A Surprising Way to time Value and Momentum: Updated Analysis

A Surprising Way to time Value and Momentum: Updated Analysis

August 28, 2014 Value Investing Research, Momentum Investing Research, Tactical Asset Allocation Research
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(Last Updated On: March 15, 2015)

Exploiting Factor Autocorrelation to Improve Risk Adjusted Returns

Abstract: 

The Fama-French three factor model is ubiquitous in modern finance. Returns are modeled as a linear combination of a market factor, a size factor and a book-to-market equity ratio (or “value”) factor. The success of this approach, since its introduction in 1992, has resulted in widespread adoption and a large body of related academic literature. The risk factors exhibit serial correlation at a monthly timeframe. This property is strongest in the value factor, perhaps due to its association with global funding liquidity risk. Using thirty years of Fama-French portfolio data, I show that autocorrelation of the value factor may be exploited to efficiently allocate capital into segments of the US stock market. The strategy outperforms the underlying portfolios on an absolute and risk adjusted basis. Annual returns are 5% greater than the components and Sharpe Ratio is increased by 86%. The results are robust to different time periods and varying composition of underlying portfolios. Finally, I show that implementation costs are much smaller than the excess return and that the strategy is accessible to the individual investor.

Alpha Highlight:

This interesting paper “Exploiting Factor Autocorrelation to Improve Risk Adjusted Returns” caught our attention. We highlighted this paper a month ago via a paper summary, but decided to dig a little deeper.

The paper claims that by using HML to switch between small value and small momentum portfolios, the strategy can generate superior returns. We conducted our own backtesting by using data from the French website.

The first part of our study is the replication of the paper’s strategy; Second part is the robustness test;  Third part is implementation discussion.

Data

Monthly returns from 01-1984 to 12-2013

  1. Value-weighted 6 Portfolios Formed on Size and Book-to-Market (2 x 3)
  2. Value-weighted 6 Portfolios Formed on Size and Momentum (2 x 3)
  3. Value-weighted 100 Portfolios Formed on Size and Book-to-Market (10 x 10)
  4. Value-weighted 25 Portfolios Formed on Size and Momentum (5 x 5)
  5. PDP, PRF total return series, 01-2006 to 12-2013,  from Bloomberg

Strategy

According to the paper:

2014-08-05 15_09_22-Exploiting Factor Autocorrelation to Improve Risk Adjusted Returns.pdf - Adobe A

We follow the same strategy:

  • IF last month’s HML > 0 and Return (value) > 0, then go into value (high b/m, small);
  • IF last month’s HML < 0 and Return (MOM) > 0, then go into MOM (high mom, small);
  • IF last month’s return < 0 then go into risk-free;
  • IF none of above exists, then go into risk-free.

Replication

VW 2 x 3 size/bm and 2*3 size/mom. We selected SMALL value and SMALL momentum, using SMALL HML (small size high bm minus small size low bm) as the switching signal. The results from our analysis and the corresponding table from the paper are tabulated below:

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

Paper results

2014-08-15 12_54_41-Exploiting factor autocorrelation to improve risk adjusted returns.pdf - Adobe R
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

$1 Dollar Growth

small val mom 6
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

Paper results

2014-08-15 12_56_49-Exploiting factor autocorrelation to improve risk adjusted returns.pdf - Adobe R
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

The results are not as good as what is stated in the paper, but still good enough to warrant further study and investigation.

Robustness test

Large caps

We still use VW 2 x 3 size/bm and 2*3 size/mom. However, we selected BIG value and BIG momentum, using BIG HML (big size high bm minus big size low bm) as the switching signal. The results drop significantly relative to the results for small-caps. However, the portfolio benefits from combing value and momentum exposures are still valid: sortino ratios are much higher and drawdowns are vastly improved.

big val mom 6 stat
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

$1 Dollar Growth

big val mom 6
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

More Refined Value and Momentum Portfolios

We use two extreme value and momentum portfolios: the value portfolio is the smallest value portfolio from the 10 x 10 size/bm portfolios cuts; the momentum portfolio is the smallest momentum portfolio from 5 x 5 size/mom cuts.

small val mom 25 100 stat
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

$1 Dollar Growth

small val mom 25 100
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

Small and concentrated portfolios generate stronger results. Wes recently had a nice post on the size effect “Does the size effect exist? Probably” if you’d like to explore further.

Implementation?

Results for small caps look good. But there are many implementation challenges. If one uses the small momentum 5 x 5 split and small value 10 x 10 split, one can easily end up with liquidity issues due to the size of firms in the portfolios. By using 2 x 3 split, one can limit liquidity issues, but the results aren’t as strong.

Are there other ways we can implement this strategy?

ETFs might be a good solution. Below we show the backtest results by using total returns of PDP (value) and PRF (momentum) from 01-2006 to 12-2013. “Portfolio” is the switch strategy between PDP and PRF based on 2 x 3 big HML signal.

pdp prf stat
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

$1 Dollar Growth

pdp prf
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

The results are strong. That said, implementing this strategy could be a challenge for the non-professional or non-quant geek investor. Good luck!

 

 

 


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




About the Author

Yang Xu

Mr. Xu is currently a managing member of Alpha Architect, where he leads the capital markets group and assists in quantitative research. Mr. Xu has unique skills related to "big data" analysis. His recent research investigates various proprietary trading algorithms, tactical asset allocation models, and longer-term security selection models. Prior to joining Alpha Architect, Mr. Xu was a Principal Data Analyst at Capital One, where he was a member of the Basel II data analysis team. Mr. Xu graduated from Drexel University with a M.S. in Finance, and from the University of International Business and Economics in Beijing, China, where he earned a BA in Economics.


  • Steve

    Love it. Takes me hours to do myself and I only generate half the stats you do…so thanks for all your work here Wes (and team!)

    As I mentioned in my other comment:
    http://www.alphaarchitect.com/blog/2014/08/26/interesting-tactical-asset-allocation-tool-hml-portfolios

    ….did you happen to try using a ‘switch’ strategy *without* an auto-correlation / trend following overlay on the strategy itself? i.e. Always in the market, in either Val or Mom? Without the risk free aspect?

    I found it to be better (2*3 portfolio, large cap, value weight).
    But just to clarify…in the “HML” part of the equation, I assumed: “Value minus Momentum”.

    i.e.

    If last months Value portfolio > Momentum portfolio, then this month is Value.
    If not, then switch.

    Then the author would say to run auto-correlation on the the strategy itself: i.e. if last month was a profitable month, then do the strategy this month…if not, then cash (at 3%)
    I found this degraded results.

    I now feel I might have tested a slightly different variation?

    My results were 14.50% CAGR on the same porftolio (2×3 large cap value weight) that you used Wes (back to 1928 or whatever)….beating both the momentum and value portfolios individually.

    Or I’ve botched something up!

    Still too many switches (I think) for a stock picker (unless ultra low brokerage I suppose), but that’s not recommended in the paper anyway….

  • Steve, I got an bullpen of geniuses grinding all this stuff. Over time I find myself on the phone 10hrs a day and my programming skills are degrading at a rapid rate. A sad state of affairs, but I guess that is the nature of things.

    Yang–who did most the work here–tried just about everything under the sun. The stories are all about the same. We also tried this on different value portfolios–like our quantitative value strat–and it doesn’t do anything. So I think it is a good concept, but the robustness is questionable…but that is the case with 99.99% of strategies, so that isn’t a knock per se.

  • Steve

    Absolutely…thanks Wes (and Yang!)

  • jlivermore

    I’ll echo that, and my hope was realized that the analysis would be extended: in this case to more extreme portfolios and real ETFs.
    The main difference to my analysis is that I always used the vanilla HML rather than calculating other versions for each set of component portfolios.
    Kevin (author)

  • Wray Grigorakis

    Interesting number crunching, Wes+team! Is there any chance that you guys can post the spreadsheet? I would be very helpful…

  • maquant

    Great work. Thank you. However I have two questions about it.

    -When I think about possible implementations…. I would need to get the HML data in realtime at least at the months end or do I miss something? Means self-calculation or approximiation with incides/ETFs.

    -What is “IF last month’s return < 0 then go into risk-free;".

    Last months portfolio return of the selected asset for the next month? Or the return of the asset that had been selected the month before?

  • 1. yep, you’d have to build out HML on your own.
    2. The return on the asset held the month before is less than 0

  • Wray, reach out via email and we can chat

  • Nick

    First of all, I love your site. Its refreshing to see people dedicated to evidence based investing!

    Has your group taken a look at one of the papers referenced in the above paper?
    Daniel K.D. and Moskowitz T.J., 2013, “Momentum Crashes” http://www.columbia.edu/~kd2371/papers/unpublished/mom10.pdf

    I’d be very interested to hear your thoughts on it.

    They had pretty impressive results as well, but I’m wary about a paper that is “unpublished”. Beyond that, it just made a lot of sense – Momentum strategies perform well, for the most part, and in varying markets the average beta of a momentum portfolio fluctuates from well above 1 in a raging bull market to below 1 in a bear market. Where you get hammered is during an extended bear market when the average beta of your momentum portfolio drifts downward, even into negative territory, and then the market makes a sudden rebound and all of a sudden you’re holding a bunch of negative beta stocks while the market is moving upward. This effect was especially amplified by the fact that their strategy included shorting the “losers” i.e. the bottom of the momentum pile, which would have left them shorting a lot of high beta stocks that would then translate into big losses on a big rebound within a bear market. They then try to overcome this by adjusting their holdings based on the average beta of the “winner” and “loser” portfolios and the amount of gap in the beta between the two. The math they use to figure that out that is a bit beyond my pay grade 🙂

    If you are so inclined, I’d like to hear what the pros (you!) have to say about the ideas in this paper.

  • Hey Nick,

    http://www.alphaarchitect.com/blog/2011/11/11/risk-managed-momentum/#.VADGtvldVMU

    We spoke about this paper at the above link.

    I like the idea and think momentum is a VERY powerful and lasting phenomenon. That said, nothing works all the time and every time…and you definitely need to figure out how to avoid a faceripping drawdown!

  • Jan Vrot

    I am not an expert on autocorrelation, so I could easily be making a mistake. When I use the Durbin-Watson test on the HML factor (30%-70%) I get a score of 1.9 (2005 to present) which does not support evidence of autocorrelation. How was autocorrelation tested in this research and could you replicate the data? I was also wondering how significant the findings were compared to randomly allocating between value and momentum and possibly the rf asset?

  • We weren’t that concerned with the autocorrelation coefficients when we did our replication and extension of this study. Our focus was on a more simple question: has this actually worked as a trading stategy–at least historically.

    Your question is a good one and “random allocation” portfolios that dump into risk-free look pretty decent over this time period–on average–because simply holding risk-free assets, and especially 10-years, is a great play. I think this strategy has a bit more mojo than random allocations, but not much (this is actually a complement to the strategy, fyi).

  • Chimpo

    Thanks for the additional analysis. I recreated the ideas from the paper as well and one thing I thought that really stands out is the improvement in the higher moments. Skewness is negative for both value and momentum individually but turns positive when combining them with the strategy. Kurtosis becomes greater too but since the skew is positive, that is not necessarily a bad thing. Just wanted to share my insights since I thought this is one of the most interesting results of the analysis.

    And by the way, if you want to extend your analysis beyond available ETFs you should check out: http://www.scientificbeta.com
    The site offers a whole range of very transparent factor indices. They share basically all the information on construction including constituents, methodology and time series. From what I can tell the construction process seem very realistic (maybe even a little too conservative from a tracking error point of view). Using those the results are not as great as with the Ken French dataset but the strategy is still ahead on a risk adjusted basis, not just in the US but also in other markets. I had to substitute the high bm with growth though as it is the closest thing availabel.

  • Thanks for sharing, Ger. I’m familiar with the scientificbeta website–super cool and thanks for highlighting for others.

  • Aaron

    Agree, I was wondering the same thing as I read the post. Just applying a trend following filter without switching between portfolios would probably give similar results.