## replace_date('14 July 2017');

### Breadth Momentum and Vigilant Asset Allocation (VAA)

• Breadth momentum quantifies risk at the universe level by the number of assets with non-positive momentum relative to a breadth protection threshold.
• Vigilant Asset Allocation matches breadth momentum with a responsive momentum filter for targeting offensive annual returns with defensive crash protection.

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 SSRN

The VAA recipe
1. Given a top selection T and a breadth protection threshold B, for each month:
2. Compute 13612W momentum for each asset
3. Pick the best performing assets in the “risk-on” universe as top T
4. Pick the best asset in the “risk-off” universe as safety asset for “cash”
5. Compute the number of assets with non-positive momentum in the “risk-on” universe (b)
6. Compute b/B and round down to multiples of 1/T as “cash fraction” CF for “easy trading”
7. Replace CF of top T by “cash” asset as selected in step 3

13612W momentum filter

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 GEM, Keller’s price relative to its 12-month simple moving average (SMA12) for PAA, or Faber’s averaged momentum over the past 1, 3, 6, and 12 months (13612) for GTAA. 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:
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
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.

Within the VAA frame work our 13612W filter is applied for both relative and absolute momentum.

## replace_date('31 May 2017');

Just in time for EOM May the Strategy Signals page is functional again. Like before, signals are based on dividend adjusted historical data, now obtained from Quandl's premium QuoteMedia EOD service (\$). Current month's data is grabbed "real time" from Google Finance. The signals are yet to be considered "experimental" in order to review data quality and table performance.

## replace_date('18 May 2017');

### Yahoo Finance API Ceased Working

Unfortunately 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.

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.

## replace_date('09 March 2017');

### Index Mapping For ETF Proxies

In order to present results as realistic as possible in our PAA-paper, we constructed long-term end-of-month data series for popular ETF proxies, like SPY, GLD and TLT (see paper appendix on SSRN). 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 EFA. The link to an example spreadsheet with all the necessary calculations is published at the end of this post.

EFA 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 MSCI website. Comparing EFA’s historical data record against the various index levels supported by MSCI like Price, Gross, Net, reveals the MSCI EAFE Net index as underlying index. Historical dividend adjusted data for EFA itself is offered by Yahoo Finance, also for free. For constructing a long-term EFA proxy the data from both sources is required.

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.

After Solver finishes the calculation cycles, the found coefficients result in high R-Squared and correlation readings.

## replace_date('24 December 2016');

### Ho, Ho, Ho: Excel VBA For Global Equities Momentum

Just in time for Santa! Based again on a foundation by InvestExcel, Denis Bergemann collaborated with me on another Excel VBA project covering Gary Antonacci's popular Global Equities Momentum (GEM).

The VBA driven Excel spreadsheet follows the official rules for GEM (see here) 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.

[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 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.

Results for both the GEM and 60/40 portfolios as well as the separate components are presented in tabular and graphical format.

## replace_date('23 October 2016');

### Flexing VBA For Quants (And Everyone Else)

Would it not be great to have the models for Protective Asset Allocation (PAA) and Global Protective Momentum (GPM) in Excel, so you can run your own backtests without AmiBroker? And not being limited to a pre-defined universe? Actually, now you can.

Based on a foundation by InvestExel, 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.

## replace_date('04 October 2016');

### Prospecting Dual Momentum With GEM

• Gary Antonacci popularized dual momentum with an effective and simple approach for dynamic asset allocation: Global Equities Momentum (GEM).
• Using simulated ETF data series, GEM’s performance over past market conditions can be approximated.
• For longer investment horizons GEM’s implementation with ETFs obtained positive returns with high consistency.
After winning first place in 2012 in the NAAIM Wagner competition, Gary Antonacci popularized his momentum investing approach in the award winning book “Dual Momentum Investing”.

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.

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.

Both in his book and on his website, 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.

Noteworthy, the rules often shared for GEM, derived from the flow chart on page 101, are not 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 PerfCharts to get their signals. However, when doing calculations with a charting program like AmiBroker, the instructions on page 98 are to be adhered instead.