKiFdE_XRlvXXy4Q4A7lAHr6n-3RvPqNNhov7G4isjDT1VA-Jw/s640/PAA2T6_MonthlyReturns.png" width="640" /></a></div>
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Rolling 1-year-returns:<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOHCh3CLvuRRYdKcqgA8kJ28o5yXTb831g9pdkQVL84YA6VdHHrwEjD9GLs-Rdo4H9nTQ3CbKI6rOBFh7HAqKGK2CroR7meLFEa8yvMj_GIkqSbTXMItV41pkZ0oAeMx_6A-TxXWGkzoQ/s1600/PAA2T6_RollingReturns.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="284" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOHCh3CLvuRRYdKcqgA8kJ28o5yXTb831g9pdkQVL84YA6VdHHrwEjD9GLs-Rdo4H9nTQ3CbKI6rOBFh7HAqKGK2CroR7meLFEa8yvMj_GIkqSbTXMItV41pkZ0oAeMx_6A-TxXWGkzoQ/s640/PAA2T6_RollingReturns.png" width="640" /></a></div>
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Rolling 1-year-return confidence channel:<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoE7ZeaB96npYcTuzzd5MmSNLuB7qOOuRuab-GCNJdbSf6dBSPDN_bBCBC4z8pjqI_A6INn6R5Ie3Ntdy7Ey-5-jcYBSkJNMhYpZmckGmZ_RKZo6vmCFfqVPJ-BqmYHwfViF5neNlPkxg/s1600/PAA2T6_RollingReturnsConfidenceChannel.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="284" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoE7ZeaB96npYcTuzzd5MmSNLuB7qOOuRuab-GCNJdbSf6dBSPDN_bBCBC4z8pjqI_A6INn6R5Ie3Ntdy7Ey-5-jcYBSkJNMhYpZmckGmZ_RKZo6vmCFfqVPJ-BqmYHwfViF5neNlPkxg/s640/PAA2T6_RollingReturnsConfidenceChannel.png" width="640" /></a></div>
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<br />
<b>“Real time” strategy signals</b><br />
<br />
Google Sheets allows for monitoring the chosen PAA strategy after the close of the month. The Gsheet shows the one year history of the Top=6 selection, the number of assets with positive momentum, the bond fraction and the rolling 1-year performance (scroll right). Below the historical table, the current selection is presented with their respective position sizes: see the two rows above the yellow warning box. Point to note: only with a BF < 100% capital is allocated to the top selection, otherwise all capital goes to the best safety asset. For interpretation of the signals please refer to the explanation on the <a href="http://indexswingtrader.blogspot.com/p/strategy-signals.html" target="_blank">Strategy Signals page</a>.<br />
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<!--<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBDX13bZUGI8rgEeDFC1ev2M-wGL_LvzlHA-b2Eotm_z-wPHE16cHP9bIjyuiOgXAzZ6RKhXLKmZ7vHy8i5Bsrs3qlhmDwIC4jObW-kxe8pbdkU0erQ3zciscMalf5_ygx3BdAb7Frv08/s1600/PAA2_SignalsForApril2016.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="252" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBDX13bZUGI8rgEeDFC1ev2M-wGL_LvzlHA-b2Eotm_z-wPHE16cHP9bIjyuiOgXAzZ6RKhXLKmZ7vHy8i5Bsrs3qlhmDwIC4jObW-kxe8pbdkU0erQ3zciscMalf5_ygx3BdAb7Frv08/s640/PAA2_SignalsForApril2016.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Gsheet with PAA2 signals for April after the close of March, 2016. </td></tr>
</tbody></table>-->
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<center>
<iframe height="450" src="https://docs.google.com/spreadsheets/d/1iZxd3MzAG7YMdYbRT5T9vv4lgd0ePQ2z78Kn8hPC65I/pubhtml?gid=1389397904&single=true&widget=true&headers=false" width="750"></iframe>
<br /><br />
<i style="color: #222222; text-align: center;"><span style="font-family: inherit;"><span style="background-color: white;">NB! No guarantee whatsoever is given for the soundness of the strategy nor the proper functioning of the table nor for the accuracy of the signals. </span></span></i><i style="text-align: left;">Data may be delayed. </i><i style="color: #222222;"><span style="font-family: inherit;"><span style="background-color: white;">Please do your own due diligence and use at your peril. The </span><b style="color: red;">Important Notice</b><span style="background-color: white;"> in the footer applies as well as the </span><a href="http://indexswingtrader.blogspot.com/p/disclaimer.html" style="color: #888888; text-decoration: none;" target="_blank">Disclaimer</a><span style="background-color: white;">.</span></span></i></center>
<br />
<br />
<b>Final remarks</b><br />
<ul>
<li>As stated in our <a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2759734" target="_blank">paper</a>, we consider the multi-market breadth approach for determining the safety asset’s capital fraction as the main innovation of Protective Asset Allocation. The routine as such may be regarded as a safety module which can be applied easily to general momentum models with volatility and/or correlation effects, like Keller’s EAA (see <a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2543979" target="_blank">paper</a> and <a href="http://indexswingtrader.blogspot.com/2015/01/a-primer-on-elastic-asset-allocation.html" target="_blank">primer</a>).</li>
<li><span style="font-size: small;"><span style="font-family: inherit;">PAA is also featured on <a href="https://allocatesmartly.com/?aff=220" target="_blank">AllocateSmartly.com</a>. By signing up through this <a href="https://allocatesmartly.com/?aff=220" target="_blank">link</a>, you support my work.</span></span> </li>
</ul>
<br />
<b>Disclosure</b>: long IEF.
<br />
<br />
The full AmiBroker code for PAA is available upon <a href="mailto:trendxplorer@gmail.com?Subject=Request%20for%20PAA%20model%20in%20AmiBroker" target="_blank">request</a>. Interested parties are encouraged to support this blog with a donation.<br />
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<br />TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-83094717100166866082016-02-22T14:54:00.001-05:002016-04-13T09:29:07.160-04:00Portfolio Level Monte Carlo AnalysisFollowing up on the prior <a href="http://indexswingtrader.blogspot.com/2015/09/strategy-stress-testing-la-monaco.html">Strategy Stress Testing</a> post: with the release of AmiBroker version 6.10.0 a new Monte Carlo mode has come available for simulating portfolio equity changes. Instead of randomizing the trade list, the new mode uses bar-per-bar percent equity changes at the portfolio level to generate permutations. Consequently cross-sectional correlations are preserved. According to AmiBroker’s developer, the new method is perfectly fine for multiple overlapped positions, provided the number of bar-per-bar equity changes is sufficiently large (> 100).<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJ-WOscNm8efytfofdyKZT1J43UwCPdEWBwsLFgzay3WmOXzQ56EaPxtiVHn0UXgWYFa8MjEhpBJ70iFmg0IZMOKa-Co9EXL1bnh8qZm6k1Hye3BvzowBAgZ35MsHHXewdRNXi5glYpk8/s1600/dreamstime_dicetower.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJ-WOscNm8efytfofdyKZT1J43UwCPdEWBwsLFgzay3WmOXzQ56EaPxtiVHn0UXgWYFa8MjEhpBJ70iFmg0IZMOKa-Co9EXL1bnh8qZm6k1Hye3BvzowBAgZ35MsHHXewdRNXi5glYpk8/s320/dreamstime_dicetower.jpg" width="213" /></a></div>
<br />
The portfolio level Monte Carlo simulation is controlled by a couple of new SetOption fields which allow for AFL implementation right into the strategy code:<br />
<script class="brush: js" type="syntaxhighlighter"><![CDATA[
// --- MonteCarloPortfolioAnalysis.afl ---
MCS = ParamToggle( "Enable Monte Carlo Simulation?", "No|Yes", 0 );
if ( MCS )
{
// settings for portfolio level analysis with multiple simultaneous or overlapping positions
SetOption( "MCEnable" , 1 ); // value == 1 enables MC only in portfolio backtests (default)
SetOption( "MCRuns" , 1000000 );
SetOption( "MCUseEquityChanges" , 1 ); // use equity changes for portfolio level analysis
SetOption( "MCChartEquityScale" , 1 ); // 1 for log scale, 0 for linear scale
SetOption( "MCLogScaleFinalEquity", 1 ); // 1 for log scale, 0 for linear scale
SetOption( "MCLogScaleDrawdown" , 1 ); // 1 for log scale, 0 for linear scale
SetOption( "MCNegativeDrawdown" , 0 ); // 1 - use negative numbers for drawdown (reverse drawdown CDF)
}
]]></script>
The Monte Carlo Portfolio Analysis code is suitable for copy/paste inside a rotational model like the familair Simple GMR code attached to the prior Monte Carlo post. However, my preferred method is to save the code as a separate file for inclusion in strategy models by calling the <a href="http://www.amibroker.com/guide/afl/_include.html" target="_blank">#include command</a>:
<br />
<a name='more'></a><script class="brush: js" type="syntaxhighlighter"><![CDATA[
// --- monte carlo analysis ---
#include <MonteCarloPortfolioAnalysis.afl>
]]></script>
The update code for Simple GMR with the #include call implemented is available on the <a href="https://drive.google.com/folderview?id=0BwovO-kzwAfgMTdZbU5iMDlnSTQ&usp=sharing" target="_blank">Google drive</a> folder connected to this post. There you will also find the Monte Carlo Portfolio Analysis code. Be sure to save the latter code in AmiBroker's dedicated Include folder otherwise the #include call will not function: <span style="color: blue;"><b>AmiBroker > Formulas > Include</b></span><br />
<br />
The Monte Carlo analysis is turned on/off by toggling the "Enable Monte Carlo Simulation?" switch through the Parameter window (equalizer icon). With the switch at "Yes" the backtest will take a little longer to finish, since your AMD/Intel cpu has to run the 1,000,000 simulations as declared in the code (see above). The Monte Carlo CDF charts are then available through the Report icon.<br />
<br />
Point to note: the #include code will override the appropriate settings made on the Monte Carlo tab of the Backtester settings (wrench icon).<br />
<br />
Enjoy!TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-54650905620890737262016-02-21T06:30:00.000-05:002016-02-21T06:35:49.337-05:00Lab Announcement<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1RXc8Zn4RS-J12wwTVEypdb9ylTgvLVEWJ9MOL5OyK-iyQ5CAuhI40-AnKSj0WDUFccC2eA-QvkdfH5FkUUWY2uA3WcQfN_U7u3TEkMYd0rMsImiei17qLGprZ_zfm8CLXuRVeD56Bh8/s1600/Fotolia_ChemLab.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1RXc8Zn4RS-J12wwTVEypdb9ylTgvLVEWJ9MOL5OyK-iyQ5CAuhI40-AnKSj0WDUFccC2eA-QvkdfH5FkUUWY2uA3WcQfN_U7u3TEkMYd0rMsImiei17qLGprZ_zfm8CLXuRVeD56Bh8/s400/Fotolia_ChemLab.jpg" width="400" /></a></div>
<br />
After spending ages on research a couple of exciting new developments will be published shorty:<br />
<ul>
<li>Portfolio level Monte Carlo analysis</li>
<li>DIY global multi asset universe with 21 ETF-proxies covering a history of 45+ years</li>
<li>“One-Click” export from Excel to multiple csv (in R)</li>
<li>Enhanced c(r)ash protection routine for tactical investment strategies</li>
<li>Dual universe support for differentiation of risk-on and risk-off assets</li>
<li>Surveying volatility driven dynamic lookback indicators
</li>
</ul>
<a name='more'></a>Stay tuned!<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_Ruf0_TPqZ5GlCN2CTqzQdmiPWjbGmONUsE9EwCH4rFZBIyHbMSAajRcEungUcMw9NuWjKIE3GR17FcCtXal3c-F2KeJL74DWAz1kLV2G0EmdqaC6VyJSwplG6oQM-2KhoXHW7TMiKcc/s1600/GTAA_N5_SHY_Equity.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="322" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_Ruf0_TPqZ5GlCN2CTqzQdmiPWjbGmONUsE9EwCH4rFZBIyHbMSAajRcEungUcMw9NuWjKIE3GR17FcCtXal3c-F2KeJL74DWAz1kLV2G0EmdqaC6VyJSwplG6oQM-2KhoXHW7TMiKcc/s640/GTAA_N5_SHY_Equity.PNG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Backtest of Mebane Faber's famous GTAA over 1971-2015 with proxies for SPY, EFA, IYR, GSG, IEF with SHY as "cash"</td></tr>
</tbody></table>
<div class="MsoNormal">
<span style="font-size: 11.0pt;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_R374zFb6zPU3PMDE3qqAsvEuuIXPk0nTl5le9vu_lCdH8VCt55qBXmBwuQgTGRGaD6Olr5hLJkqcTT68XWHOGrctbseY7OcmWHYYNTduhiOD8CtPS0U-jdYyAG1pJ2MEzSzPVlJbVFk/s1600/GTAA_N5_SHY_MAD.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="322" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_R374zFb6zPU3PMDE3qqAsvEuuIXPk0nTl5le9vu_lCdH8VCt55qBXmBwuQgTGRGaD6Olr5hLJkqcTT68XWHOGrctbseY7OcmWHYYNTduhiOD8CtPS0U-jdYyAG1pJ2MEzSzPVlJbVFk/s640/GTAA_N5_SHY_MAD.PNG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Manhattan Allocation Diagram for GTAA over 1971-2015</td></tr>
</tbody></table>
</span></div>
<br />
GTAA source:<span style="font-weight: normal;"> <a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=962461" target="_blank">A Quantitative Approach to Tactical Asset Allocation</a>
</span>TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-58668182059776886932015-09-19T06:34:00.002-04:002023-07-29T12:16:26.989-04:00Strategy Stress Testing à la MonacoAfter a short, admittedly rather superfluous, historical digression, this post will introduce Monte Carlo Analysis. What is Monte Carlo Analysis? Why is such analysis useful if not prerequisite for a strategy trader? What does it supplement to customary backtest information? By exploring the darker corners of a strategy the objective of this post is revealing real risk.<br />
<br />
<b>Crunching numbers in a monastery</b><br />
<br />
During the first half of the 1600s a French monk, Marin Mersenne, had many acquaintances in the scientific world. Mersenne studied (and taught) theology, philosophy, mathematics and music. He communicated extensively with other scholars like Descartes, Pascal, Huygens and Galilei. <br />
<br />
In spite of being a theologian and philosopher primarily, Mersenne’s name is associated with prime numbers that compound to M<sub>n</sub> = 2<sup>n</sup> – 1. Such numbers are called Mersenne primes. The first four Mersenne primes are 3, 7, 31 and 127 and significantly a Mersenne prime (2<sup>19937</sup>−1) is elementary for the most commonly used version of the Mersenne Twister.<br />
<br />
The Mersenne Twister is a fast generator of high-quality pseudorandom integers. Recently AmiBroker’s already extensive feature set was expanded with a Mersenne Twister based Monte Carlo simulator which is capable of rendering 30+ million trades per second (!). More specific, the Monte Carlo simulator runs series of trade sequences based on backtest output and uses the high-quality Mersenne Twister for randomizing the order of the trades.<br />
<br />
And so we finally arrive down the stairs of the famous "Casino de Monte-Carlo" in mondain Monaco ;-)<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVkZ6668LdXkh9K_MxnaMVsMrfUcDkJcW8e0zB2YAJHOMh4tlrqO3jupPNzOeM1IcPcif6ay7CERzgrcr39nKIDQb-54obz1oh9ABIYmwm3bhhFYfML-kq2KbktECt6YdpfI_AfQzXIW0/s1600/roulette_yaymicro.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVkZ6668LdXkh9K_MxnaMVsMrfUcDkJcW8e0zB2YAJHOMh4tlrqO3jupPNzOeM1IcPcif6ay7CERzgrcr39nKIDQb-54obz1oh9ABIYmwm3bhhFYfML-kq2KbktECt6YdpfI_AfQzXIW0/s400/roulette_yaymicro.jpg" width="400" /></a></div>
<br />
<b>Why stress test strategies with Monte Carlo Analysis?</b><br />
<br />
Before we start familiarizing ourselves with Monte Carlo Analysis let’s first pick a sample strategy for illustration purposes: <a href="http://seekingalpha.com/instablog/709762-varan/3118475-simple-gmr" target="_blank">SeekingAlpha's contributor Varan's Simple GMR</a>. Each month all available trading capital is re-allocated to the top performing ETF out of a basket with IJJ, EFA, IEV, EPP, QQQ, EEM and TLT. See Varan's post for details. For establishing points of reference and collecting the trade data required for a Monte Carlo Analysis, a backtest is run starting at year-end 2003 and ending August 2015 using high-quality monthly total return data as provided by <a href="http://www.premiumdata.net/" target="_blank">Norgate Premium Data</a> (Alpha-tester program).<br />
<br />
The equity curve as well as the distribution of the yearly returns obtained from the backtest look reasonable, even considering the 2008 drawdown when compared to the market in general. Volatility is not too high. Actually, the ratios for Sharpe, Sortino and Calmar are quite nice. The complete chart suite is available in the <a href="https://drive.google.com/folderview?id=0BwovO-kzwAfgYnpOOGR3N2NpNHM&usp=sharing" target="_blank">Google drive folder</a> connected to this post (zooming required!).<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeaAL5mdu0_wDO3aUWWEskAjQxA4ccLe2ml4WcyEbg7z80MHV3bMtNBvLRQMRHUVFbrDGIkVBveH7iZdKA_CHiYPpGVehsq_U2BvnUphWfRWu0VfOMu6VjBkA4yKrnvz-X-iug2SB-TII/s1600/GMR_Simple_Equity.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="432" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeaAL5mdu0_wDO3aUWWEskAjQxA4ccLe2ml4WcyEbg7z80MHV3bMtNBvLRQMRHUVFbrDGIkVBveH7iZdKA_CHiYPpGVehsq_U2BvnUphWfRWu0VfOMu6VjBkA4yKrnvz-X-iug2SB-TII/s640/GMR_Simple_Equity.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Portfolio performance over 2004 - 2015</td></tr>
</tbody></table>
<a name='more'></a><br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIclq_XXI8LwKjx11BEL_qESocjOzT0W9uaOqXI6UBnMwAKWouRhhHA4RTrQTu2_CZhtlqzKtjE2F7fpU50SjS9IHVldgajs8aVfeKdt1RVUA9UWg7l37H1z4kUbaIkHLfLeb70kCo16A/s1600/GMR_Simple_TearlyProfits.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="432" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIclq_XXI8LwKjx11BEL_qESocjOzT0W9uaOqXI6UBnMwAKWouRhhHA4RTrQTu2_CZhtlqzKtjE2F7fpU50SjS9IHVldgajs8aVfeKdt1RVUA9UWg7l37H1z4kUbaIkHLfLeb70kCo16A/s640/GMR_Simple_TearlyProfits.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Yearly returns</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikeMA6V6qFCM51GPLPO5jmh9DHgzEV0tM9x7deqsw5fCQjjpRD8Fc7iDAxjFaznBBiFcFg7HMM82cqn4IIb49xqih_dd2zYG1gD8buCA4x2hJQScn17VArC-jSLVXanA0t1oVwwXsPoY4/s1600/GMR_Simple_ProfitContribution.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="430" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikeMA6V6qFCM51GPLPO5jmh9DHgzEV0tM9x7deqsw5fCQjjpRD8Fc7iDAxjFaznBBiFcFg7HMM82cqn4IIb49xqih_dd2zYG1gD8buCA4x2hJQScn17VArC-jSLVXanA0t1oVwwXsPoY4/s640/GMR_Simple_ProfitContribution.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Profit contribution</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2lgOY4WYjEBhORWtC4e5gwB7hXdRT1rm1HF35VMdzyh2tNlJGPeF6qUUDVvj_W3hxNH5CtMQbP6XM6TjsWt7adaUxQCbwRm8g1DY8yl0LhTRVtiz_5O961301VDs-9o5ROgmrwF8kGZw/s1600/GMR_Simple_TradeReturns.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="434" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2lgOY4WYjEBhORWtC4e5gwB7hXdRT1rm1HF35VMdzyh2tNlJGPeF6qUUDVvj_W3hxNH5CtMQbP6XM6TjsWt7adaUxQCbwRm8g1DY8yl0LhTRVtiz_5O961301VDs-9o5ROgmrwF8kGZw/s640/GMR_Simple_TradeReturns.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Monthly trade results</td></tr>
</tbody></table>
<br />
Looking at the charts and the key performance metrics, the strategy appears to be profitable. But how confident can a trader really be that “live” application of the strategy will yield approximately the same results? After all, the backtest rendered just one single equity curve and nobody knows what the future will look like. What the trader needs to do is examine the likelihood of the reported backtest metrics to reflect “live” trading results with a suitable degree of confidence. Welcome to the “Casino de Monte-Carlo”! <br />
<br />
<b>What is Monte Carlo Analysis?</b><br />
<br />
For judging the probability of a specific outcome, Monte Carlo Analysis is applied. A Monte Carlo simulation is performed to address problems too complex for equations. It relies on repeated random sampling from a set of trades to estimate the mean and distribution of performance metrics by applying statistics. As <a href="http://www.blueowlpress.com/" target="_blank">Howard Bandy</a> <a href="https://groups.yahoo.com/neo/groups/amibroker/conversations/topics/151449" target="_blank">once</a> put it: <i> </i><br />
<blockquote class="tr_bq">
<i>"Monte Carlo Analysis is used to rearrange the sequence of trades many times. Typically many sequences are used -- 1000 or more -- each of many trades -- 100 or more. After all 1000 runs, all of the equity curves are draw on a single chart and statistics computed that will allow you to estimate the final equity and probability of both going broke and retiring wealthy. The plot looks like a straw broom with the straws angled upward to the right."</i></blockquote>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfDkIBFwgbPXYVA5cVBptgXZCgnDzG1cWaL9517iKVMaPduuVap0F3e54bVwN1RE_N66sE_UwtYWOvRteDwf4kRiZFyYzGcUwzGiZBkypFHx0rdmEWNqi2CZxcKFyTxW3-YSZYLZ1Uln8/s1600/GMR_Simple_MC_StrawBroom.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="432" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfDkIBFwgbPXYVA5cVBptgXZCgnDzG1cWaL9517iKVMaPduuVap0F3e54bVwN1RE_N66sE_UwtYWOvRteDwf4kRiZFyYzGcUwzGiZBkypFHx0rdmEWNqi2CZxcKFyTxW3-YSZYLZ1Uln8/s640/GMR_Simple_MC_StrawBroom.png" width="640" /></a> <br />
<br />
The above “straw broom” chart paints 10 individual random sequences of the change in equity (in gray) that were performed in the backtest with Simple GMR universe as well as the average of all simulated sequences as an approximation of the expected change in equity (in blue). Note that these 10 example sequences are equally likely, there are many more possibilities (140<sup>140</sup> to be precise), only one sequence will materialize and nobody can predict which sequence that is going to be. <br />
<br />
In his book "<a href="http://www.modelingtradingsystemperformance.com/" target="_blank">Modeling Trading System Performance</a>" Howard Bandy states: <span style="color: blue;"> </span><br />
<blockquote class="tr_bq">
<i>The
result of a single simulation ( such as a single backtest run ) is a
qualified statement. For example, "The system appears to be profitable". </i><br />
<i>The result of a probabilistic <span class="il">Monte</span> <span class="il">Carlo</span>
simulation is a quantified probability. For example, "There is an 80%
probability that the system will have a compound annual rate of return
of 12% or more."</i></blockquote>
Put differently, Monte Carlo Analysis is all about gaining confidence based on statistical probability. In trading nearly any outcome is possible, but the trader wants to know the probability of his expectations. By imposing a reasonably conservative confidence level of 95% to himself, the trader can assess the probability of a specific outcome. However, even with 95% confidence, still a 5% risk lies in wait for embarrassing the trader’s statistically founded expectations and, more important, to wreak havoc to his account.<br />
<br />
Croupier chorus (joyful chanting): <i>“Il n'y pas de certitude!”</i> (encore)<br />
<br />
<b>Monte Carlo stress test results</b><br />
<br />
By backtesting IJJ, EFA, IEV, EPP, QQQ, EEM and TLT over 2004 - 2015 with monthly reforms into the top performing fund, the backtest spans 11 years and 8 months or 140 trades. The results of each of these 140 trades are the sample set used by the Mersenne Twister to randomize the sequence. In their twisted sequences trades may occur in a different order, trades may be omitted or trades may be duplicated. See <a href="https://www.amibroker.com/guide/h_montecarlo.html" target="_blank">AmiBroker's website</a> for an explanation of the general methodology. Due to the blazing speed of AmiBroker’s Monte Carlo engine 1,000,000 simulations were applied for generating the following metrics and graphs (total i7-CPU time: 6s (!)).<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhieP_Liuv_gJF5yGtUNPl1ba4Pc53Lqx2vMzm5S3x3KxQPdFMZpZpEqpLWpHVl7AZxyvZaIdSu47XDcyIv-EgzmqcUnclqfDnds9ivAcVcASr2z58cXCxmXfKgaQHvRuseXvklUlv2peM/s1600/GMR_Simple_MC_Table.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="203" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhieP_Liuv_gJF5yGtUNPl1ba4Pc53Lqx2vMzm5S3x3KxQPdFMZpZpEqpLWpHVl7AZxyvZaIdSu47XDcyIv-EgzmqcUnclqfDnds9ivAcVcASr2z58cXCxmXfKgaQHvRuseXvklUlv2peM/s400/GMR_Simple_MC_Table.png" width="400" /></a></div>
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The above table is very helpful by interpreting the results from the graphs about to follow, so there is no need to "guess" these readings each time from the graphs.<br />
<br />
The CAR level as reported by the backtester (see first chart in this post) is 24.71%. This is a near match to the 50 percentile score on the above numerical table. In other words, the table informs the trader that there is (only) a 50% probability that CAR will be around this level or perhaps higher. Of course, sitting at the 50 percentile level, the likelihood of a lower CAR is equally high, so 50% too.<br />
<br />
Given the earlier adopted reasonably conservative 95% confidence level, probability states that CAR
will be 14.62% or higher as is shown on the following Monte Carlo CAR graph.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmnjjnGCFk3khUPLG2L7zqBKXe1zpYLJAE_LziQ3S4Gwkq_yThjDRNY_wxK1tfpJbVqHULStYi_G3zmfOJduwcbnhVCxmLe-tPjRJdFZMm1YXa-6rUU7_z8os4jd0OftMFPvsvo6QGRuM/s1600/GMR_Simple_MC_CAR.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="444" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmnjjnGCFk3khUPLG2L7zqBKXe1zpYLJAE_LziQ3S4Gwkq_yThjDRNY_wxK1tfpJbVqHULStYi_G3zmfOJduwcbnhVCxmLe-tPjRJdFZMm1YXa-6rUU7_z8os4jd0OftMFPvsvo6QGRuM/s640/GMR_Simple_MC_CAR.png" width="640" /></a></div>
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Regarding drawdown, the below Monte Carlo graph informs the trader his maximum drawdown percentage will probably be 33.42% or better. So the registered 14.40% maximum drawdown from the backtest isn’t really informative at all. Frankly, in view of this 95 percentile score, one could maintain that the reported -14.40% drawdown is rather deceptive. The likelihood that the incurred maximum drawdown will be near the reported -14.40% or better is only about 10%.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTJj9lKKlFRdB9hoOyRV3ZKRIERRXSi__W7EeqwiOnXDjNhCA8NUd7d7de7Mg3OBaENZQuVlAjagu4KoWKdNQZUuCem7ML_7IPWVpuoX3Ia6NWZqLokyC633TNCyoB4Uy1G915wVC5dwY/s1600/GMR_Simple_MC_MaxDD.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="444" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTJj9lKKlFRdB9hoOyRV3ZKRIERRXSi__W7EeqwiOnXDjNhCA8NUd7d7de7Mg3OBaENZQuVlAjagu4KoWKdNQZUuCem7ML_7IPWVpuoX3Ia6NWZqLokyC633TNCyoB4Uy1G915wVC5dwY/s640/GMR_Simple_MC_MaxDD.png" width="640" /></a></div>
<br />
Lastly the trader may be quite confident that a wipe-out of his account is very unlikely to happen: given an initial capital of $100,000, there is only a 1% probability that the trader will lose more than $26,000 from his starting capital.<br />
<br />
Wrapping up, Monte Carlo Analysis takes away any false expectations entertained by a trader from a (single) backtest and it enables him to become realistic about the prospects of a strategy and his financial future.<br />
A simplified rule of thumb for Monte Carlo based probability derived from a backtest might be: split CAR in half and double MaxDD. <br />
<br />
<b>Final remarks</b><br />
<br />
AmiBroker's developer, <span class="st">Tomasz Janeczko, informed me that using Monte Carlo Analysis is not feasible for models that invest in multiple ETFs at the same time. </span>Compounding by itself is not a problem as long as there are no
overlapping trades. I have yet to fully understand why, but please take notice.<br />
<br />
For for the graphs in this post the following AFL driven code was used:<br />
<script class="brush: js" type="syntaxhighlighter"><![CDATA[
// --- Monte Carlo settings ---
MCS = ParamToggle( "Enable Monte Carlo Simulation?", "No|Yes", 0 );
if ( MCS )
{
SetOption( "MCEnable" , 1 ); // value == 1 enables MC only in portfolio backtests (default)
SetOption( "MCRuns" , 1000000 ); // define number of MC simulation runs (realizations)
// MCPosSizeMethod:
SetOption( "MCPosSizeMethod", 3 ); // 0 (default) - "Don't change" : MC simulator uses trades as they are coming from the backtester without changing position size and profit as it is reported from the backtester.
// 1 - "Fixed size" : MC simulator uses fixed number of shares/contracts per trade
// 2 - "Constant value" : MC simulator uses fixed dollar amount for opening any trade
// 3 - "Percent of equity": MC simulator uses defined percent of current simulated equity value
SetOption( "MCPosSizePctEquity", 100 ); // re-invest 100% of equity at each portfolio reformation (here: monthly)
}
]]></script> <br />
The full code for Simple GMR including the Monte Carlo routine is available on the <a href="https://drive.google.com/folderview?id=0BwovO-kzwAfgYnpOOGR3N2NpNHM&usp=sharing" target="_blank">Google drive</a> folder connected to this post. Run the code on monthly periodicity. On the <a href="https://drive.google.com/folderview?id=0BwovO-kzwAfgYnpOOGR3N2NpNHM&usp=sharing" target="_blank">Google drive</a> also the full trades list is shared in html format allowing import into Excel for further analysis or even Monte Carlo DIY.<br />
<br />
<b>Further reading </b><br />
<br />
Howard Bandy provides in-depth coverage about Monte Carlo Analysis as well as probability based position sizing in his aforementioned book "<a href="http://www.amazon.com/Modeling-Trading-System-Performance-Howard/dp/0979183820/ref=asap_bc?ie=UTF8" target="_blank">Modeling Trading System Performance</a>", including instructions for applying Monte Carlo Analysis with Excel.<br />
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<br />TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-83287841940187562802015-07-10T06:08:00.000-04:002016-01-16T09:10:42.371-05:00Holiday Reading<center>
<table><tbody>
<tr><td><div class="separator" style="clear: both; text-align: center;">
<a href="http://www.amazon.com/Stocks-Move-Beating-Momentum-Strategies/dp/1511466146/ref=sr_1_1?s=books&ie=UTF8&qid=1436522172&sr=1-1&keywords=clenow+stocks+on+the+move" target="_blank"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivI0nVPNAR-YvYWZeYHwwo5emZJVLUwqlLVr2oPTNz8Ytu8H_JwvmiyNl00dRuuIOC1-egxt7BQ0w-g35thz_09tUQrpXPDhHaJidgegsQHNX0gKNNN27UaQZKl2b9gpUxyU5xGN8SKwc/s320/stocksonthemove.jpg" width="207" /></a>
</div>
</td>
<td><div class="separator" style="clear: both; text-align: center;">
<a href="http://www.amazon.com/Quantitative-Technical-Analysis-integrated-development/dp/0979183855/ref=sr_1_1?s=books&ie=UTF8&qid=1436522226&sr=1-1&keywords=bandy" target="_blank"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHtbrPUes5GcpQCt3rNs8vVNCEgMmD0sbMIxHdaYYhiV0NGNorjboc90yRsqi86YFRDM6sgRDdzGvzR2Gzb7hyNjNZ60BpHSSG3p_NnW8wled0Lz5vMRmQIGNt6M4x_lcyXh4qBlkzbnM/s320/qta.jpg" width="224" /></a>
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</td></tr>
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</center>
TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-84369049463901281492015-05-06T08:49:00.002-04:002016-01-16T09:14:29.742-05:00EAA Piloting Quarterly Sector Rotation With C(r)ash ProtectionThis post will cover a detailed look into quarterly sector investing using the EAA-model previously introduced (see <a href="http://indexswingtrader.blogspot.com/2015/01/a-primer-on-elastic-asset-allocation.html" target="_blank">here</a>). For the sector investor Fidelity is the place to be. Currently Fidelity offers <a href="https://www.fidelity.com/fund-screener/evaluator.shtml#!&ft=SSTK_all&rsk=5&mgdBy=F&ntf=Y&expand=%24FundType" target="_blank">46 sector mutual funds</a>. Lots of these funds have at least 21 years of historical prices available. Those are the ones collected in the universe under investigation in this post to allow for comparability with <a href="http://indexswingtrader.blogspot.com/2015/04/sampling-universes-for-eaa.html" target="_blank">prior</a> backtests.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlkOSQ98nYwwhGkQWPj973UIp-TTbIrlN_uAoL6rAM8pxyHq0gWJbftBC1iqNt-FXeZABeBKdXKXHgzzpqJgZ3vRHiZH3oc8hgiLiXq0gbOuKA3EdMGNuzUhtnlVJtR7_guUDbriFX2bQ/s1600/buoys_yaymicro.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlkOSQ98nYwwhGkQWPj973UIp-TTbIrlN_uAoL6rAM8pxyHq0gWJbftBC1iqNt-FXeZABeBKdXKXHgzzpqJgZ3vRHiZH3oc8hgiLiXq0gbOuKA3EdMGNuzUhtnlVJtR7_guUDbriFX2bQ/s1600/buoys_yaymicro.jpg" width="400" /></a></div>
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<b>Fidelity Sector Select Universe</b><br />
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The above stated data history requirement is met by 34 from the 46 available sector funds. With these 34 funds not only 10 economical sectors plus precious metals are covered, but it also ensures for a well diversified basket to select investments from.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAycI3ui6TPbZDxeFa0mQ0uW2ND_FfdgPO-FKHD-OZZepmSzTqx3OHchyphenhyphenf2Xybs7MZfw9k_lup2HNWBLvK8cxrrAsoKFu1yARLhzi35U3KjQyjNJMlndLF6oLRvLW9id8DtDUk7rkog5w/s1600/FidelitySectorTable.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="568" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAycI3ui6TPbZDxeFa0mQ0uW2ND_FfdgPO-FKHD-OZZepmSzTqx3OHchyphenhyphenf2Xybs7MZfw9k_lup2HNWBLvK8cxrrAsoKFu1yARLhzi35U3KjQyjNJMlndLF6oLRvLW9id8DtDUk7rkog5w/s1600/FidelitySectorTable.png" width="640" /></a></div>
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In the above table funds are sorted on sectors. Furthermore the performance of each fund over 1995 - 2014 is shown and broken down into the average yearly return (<b>R</b>), the fund's volatility (<b>V</b>) and the worst draw down (<b>D</b>) during those 20 years.<br />
<a name='more'></a><br />
As C(r)ash Protection Fund another Fidelity mutual fund is used: FIBIX. However, since FIBIX' data falls short on the mandatory data history, it was synthetically extended using Vanguard's VFITX data (see <a href="http://indexswingtrader.blogspot.com/2014/05/composing-synthetic-prices-for-extended.html" target="_blank">here</a> or <a href="http://indexswingtrader.blogspot.com/2014/12/about-time-leverage-and-few-grains-of.html" target="_blank">here</a>). <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBFS5Kz5WlguitLucObqVGIy5LQgBXmbcypWzLudNFnO0RaU8deIqQyNtc-J6kIk5mF-H976FzDZbfd8nfy5xhhxInb_diQ6h-CUZU19ILiq4PXz_jVR1ALzTqzpTMThKrUllNw0koxO0/s1600/FIBIX_Table.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="24" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBFS5Kz5WlguitLucObqVGIy5LQgBXmbcypWzLudNFnO0RaU8deIqQyNtc-J6kIk5mF-H976FzDZbfd8nfy5xhhxInb_diQ6h-CUZU19ILiq4PXz_jVR1ALzTqzpTMThKrUllNw0koxO0/s1600/FIBIX_Table.png" width="640" /></a></div>
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Backtests are performed with <a href="https://www.amibroker.com/" target="_blank">AmiBroker's Professional edition</a> using monthly total return data obtained from <a href="http://finance.yahoo.com/" target="_blank">Yahoo! Finance</a>. Below the performance is shown for monthly as well as quarterly portfolio re-balancing as piloted by the EAA-model in Equal Weighted Hegded mode (see <a href="http://indexswingtrader.blogspot.com/2015/01/a-primer-on-elastic-asset-allocation.html" target="_blank">here</a>). Portfolios are reformed at the end of each month/quarter. Transaction costs are not taken into consideration. In the table the monthly/quarterly re-balanced Equal Weight portfolios
of the 34 asset universe are used as benchmarks along with a 20 year
Buy&Hold investment in SPY.<br />
<br />
The monthly strategy allocates capital to a maximum of 6 funds (in accordance with the round( sqrt( 34 ) ) proposition implemented in the EAA-code) supplemented by a proportional fraction of portfolio capital to the cash proxy fund (here: FIBIX) for every asset with non-positive return (the c(r)ash protection routine). To account for the higher volatility related to the lower re-balancing frequency of the quarterly strategy a maximum of 7 funds is applied instead. However with a maximum of 8 selection the volatility of the quarterly strategy would have been a near match compared to the monthly strategy, but only at the cost of lower CAR and worser MaxDD. <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgWJCbnNSv1Auog09rFDd0uvgwOfj7Pa4CFC4awtnLYmO_wMIfwdJCC-ZjMGfW6WMp1q1V-X07Z-mlfKfKswnJ4-BOuAptN5Y1ykc-twhAtAMMZT8PlfvNyGI3M82yIW8iPJcR7QU5PLk/s1600/EAA_Fidelity_Stats.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="223" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgWJCbnNSv1Auog09rFDd0uvgwOfj7Pa4CFC4awtnLYmO_wMIfwdJCC-ZjMGfW6WMp1q1V-X07Z-mlfKfKswnJ4-BOuAptN5Y1ykc-twhAtAMMZT8PlfvNyGI3M82yIW8iPJcR7QU5PLk/s1600/EAA_Fidelity_Stats.png" width="400" /></a></div>
<br />
Note the monthly metrics are just for illustration purposes, since with
monthly reforms the investor most likely would risk incurring short-term
trading fees quite frequently due to the redemption periods for the Fidelity
Select funds stretching from 30 until 90 days.<br />
<br />
<b>Quarterly Sector Rotation In Detail</b><br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjW0JNBx3i_i0wdfDwBESFefKUm8R5yU0-g0-MwD8GgSB59C2WTyaSvxIGzBiPaelvqv6COmXTq6w3GqGeSE4jY2o6SzCGGfEksuYnHqBPs3VODre44Tv7GoKoF2lrhM0J_oBugSwiuRss/s1600/EAA_Q_F34_EquityKPI.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="386" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjW0JNBx3i_i0wdfDwBESFefKUm8R5yU0-g0-MwD8GgSB59C2WTyaSvxIGzBiPaelvqv6COmXTq6w3GqGeSE4jY2o6SzCGGfEksuYnHqBPs3VODre44Tv7GoKoF2lrhM0J_oBugSwiuRss/s1600/EAA_Q_F34_EquityKPI.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fidelity 34+1 Quarterly Strategy: equity graph with key performance indicators</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhs4RQfOfB1K4Pk5P-CK8ECJYgUaQnZej382r1mMnp34K_M5V6WdOFj_NqQjK3mdOnpPDUuJNzZpZsT9uhUiDO4Tb4H9W9mFpPUXRbxSwOs9NOkqQEBi2Rc-VhkDR1ZmbNsggkOMqyv2b8/s1600/EAA_Q_F34_YearlyReturns.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="386" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhs4RQfOfB1K4Pk5P-CK8ECJYgUaQnZej382r1mMnp34K_M5V6WdOFj_NqQjK3mdOnpPDUuJNzZpZsT9uhUiDO4Tb4H9W9mFpPUXRbxSwOs9NOkqQEBi2Rc-VhkDR1ZmbNsggkOMqyv2b8/s1600/EAA_Q_F34_YearlyReturns.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fidelity 34+1 Quarterly Strategy: yearly return chart</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiS6snGwWCKkm-3Wuxht7PpBDb7sWbFPip427gev4wvtTcynf3EGb52pPxdkY4NCFZqDD9eMuKZUGFzyvlyCGWodZiqYDgq3KvxJ8tF2Tx0YjEHQM0DwCjN_LwMpTPOPHJLrMqW6Q-Mso4/s1600/EAA_Q_F34_ProfitTable.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="492" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiS6snGwWCKkm-3Wuxht7PpBDb7sWbFPip427gev4wvtTcynf3EGb52pPxdkY4NCFZqDD9eMuKZUGFzyvlyCGWodZiqYDgq3KvxJ8tF2Tx0YjEHQM0DwCjN_LwMpTPOPHJLrMqW6Q-Mso4/s1600/EAA_Q_F34_ProfitTable.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fidelity 34+1 Quarterly Strategy: monthly profit table with yearly CARs and MaxDDs</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-aMIz-Mv9UoAqZzn2fzY3seuHdkF9BDAWVS2Be2SQJTI5qQN-eYlAI2AObGK3D45MPQrXo8zXp-gsB_SuTAkFSaAdc-Huxx0tA8WOP6d64qe4t0Elx827BV_SzeEm0UF19GLwPywHPng/s1600/EAA_Q_F34_DrawDown.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="385" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-aMIz-Mv9UoAqZzn2fzY3seuHdkF9BDAWVS2Be2SQJTI5qQN-eYlAI2AObGK3D45MPQrXo8zXp-gsB_SuTAkFSaAdc-Huxx0tA8WOP6d64qe4t0Elx827BV_SzeEm0UF19GLwPywHPng/s1600/EAA_Q_F34_DrawDown.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fidelity 34+1 Quarterly Strategy:monthly draw down graph</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6tjkDbErze8b82QS2oeaS5D_y5McXX_dOU0XXsdsTrj9TG_Xyb4E2mCbpe0pANnUu9EtvtOcW-Q1aJQPvfEgEdB3WNCAwvfCTf2DHhyeCgfLDtvqGTwC1x6MD3bqr66pF__Sk2OUGEts/s1600/EAA_Q_F34_Allocation.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="430" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6tjkDbErze8b82QS2oeaS5D_y5McXX_dOU0XXsdsTrj9TG_Xyb4E2mCbpe0pANnUu9EtvtOcW-Q1aJQPvfEgEdB3WNCAwvfCTf2DHhyeCgfLDtvqGTwC1x6MD3bqr66pF__Sk2OUGEts/s1600/EAA_Q_F34_Allocation.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fidelity 34+1 Quarterly Strategy: capital allocation per fund (%)</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjC6mdbeohhR7rmWagFVbiz0RAE26irYz_hJddRU3UYvB-h2M2bpawr25niNZHfOG4hPmvA1NuMkAO7G9anfXFNXaKb50OQvONodk0Qc7FSsoPjZldb5YRy-YQTP5KbPHxz92HXBeurEoY/s1600/EAA_Q_F34_ProfitContribution.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="274" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjC6mdbeohhR7rmWagFVbiz0RAE26irYz_hJddRU3UYvB-h2M2bpawr25niNZHfOG4hPmvA1NuMkAO7G9anfXFNXaKb50OQvONodk0Qc7FSsoPjZldb5YRy-YQTP5KbPHxz92HXBeurEoY/s1600/EAA_Q_F34_ProfitContribution.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fidelity 34+1 Quarterly Strategy:profit contribution per fund</td><td class="tr-caption" style="text-align: center;"><br /></td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhk5g_x6qblmRtDFujFSpJfEogkvqiUD9sUzyVTNmJVhPhmf5MtyCgthr40ExBC4kZgQMLh1FbJsBtRhrKsexr3FBS0A62NoxTB3tgHMB7eQ_GlHDiJs0wmlp6NvoKVWNFA5d4c5vcmmW4/s1600/EAA_Q_F34_ManhattanAllocationDiagram.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="276" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhk5g_x6qblmRtDFujFSpJfEogkvqiUD9sUzyVTNmJVhPhmf5MtyCgthr40ExBC4kZgQMLh1FbJsBtRhrKsexr3FBS0A62NoxTB3tgHMB7eQ_GlHDiJs0wmlp6NvoKVWNFA5d4c5vcmmW4/s1600/EAA_Q_F34_ManhattanAllocationDiagram.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fidelity 34+1 Quarterly Strategy: Manhattan allocation diagram with fund selection for every quarter </td></tr>
</tbody></table>
<br />
Please feel welcome to put forward idea's regarding broad and diversified universes of ETFs (N >= 50) for backtesting and do leave remarks and suggestions in the comment section below.<br />
<br />
<br />
<br />TrendXplorerhttp://www.blogger.com/profile/02941240592194512455noreply@blogger.comtag:blogger.com,1999:blog-1198390932304068379.post-71369915117228003032015-04-12T15:13:00.005-04:002023-07-29T12:17:45.704-04:00Sampling Universes with EAAIn this post several universes will be sampled using the <a href="http://indexswingtrader.blogspot.com/2015/01/a-primer-on-elastic-asset-allocation.html" target="_blank">Elastic Asset Allocation model</a>. The universes under review are:<br />
- <a href="http://www.cxoadvisory.com/subscription-options/?wlfrom=%2F18886%2Fmomentum-investing%2Fsimple-asset-class-etf-momentum-strategy-performance%2F" target="_blank">CXO Advisory's 8 assets simple momentum universe</a><br />
- <a href="http://indexswingtrader.blogspot.com/2013/10/conceptual-sketch-for-all-weather.html#comment-1094150234" target="_blank">Stefan Solomons 12 assets tactical allocation universe</a><br />
- <a href="http://etfdb.com/compare/volume/" target="_blank">ETFdb.com's most popular ETFs</a><br />
- CXO's on steroids: a 300% leveraged universe<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiw44OeYKIxIYgjMaV9dEQzxwDUyBzcLfAED1yHzO6J5fRXFuLwlgokV-5MrEqCkvYvpRczWpEKVR-8mI2I9ilp1Fn03gTGnKP8DPt27n3U5QaxmWiRVsl26XWOn2XHdwzkrujBeACJm4/s1600/yay-sampling.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiw44OeYKIxIYgjMaV9dEQzxwDUyBzcLfAED1yHzO6J5fRXFuLwlgokV-5MrEqCkvYvpRczWpEKVR-8mI2I9ilp1Fn03gTGnKP8DPt27n3U5QaxmWiRVsl26XWOn2XHdwzkrujBeACJm4/s1600/yay-sampling.jpg" width="400" /></a></div>
<br />
The backtests are performed using monthly <a href="http://finance.yahoo.com/" target="_blank">Yahoo! Finance</a> total return data with EAA in Equal Weigted Hedged mode with monthly reforms. So each month assets are (re-)alloced according to the below simplified formula:<br />
<center>
<span style="font-size: large;">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow>
<mrow>
<mi mathvariant="italic">wi</mi>
<mo stretchy="false">∼</mo>
<mi mathvariant="italic">zi</mi>
<mo stretchy="false">=</mo>
<msup>
<mrow>
<mo fence="true" stretchy="false">(</mo>
<mrow>
<mrow>
<mrow>
<mo fence="true" stretchy="false">(</mo>
<mrow>
<mrow>
<mn>1</mn>
<mo stretchy="false">−</mo>
<mi mathvariant="italic">ci</mi>
</mrow>
</mrow>
<mo fence="true" stretchy="false">)</mo>
</mrow>
<mo stretchy="false">⋅</mo>
<mi mathvariant="italic">ri</mi>
</mrow>
</mrow>
<mo fence="true" stretchy="false">)</mo>
</mrow>
<mi mathvariant="italic">eps</mi>
</msup>
</mrow>
<mi>,</mi>
</mrow>
<annotation encoding="StarMath 5.0">wi sim zi = ((1-ci) cdot ri ) ^ eps,</annotation> </semantics></math></span> if ri > 0 else wi = zi = 0</center>
ETFs are <a href="http://indexswingtrader.blogspot.com/2014/05/composing-synthetic-prices-for-extended.html" target="_blank">extended</a> using mutual fund data to attain a backtest period of 20 years (1995 - 2014)<b>*</b>.<br />
<br />
<b>CXO Advisory's 8 assets simple momentum universe</b><br />
<br />
The line-up for CXO's is DBC, EEM, EFA, GLD, IWM, IYR, SPY and TLT. Since the liquidity of CXO's original IWB is way lower than that of its bigger sibling SPY, the latter was used. IEF is deployed as c(r)ash protection fund (CPF), but is kept outside the regular allocation basket. The maximum number of assets for capital allocation is limited to 3+1.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFft5Cbd6g6yPvy-5vqTW2gSZH7KSa3FMP63swZsZwhqv6NBV6MpWaeTp-BBn5tcxAXATC8-tQcc6EuVxHATzoiYshCAKZsJzHR7STeC-Jo0iioNGQTkleRXemkpT1Lo22A01-99wf6bU/s1600/EAA_EWH_CXO_Comparison.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="190" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFft5Cbd6g6yPvy-5vqTW2gSZH7KSa3FMP63swZsZwhqv6NBV6MpWaeTp-BBn5tcxAXATC8-tQcc6EuVxHATzoiYshCAKZsJzHR7STeC-Jo0iioNGQTkleRXemkpT1Lo22A01-99wf6bU/s1600/EAA_EWH_CXO_Comparison.png" width="640" /></a></div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz8UWJDfah03KGhkHQue_wrzC7gVNxNswaiTrR9DHQjrtSKZ8BYDgogTdvkKt_Sw2h7FuxpsWhHjC-KWnrTUEqtEBZufldZSnTf7jesrlvTf5nHXoHe5gr4aeOkRcV16lE3Tf-1sL5Lgg/s1600/EAA_CXO_KPI.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="390" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz8UWJDfah03KGhkHQue_wrzC7gVNxNswaiTrR9DHQjrtSKZ8BYDgogTdvkKt_Sw2h7FuxpsWhHjC-KWnrTUEqtEBZufldZSnTf7jesrlvTf5nHXoHe5gr4aeOkRcV16lE3Tf-1sL5Lgg/s1600/EAA_CXO_KPI.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">CXO: equity curve with key performance indicators</td></tr>
</tbody></table>
<a name='more'></a><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMOYCtxc2sTF9THcO83QpQDXPaQt-8RpSI9TDTYpsn4xBqlRJb9TyRExY_slPTyC6YnPvgepvAKvMR3g_BbXV34j5z_1EyPung8iWPdqUqJ9heKj4ApRRYsKsXQMS6sQoM1nkqdgQDlTQ/s1600/EAA_CXO_YR.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="392" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMOYCtxc2sTF9THcO83QpQDXPaQt-8RpSI9TDTYpsn4xBqlRJb9TyRExY_slPTyC6YnPvgepvAKvMR3g_BbXV34j5z_1EyPung8iWPdqUqJ9heKj4ApRRYsKsXQMS6sQoM1nkqdgQDlTQ/s1600/EAA_CXO_YR.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">CXO: yearly returns</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1ziomUftDGBdfdFxwwrwSF0e8_G_X4Aptx8sWLFg1-X0j8RgJya5YSSifHDVPEs8hb6XBgi-Y-z3mCC0tVgXCt8BNGoNVGxAH0GnoK3eqZHKWn6bohgL8tlHrXq4Yu_CP-7iGFofcKO0/s1600/EAA_CXO_PC.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="394" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1ziomUftDGBdfdFxwwrwSF0e8_G_X4Aptx8sWLFg1-X0j8RgJya5YSSifHDVPEs8hb6XBgi-Y-z3mCC0tVgXCt8BNGoNVGxAH0GnoK3eqZHKWn6bohgL8tlHrXq4Yu_CP-7iGFofcKO0/s1600/EAA_CXO_PC.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">CXO: profit contributions</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg34wmHSidM7fveNzINYIuphxKl6Q3W8md0yO-tvQdLqAIdSF45EIR0Ell-BlnHXc9VpBhVUiKCSIS8Gx-NnY-htMlN5MeKWProhFf7gX7eIq0HOTtTgK8-FYqbj5X4Lp-Bz_3W6Hl9E3I/s1600/EAA_CXO_CC.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="392" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg34wmHSidM7fveNzINYIuphxKl6Q3W8md0yO-tvQdLqAIdSF45EIR0Ell-BlnHXc9VpBhVUiKCSIS8Gx-NnY-htMlN5MeKWProhFf7gX7eIq0HOTtTgK8-FYqbj5X4Lp-Bz_3W6Hl9E3I/s1600/EAA_CXO_CC.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">CXO: 2 standard deviations confidence channel (95%) for rolling 1 year returns</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjL3XySjMfkUpwOfB0s_-J7JganAr8BVSuJu2VI8fYm5uG52kydTAhRIwyxF1UWb1rg3yAsUFaMgOCyOqzVcvksiQO1J1vGVuM3nScMJf8b0A7QGs6HBJWQUVwpdnul0DvsNX_VVLJuB0M/s1600/EAA_CXO_MAD.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="211" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjL3XySjMfkUpwOfB0s_-J7JganAr8BVSuJu2VI8fYm5uG52kydTAhRIwyxF1UWb1rg3yAsUFaMgOCyOqzVcvksiQO1J1vGVuM3nScMJf8b0A7QGs6HBJWQUVwpdnul0DvsNX_VVLJuB0M/s1600/EAA_CXO_MAD.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">CXO: Manhattan allocation diagram showing the waxing and waning of the CPF (upwards from bottom)</td></tr>
</tbody></table>
<br />
<b>Stefan Solomons 12 assets tactical allocation universe</b><br />
<br />
Some 18 months ago Stefan joined the discussion about the <a href="http://indexswingtrader.blogspot.com/2013/10/conceptual-sketch-for-all-weather.html" target="_blank">Conceptual Sketch post</a>. In one of his comments, he stated the ETFs selection is the key
piece of this type of system. At that time Stefan settled for: SPY, IWM, EFA, EEM, ICF, RWX, HYG, EMB, DBC, GLD, TLT, LTPZ. With 12 assets in the basket and IEF as CPF, this universe is given an allocation limit of 4+1 funds, which actually yields a better performance on all but one metrics compared to the 3+1 limit (CAR is 0.28% lower). <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMHE-DQwvaYIOs0XaSvPyhr74HiwP5R7iDMX8ROmSDGh76A98zLfU3QMdmaaomd7E2-qMRYKEqaBAbO8oYSYKuncl6sHQMobVYhXgXOx5tzdLLgZ2eQ3v7GV7ns_UYgiqaJj5Ahndikeg/s1600/EAA_EWH_SS12_Comparison.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="188" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMHE-DQwvaYIOs0XaSvPyhr74HiwP5R7iDMX8ROmSDGh76A98zLfU3QMdmaaomd7E2-qMRYKEqaBAbO8oYSYKuncl6sHQMobVYhXgXOx5tzdLLgZ2eQ3v7GV7ns_UYgiqaJj5Ahndikeg/s1600/EAA_EWH_SS12_Comparison.png" width="640" /></a></div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5Vj9QJEJgbhO8-LWqv5xLBGLEnwN2zJeFRxxNRNaf8H0DUpSg2EhghJDMkICIoECXb4rerXpBTw9n_w5DR2b0IZP6hJ92jDlfyMcta5ZfzGDbjzF8kpqzm1HSthR3Nw3SA9qFzCBjIhI/s1600/EAA_EWH_SS12_KPI.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="392" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5Vj9QJEJgbhO8-LWqv5xLBGLEnwN2zJeFRxxNRNaf8H0DUpSg2EhghJDMkICIoECXb4rerXpBTw9n_w5DR2b0IZP6hJ92jDlfyMcta5ZfzGDbjzF8kpqzm1HSthR3Nw3SA9qFzCBjIhI/s1600/EAA_EWH_SS12_KPI.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">SS12: equity curve with key performance indicators</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhK3YtsZ3V406LZu7uNl57p6Os8oaBVLN-OBTygymx9QD4edmg73dKJTTC79xJhqGcqTxSH_ailh1d9PrSwT88Py17G61opu8DA0CV2MME-6gcaVNlj62UKdf3DTJbxmUwXpf9Uoslf3gA/s1600/EAA_EWH_SS12_YR.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="390" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhK3YtsZ3V406LZu7uNl57p6Os8oaBVLN-OBTygymx9QD4edmg73dKJTTC79xJhqGcqTxSH_ailh1d9PrSwT88Py17G61opu8DA0CV2MME-6gcaVNlj62UKdf3DTJbxmUwXpf9Uoslf3gA/s1600/EAA_EWH_SS12_YR.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">SS12: yearly returns</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-tgAJ6Ss5o6UIshMm6PC9YeJoeT_YLpcZvbXRHm5gyoxRfB_pEL59jqacVqV6zgAI3IyxE_uNhREPx17jet5n39uB_D6Dpi9-6CZegF7oIKOr0-N2Rw_X8hRDjFxDzd3JjGCRYNZB8i4/s1600/EAA_EWH_SS12_PC.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="392" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-tgAJ6Ss5o6UIshMm6PC9YeJoeT_YLpcZvbXRHm5gyoxRfB_pEL59jqacVqV6zgAI3IyxE_uNhREPx17jet5n39uB_D6Dpi9-6CZegF7oIKOr0-N2Rw_X8hRDjFxDzd3JjGCRYNZB8i4/s1600/EAA_EWH_SS12_PC.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">SS12: profit contributions</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiclo0Uk2I8P6QKLM-OOdE4cOFRl5FhJiWpT1GZVUolCVlNYWr5TOJE9zLY8sQbUL1A2eFEfwipqwN0VRrm9W4jyeEQqwvHYVwCNWuQKGRUGym7ouz7boKAEJ6l3lF0_nQJvTW9J0OQz70/s1600/EAA_EWH_SS12_CC.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="390" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiclo0Uk2I8P6QKLM-OOdE4cOFRl5FhJiWpT1GZVUolCVlNYWr5TOJE9zLY8sQbUL1A2eFEfwipqwN0VRrm9W4jyeEQqwvHYVwCNWuQKGRUGym7ouz7boKAEJ6l3lF0_nQJvTW9J0OQz70/s1600/EAA_EWH_SS12_CC.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">SS12: 2 standard deviations confidence channel (95%) for rolling 1 year returns</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLNi7uRXcI-_7lqJ_KD_k5S51P-NVaM_urytl3qIr1hT0Px5q9Jy3Ry-yYfo38-nQ4tpAgDpBZTMjSUVA4Pusbe8CTTCk3aRIGaxsSp7PGYq1rp1SCGBzGjfdVgcn2LmqVNrQluktsgOI/s1600/EAA_EWH_SS12_MAD.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="212" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLNi7uRXcI-_7lqJ_KD_k5S51P-NVaM_urytl3qIr1hT0Px5q9Jy3Ry-yYfo38-nQ4tpAgDpBZTMjSUVA4Pusbe8CTTCk3aRIGaxsSp7PGYq1rp1SCGBzGjfdVgcn2LmqVNrQluktsgOI/s1600/EAA_EWH_SS12_MAD.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">SS12: Manhattan allocation diagram</td></tr>
</tbody></table>
<br />
<b>Most popular Top25 universe</b><br />
<br />
<a href="http://etfdb.com/compare/volume/" target="_blank">ETFdb</a> keeps track of the Top100 most heavily traded exchange-traded products. Inspired by this list the Top25 universe is a selection with non-leveraged ETFs only: AGG, DBC, EEM, EFA, EWJ, FEZ, FXI, GLD, IWM, IYR, JNK, LQD, MDY, QQQ, SHY, TLT, XLB, XLE, XLF, XLI, XLK, XLP, XLU, XLV and XLY. With 25 assets and IEF kept outside the basket as CPF, the allocation limit for this universe is set to 5+1.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJ9IXGI9_U3ISWFi6imT173y-v0T5HRuiO2mPrsBISHmoj5AUFV8gtPgXxlY11eyMvpC_1ciH9scNmkttINFAZoRSm_-7wyxtPKbi7Cn5I9rpAf5VDaMfUqDauaFydJzbz-6eaa8uwyxs/s1600/EAA_EWH_T25_Comparison.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="190" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJ9IXGI9_U3ISWFi6imT173y-v0T5HRuiO2mPrsBISHmoj5AUFV8gtPgXxlY11eyMvpC_1ciH9scNmkttINFAZoRSm_-7wyxtPKbi7Cn5I9rpAf5VDaMfUqDauaFydJzbz-6eaa8uwyxs/s1600/EAA_EWH_T25_Comparison.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHfEyh8CEmO36Vo-EM2YZwgt2IDk0hDeZLAYKFKbV1fnxeHc7pcWBJXrHNizcFWSesK2iVI9g0kNXOfZyjlfaSbzelPFvC8f8OqvZumlbM0AEJuRZe-9dBkcInBiwf4GGANDlKg_LGZHI/s1600/EAA_EWH_T25_KPI.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="392" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHfEyh8CEmO36Vo-EM2YZwgt2IDk0hDeZLAYKFKbV1fnxeHc7pcWBJXrHNizcFWSesK2iVI9g0kNXOfZyjlfaSbzelPFvC8f8OqvZumlbM0AEJuRZe-9dBkcInBiwf4GGANDlKg_LGZHI/s1600/EAA_EWH_T25_KPI.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Top25: equity curve with key performance indicators</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-ZX8Q5W-3KK9eEdVOfm9rQ3Gq4j7nRUoi8YhU5MF6vs-SQmBQoUOGHKyfvRQfHvc2hMygotosJYK5wxWWNUw54twx5eHjUyCaQLq-KwzzXDAu1orpwY73cw2IJkfEA-EaBetDeynDD0s/s1600/EAA_EWH_T25_YR.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="392" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-ZX8Q5W-3KK9eEdVOfm9rQ3Gq4j7nRUoi8YhU5MF6vs-SQmBQoUOGHKyfvRQfHvc2hMygotosJYK5wxWWNUw54twx5eHjUyCaQLq-KwzzXDAu1orpwY73cw2IJkfEA-EaBetDeynDD0s/s1600/EAA_EWH_T25_YR.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Top25: yearly returns</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMBVJqwe0rByB5PShWlIV02BNmH7tG9yP7EiHusmEA1RSp3Ppinli8Rr24duHVYq37pwbIiHysGEsbuLa_otyWiiBubssssFKGhs3pYwnlrcxhFle6CABymAX64qOX8-i8Li4jmqgYWMA/s1600/EAA_EWH_T25_PC.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="212" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMBVJqwe0rByB5PShWlIV02BNmH7tG9yP7EiHusmEA1RSp3Ppinli8Rr24duHVYq37pwbIiHysGEsbuLa_otyWiiBubssssFKGhs3pYwnlrcxhFle6CABymAX64qOX8-i8Li4jmqgYWMA/s1600/EAA_EWH_T25_PC.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Top25: profit contributions</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXZ0wfHhdW0kL549qYO-v2Xf-RbeCfqdxt8rV3dgfyopIXT4IlWlTb-E3UyGiXkoQloVrvQPjq042rtiHG-1KPyfnyVv4k-9H1tRVCGRa6zuMQY7u-z7PjetjRHill23vMrt65cR3kdWE/s1600/EAA_EWH_T25_CC.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="394" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXZ0wfHhdW0kL549qYO-v2Xf-RbeCfqdxt8rV3dgfyopIXT4IlWlTb-E3UyGiXkoQloVrvQPjq042rtiHG-1KPyfnyVv4k-9H1tRVCGRa6zuMQY7u-z7PjetjRHill23vMrt65cR3kdWE/s1600/EAA_EWH_T25_CC.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Top25: 2 standard deviations confidence channel (95%) for rolling 1 year returns</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUMhLGw_RdYHM5RIMDnnxSZEWEKfROzwl3v0e3d507xSZDGsZD1uigehup_VmAphF3U4jc-cteDJs2Lh6jQRTERSfsN6wqLdSwM1LtqXTO4ZCS_Mf_dfinpbUsZD_8LWQh6x7juwY01u8/s1600/EAA_EWH_T25_MAD.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="212" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUMhLGw_RdYHM5RIMDnnxSZEWEKfROzwl3v0e3d507xSZDGsZD1uigehup_VmAphF3U4jc-cteDJs2Lh6jQRTERSfsN6wqLdSwM1LtqXTO4ZCS_Mf_dfinpbUsZD_8LWQh6x7juwY01u8/s1600/EAA_EWH_T25_MAD.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Top25: Manhattan allocation diagram</td></tr>
</tbody></table>
<br />
<b>CXO's on steroids </b><br />
<br />
From CXO's original basket EEM, EFA, IWM, IYR, SPY and TLT are replaced with their 300% leveraged versions, resulting in the following universe: DBC, DRN, DZK, EDC, GLD, TMF, TNA and UPRO (the replication process as well as the necessity for some salt is <a href="http://indexswingtrader.blogspot.com/2014/12/about-time-leverage-and-few-grains-of.html" target="_blank">explained here</a>). Again IEF is used as the external CPF. For this wild pack faster settings for EAA are suitable resulting in a responsive model. Therefore <b>ri</b> is based on 1 and 3 month returns only.<br />
Acknowledgement for researching CXO's tripled universe goes to Aurelia. Nice trouvé.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio43_UfwICwQZJb5PMXMPKHeJ33OlXKtDgk9BP12STdid_WjhLUoLq0xXBnixxTWdD5wh58gM_p6acWWRg-lwMOykNMIjF5BD7KZlIkpaY82VD1PJyvVX_J9R0Y4EnBO4c-k9Tdn7zG7M/s1600/EAA_EWH_3xCXO_Comparison.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="190" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio43_UfwICwQZJb5PMXMPKHeJ33OlXKtDgk9BP12STdid_WjhLUoLq0xXBnixxTWdD5wh58gM_p6acWWRg-lwMOykNMIjF5BD7KZlIkpaY82VD1PJyvVX_J9R0Y4EnBO4c-k9Tdn7zG7M/s1600/EAA_EWH_3xCXO_Comparison.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEje_8DPkWLSu0fBPs_l3Wc7GFnTZnWDAKUwWG6oQA033LsfofXEX73P3eX6TdUSlpOGpFCsJt5RnwSEvnsLreFwUsg2ztRhGebTBIKNkibN83rny0WB22S9JtMfoO6QyrZJBJXbbK9OSB0/s1600/EAA_EWH_3xCXO_KPI.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="392" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEje_8DPkWLSu0fBPs_l3Wc7GFnTZnWDAKUwWG6oQA033LsfofXEX73P3eX6TdUSlpOGpFCsJt5RnwSEvnsLreFwUsg2ztRhGebTBIKNkibN83rny0WB22S9JtMfoO6QyrZJBJXbbK9OSB0/s1600/EAA_EWH_3xCXO_KPI.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">3xCXO: equity curve with key performance indicators</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9I-Gh01-QYfyphw6STfx5IdpoAho571ORaUsW-X2epIPyi6FGhnCQ4sIDjNA-_pY8rE3fW7Z4Px2a7Zc5g03UaMYW2Ys9oHqCd07yvpFEABT_DBesLcxoZ3KQy3zbHeDhMy4om3HQ88c/s1600/EAA_EWH_3xCXO_YR.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="392" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9I-Gh01-QYfyphw6STfx5IdpoAho571ORaUsW-X2epIPyi6FGhnCQ4sIDjNA-_pY8rE3fW7Z4Px2a7Zc5g03UaMYW2Ys9oHqCd07yvpFEABT_DBesLcxoZ3KQy3zbHeDhMy4om3HQ88c/s1600/EAA_EWH_3xCXO_YR.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">3xCXO: yearly returns</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizfu8qRoHa1bqXGrIA-zsBRfVEJb8ITOxFhSeLBBgDMEpqQSL3UtBsGyM7BM9w2_7YlQXLMZv0T5ineUJjKuGUaKN8E0_jYIPMpY0-h6uVNt0J2TBLK4aZ8RR-gblBY07rT1gexp-Lzto/s1600/EAA_EWH_3xCXO_PC.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="394" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizfu8qRoHa1bqXGrIA-zsBRfVEJb8ITOxFhSeLBBgDMEpqQSL3UtBsGyM7BM9w2_7YlQXLMZv0T5ineUJjKuGUaKN8E0_jYIPMpY0-h6uVNt0J2TBLK4aZ8RR-gblBY07rT1gexp-Lzto/s1600/EAA_EWH_3xCXO_PC.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">3xCXO: profit contributions</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5_Wgg0KbpnJcVJcK-T4i0jW24v9mEPvQirqi5jOCc-W40mYqIJlymj9rqOXUZ-rsPSge20bvtLNsVazq7FFjSftq1V7uQBHzrKxtHaTul1vyk5Wz52RKS4iYqG_AeoTDpK2lnMrEYh0Y/s1600/EAA_EWH_3xCXO_CC.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="392" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5_Wgg0KbpnJcVJcK-T4i0jW24v9mEPvQirqi5jOCc-W40mYqIJlymj9rqOXUZ-rsPSge20bvtLNsVazq7FFjSftq1V7uQBHzrKxtHaTul1vyk5Wz52RKS4iYqG_AeoTDpK2lnMrEYh0Y/s1600/EAA_EWH_3xCXO_CC.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">3xCXO: 2 standard deviations confidence channel (95%) for rolling 1 year returns</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDWt_v2jncoV6f1m4J_Thp_2O5pB65XFcdYJyVzPmfjsoYBZQ3kPnLF-7QJyBDlvbsUt-RkTBO6FKlSo3wUrRBQxrqD4-MnbGOSxG_FQp65bm67IRQnxz9kbi9KeFQrXH07AMraI-8Ce0/s1600/EAA_EWH_3xCXO_MAD.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="212" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDWt_v2jncoV6f1m4J_Thp_2O5pB65XFcdYJyVzPmfjsoYBZQ3kPnLF-7QJyBDlvbsUt-RkTBO6FKlSo3wUrRBQxrqD4-MnbGOSxG_FQp65bm67IRQnxz9kbi9KeFQrXH07AMraI-8Ce0/s1600/EAA_EWH_3xCXO_MAD.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">3xCXO: Manhattan allocation diagram</td></tr>
</tbody></table>
<br />
<b>Leveraged CXO's untamed </b><br />
<br />
Switching off EAA's c(r)ash protection routine unleashes the triple leveraged universe to its full extent.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjggZbtj-SFxNc4HVkDHFB5Cd06G_kt2oBgILytAG3HfKMSPz5d50IxI_cCq0PNLB9h4RjvVzasYPdtDjZwYd353U0fW-1HJU86ghtoWyuEzkvvmgnSwl6fnqVvaioNDdUU2YSl9uo9008/s1600/EAA_NoAllocation.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="367" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjggZbtj-SFxNc4HVkDHFB5Cd06G_kt2oBgILytAG3HfKMSPz5d50IxI_cCq0PNLB9h4RjvVzasYPdtDjZwYd353U0fW-1HJU86ghtoWyuEzkvvmgnSwl6fnqVvaioNDdUU2YSl9uo9008/s1600/EAA_NoAllocation.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">EAA-model settings for 3xCXO CPF off</td></tr>
</tbody></table>
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmdj5xtmdtHR-d9jQSR-Ujirp6jJFozmrm1O_uaygIK6njrt1X2gxVErOWMosfxQr5ar0EupZH0HvB2ZyTYxY29Rlou1lZtueIfKkP_kqD_bV0w0Bg_PADamNrYa4vaFztR-arO1RxIaI/s1600/EAA_EWH_3xCXOnoCPF_Comparison.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="190" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmdj5xtmdtHR-d9jQSR-Ujirp6jJFozmrm1O_uaygIK6njrt1X2gxVErOWMosfxQr5ar0EupZH0HvB2ZyTYxY29Rlou1lZtueIfKkP_kqD_bV0w0Bg_PADamNrYa4vaFztR-arO1RxIaI/s1600/EAA_EWH_3xCXOnoCPF_Comparison.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggJwrspjCCiakLaZBdoad6QVnPQR8I6iVbGUqMQnyep3Eoe0E9pNIL06z6xWLKfihbIHKbFeIxMghSWF5wMpeWllDnFPk-Cdbl0ysf94K086Z8mX-zx5Kqa9y2AL__aPRI7xlZDU4NkE8/s1600/EAA_EWH_3xCXOnoCPF_KPI.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="390" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggJwrspjCCiakLaZBdoad6QVnPQR8I6iVbGUqMQnyep3Eoe0E9pNIL06z6xWLKfihbIHKbFeIxMghSWF5wMpeWllDnFPk-Cdbl0ysf94K086Z8mX-zx5Kqa9y2AL__aPRI7xlZDU4NkE8/s1600/EAA_EWH_3xCXOnoCPF_KPI.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">3xCXO CPF off: equity curve with key performance indicators</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbWuLdgs8dHnOpcTXWFQeRl6L5ayHQdLRMdBc8VLbrs7QyZoRe7ov4EeGg97TS_ci-mnumNEw2xnjaMztVof82Ku7Z_UxUZxA3FgKI4AfrSJX0bVsYBogWPC4-u8qhiBILIxLxAVcVhKE/s1600/EAA_EWH_3xCXOnoCPF_YR.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="390" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbWuLdgs8dHnOpcTXWFQeRl6L5ayHQdLRMdBc8VLbrs7QyZoRe7ov4EeGg97TS_ci-mnumNEw2xnjaMztVof82Ku7Z_UxUZxA3FgKI4AfrSJX0bVsYBogWPC4-u8qhiBILIxLxAVcVhKE/s1600/EAA_EWH_3xCXOnoCPF_YR.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">3xCXO CPF off: yearly returns</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhq2Fc04dqIwbXx_Eb-q93kTOIv4GacZ9nul-UmUcMacP1dp1D9egCGQsgOb0F4jD8uNIb1WuopOMhixrKcSWeClF4UPTWDfwPKbXyEVc-c1aeq5H4z40unxm-7mMSFn4fNQjQs2Q3M7kM/s1600/EAA_EWH_3xCXOnoCPF_PT.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="456" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhq2Fc04dqIwbXx_Eb-q93kTOIv4GacZ9nul-UmUcMacP1dp1D9egCGQsgOb0F4jD8uNIb1WuopOMhixrKcSWeClF4UPTWDfwPKbXyEVc-c1aeq5H4z40unxm-7mMSFn4fNQjQs2Q3M7kM/s1600/EAA_EWH_3xCXOnoCPF_PT.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">3xCXO CPF off: monthly profit table with yearly CARs and MaxDDs</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAIPPxN8mw7oz_Tm-JogzH8oIZgMJMDwpnu76t6DgIha1Qw9KWVRThyUOQeohKaG5atqTbY7SOIYgFbEpIGbDIRaWWhpRfrPx1-x-oJAiKTuPMuOgN8NQJuXOLjFTK-Y772WPS9xakSO0/s1600/EAA_EWH_3xCXOnoCPF_MAD.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAIPPxN8mw7oz_Tm-JogzH8oIZgMJMDwpnu76t6DgIha1Qw9KWVRThyUOQeohKaG5atqTbY7SOIYgFbEpIGbDIRaWWhpRfrPx1-x-oJAiKTuPMuOgN8NQJuXOLjFTK-Y772WPS9xakSO0/s1600/EAA_EWH_3xCXOnoCPF_MAD.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">3xCXO CPF off: Manhattan allocation diagrams. Notice the difference with the above MADs.</td></tr>
</tbody></table>
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<b>*</b> Please note 1994 is not part of the backtest period for comparability reasons. However 1994 was a particular nasty year for all presented universes resulting in worse performance metrics by a few tenths of a percent for the non-leveraged universes. This affects CAR as well as MaxDD. For the leveraged universe differences are somewhat bigger:<br />
<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoN43G7esdmHkItAcOhanUvhNZQnFDmYxEZI1tza5atRq3FRT5Iptg1leYNB3BPizI9kbsRnN5FaE-7c3p3SLOgzYV1GQ5d0JSLbsqSVAdR6jFi0d6GF6WAPykp4A_HNEtfZPo3fH9qCI/s1600/EAA_EWH_3xCXO_1993-2014.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="388" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoN43G7esdmHkItAcOhanUvhNZQnFDmYxEZI1tza5atRq3FRT5Iptg1leYNB3BPizI9kbsRnN5FaE-7c3p3SLOgzYV1GQ5d0JSLbsqSVAdR6jFi0d6GF6WAPykp4A_HNEtfZPo3fH9qCI/s1600/EAA_EWH_3xCXO_1993-2014.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">3xCXO CPF off covering 1993 - 2014</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXNwWIPW9I4ArAoyPr4IvM2nxtxx1yw4KftlePwlWK6UPvWGQ3Sd9PsC_1A7adjL-hx5URrz3WZBDEH_kjd050DrsK67dyOTVY_q8egjkSqS7WYrNNjJJzkUljndhCqNoaOtfcH_pYyYw/s1600/EAA_EWH_3xCXO_1993-2014_DD.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="390" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXNwWIPW9I4ArAoyPr4IvM2nxtxx1yw4KftlePwlWK6UPvWGQ3Sd9PsC_1A7adjL-hx5URrz3WZBDEH_kjd050DrsK67dyOTVY_q8egjkSqS7WYrNNjJJzkUljndhCqNoaOtfcH_pYyYw/s1600/EAA_EWH_3xCXO_1993-2014_DD.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Draw down chart for 3xCXO CPF off covering 1993 - 2014</td></tr>
</tbody></table>
<br />
The modified version of the AmiBroker code is available upon <a href="mailto:trendxplorer@gmail.com?Subject=Request%20for%20EAA%20model%20in%20AmiBroker" target="_blank">request</a>. The model now has quarterly reforms and three CP settings implemented too. Interested parties are encouraged to support this blog with a donation.<br />
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