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.

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.

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.

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.


Launched only recently, 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 free limited membership or sign up for full membership to access all the neat features.

Disclaimer: Signing up to through my blog provides support for my work.

Deciphering Correlation Hedged Momentum

In a new SeekingAlpha contribution 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.

The correlation hedge is a simplified version of Keller and Butler’s EAA-formula (see paper or primer). For GPM we only use return and correlation information as momentum metric. We do so with two variations:
  • GPMxM: the correlation multiplied return metric ri * ( 1 – ci )
  • GPMxF: the correlation fractioned return metric ri / ( 1 + ci )
where x is the degree of crash protection, ri is the average return of asset i over 1, 3, 6 and 12 months, and ci the 12-month correlation of asset i with the equal weighted “risky” investment universe. The correlation multiplier ( 1 – ci ) is based on the EAA-model, the correlation fraction 1 / ( 1 + ci ) was recently suggested by Wouter Keller. For the mechanics of the crash protection algorithm, see the PAA-post.

In the graph below, the two correlation hedge variations are painted.