Flexible Asset Allocation

Flexible Asset Allocation

January 3, 2013 Research Insights
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(Last Updated On: January 13, 2017)

Generalized Momentum and Flexible Asset Allocation (FAA) An Heuristic Approach

  • Wouter J. Keller and Hugo S.van Putten
  • A recent version of the paper can be found here.
  • Note: CXO Advisory has a recent post on this, but I was 90% done with this post so I’m posting anyway. CXO has a more detailed analysis for subscribers to their site.


In this paper we extend the timeseries momentum (or trendfollowing) model towards a generalized momentum model, called Flexible Asset Allocation (FAA). This is done by adding new momentum factors to the traditional momentum factor R based on the relative returns among assets. These new factors are called Absolute momentum (A), Volatility momentum (V) and Correlation momentum (C). Each asset is ranked on each of the four factors R, A, V and C. By using a linearised representation of a loss function representing risk/return, we are able to arrive at simple closed form solutions for our flexible asset allocation strategy based on these four factors. We demonstrate the generalized momentum model by using a 7 asset portfolio model, which we backtest from 1998-2012, both in- and out-of-sample.

Data Sources:


Strategy Summary:

  • Test a few different signals for market and asset class timing.  The authors then combine these signals.  They are using 7 asset classes described here:
    • Our example universe consists of 7 index funds (so U=7), i.e. 3 for global stocks (VTSMX, FDIVX, VEIEX) covering US, EAFE and EM regions, 2 for US bonds (VFISX, VBMFX) and a commodity and REIT index fund (QRAAX, VGSIX). Users only interested in recent years can use the corresponding ETFs (eg. VTI, VEA, VWO, SHY, BND, GSG, and VNQ) which follow the same indices as our index funds.
  • They use a 4 month lookback for prices in the paper.
  • Each month, rank all 7 based on relative momentum (higher is better), volatility (lower is better), and correlations (lower is better).  So each of the seven assets has a rank from 1-7 for the 3 factors.
  • Then rank using this equation:
    • Li = wR * rank(ri) + wV * rank(vi) + wC * rank (ci)
    • Authors arbitrarilly set wR=1, wV=0.5, and wC=0.5.
  • This new variable “Li” now ranks all the assets on relative momentum, volatility, and correlations.  Pick the top 3 assets each month and equal weight these.
    • Last, for each of the top 3 assets chosen above, check their absolute momentum – if this is negative, just go into cash.
  • Make money!

Strategy Commentary:

  • Simple way to combine absolute momentum, relative momentum, volatility, and correlations.
  • Paper also shows better returns when not equal weighting the top 3 assets, but this is more complicated.
  • Cool paper…but one gripe…

Translation of the very obtuse abstract:

We mix momentum, risk parity, and correlation factors–factors all known to work in sample for tactical asset allocation models–and compile them into a model that tells us what we already know: these factors work historically. We forgot to include a test of our model against Meb Faber’s ridiculously easy long-term moving average rule as a benchmark comparison (instead opting to include the buy&hold benchmark, which sucks), because that would make all our complicated models seem worthless.

One paper you might want to explore if this sort of stuff turns you on is Gary Antonacci’s piece:



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Definitions of common statistics used in our analysis are available here (towards the bottom)

About the Author

Wesley R. Gray, Ph.D.

After serving as a Captain in the United States Marine Corps, Dr. Gray earned a PhD, and worked as a finance professor at Drexel University. Dr. Gray’s interest in bridging the research gap between academia and industry led him to found Alpha Architect, an asset management that delivers affordable active exposures for tax-sensitive investors. Dr. Gray has published four books and a number of academic articles. Wes is a regular contributor to multiple industry outlets, to include the following: Wall Street Journal, Forbes, ETF.com, and the CFA Institute. Dr. Gray earned an MBA and a PhD in finance from the University of Chicago and graduated magna cum laude with a BS from The Wharton School of the University of Pennsylvania.

  • nlavery

    Wes, your analysis of this paper is excellent (and funny). Too bad the paper was so poorly written. Toby

  • wkeller

    Hi Wes

    Thanks for your nice review of our paper, sorry for the “very obtuse” abstract.

    The results of Meb’s long-term moving average as benchmark would be comparable to our model with only the A-factor (absolute momentum). This simple model has a Sharpe(0%) of 1.0, compared to a Sharpe of 1.6 for the full 4-factor (A+R+V+C) model in the paper. Alternatively, you could consider the A+R model in the paper as a benchmark.

    I am happy to look into a simple MA model. We think, however, that absolute momentum is more appropriate in our momentum context, as is explained in the paper. And I am sure the MA results will be comparable to the results of absolute momentum mentioned above.

    Since English is not my native language, can you give me some suggestions to make the abstract (or paper) less “obtuse”?

    Wouter J. Keller
    Flex Capital

  • CyberTrader123


    Any clue what the Authors might have used to calculate “Relative Momentum”? I have tried RSI(80) for 4 months relative momentum and no matter what I do I can’t produce the results the authors mentioned just with “Relative Momentum” using funds (VTSMX, FDIVX, VEIEX) (VFISX, VBMFX) (QRAAX, VGSIX).


  • we are in the middle of attempting to replicate the results as well–having fits in the process. Will let you know what we find.

  • wkeller

    @CyberTrader123: Return momentum is simply Rx=(Pt/Pt-x)-1 where Pt is the (dividend adjusted) price at the close of month t and Pt-x idem of month t-x, with eg. x=4m. Then (for the simple factor R model) you rank the 7 assets on Rx and buy the Top3 out of 7 at the open of the new month with equal capital shares. Dont forget that with R+A we replace the assets with Rx<0 by Cash. Data from Yahoo.

  • wkeller

    @Wes: I bought your book Quantitative Value and found it very interesting and well written. But I noticed that you seem to use the buy&hold S&P500 as benchmark all-over in the book. Doesn’t that “sucks”, in view of your remarks above? I also would like to have seen more on value investments in other assets than US stocks. Did you see the paper on Value and Momentum Everywhere from AQR?

  • Hi,
    We also include the Magic Formula to ensure we have a “sophisticated” benchmark in addition to the benchmark that everyone knows and loves. We were also looking at long-only so we focused on long-only benchmarks.
    We would have like to include some more results on markets out of the US, but our editor wanted us to stay focused.
    Thanks for your suggestions.

  • wkeller

    In our paper we also include the R, RA, and RAV benchmarks to ensure we have several “sophisticated” benchmarks in addition to the “sucking” 7-assets global B&H benchmark. So far for our “very obstute” abstract/paper. (Sorry, I could not resist.)

    Thanks for your suggestions. We consider to include Value as long (5y) negative momentum in a revision of the paper. Preliminary tests show that that seems to work.

  • wkeller

    For anyone trying to replicate our model, we have some in-between results for the RAV model available for starters (in an Excel sheet).

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  • (From a TKA reader)
    I was able to replicate Keller Putten’s FAA study, but came to a troubling conclusion in the process: their study results are entirely dependent on the end of month calendar anomaly.

    Until I forced trades to occur on the first day of the calendar month with the ranking on the last day of the previous calendar month, my results were horribly different from the study. When I required that I hold a trade for one “holding” month (21 trading bars) and then select and rebalance after each “holding” month (vs “calendar” month), my results did not match the study. Using a 21 day holding month, my trades tended to drift into different parts of a calendar month as 21 trading bars did not match exactly to trading days in a calendar month; I ended up trading on days different from the first day of the calendar month. Nonetheless, I always kept the 4 month (using 21 day holding months) lookback constant.

    So, using holding vs calendar month the following comparison of My results vs Ketter & Putten (KP) results occurred:

    1. My returns for 4 month momentum lookback were about the same as KP at 9% CAGR, but the holding month had lower drawdowns.

    2. My returns for 4 month momentum lookback with 4 month absolute ROC > 0 was worse, as I held at 9% CAGR while the KP study improved to 11% CAGR with reduced drawdown

    3. My returns for #2 with Volatility – I came in at 6% CAGR while the KP study progressed nicely to 12% CAGR

    4. Finally, my returns for #3 and Correlation – I came in at 5% while the KP study blossomed to 14%.

    Basically, by not having hard cut-offs at calendar month end my asset holdings did not always get out in time to avoid large drawdowns. My drawdowns using holding vs calendar months were terrible.

    So I made one change to my code: I used a calendar month to decide when to rotate. And voila, month-end anomaly magic happened. I replicated Keller & Putten.

    My code is in Amibroker.

    BTW, the problem with Faber’s 10 Month Moving average results is that it is dependent on the month end effect as well.

    I have thoughts on how to use a more abstract concept of “cycles” to capture the month-end effect without depending on the calendar, but that is for another day.


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