Mind the Gap: A Way to Enhance Momentum Profits

Mind the Gap: A Way to Enhance Momentum Profits

November 5, 2014 Research Insights, Momentum Investing Research
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(Last Updated On: January 18, 2017)

The Momentum Gap and Return Predictability

Abstract: 

Momentum strategies have historically delivered high Sharpe ratios and large positive alphas. However, returns to these strategies also display significant time-variation that is not very well understood. I show that expected momentum returns vary negatively and monotonically with the formation period return difference between past winners and losers, which I term the momentum gap. A one standard deviation increase in the momentum gap predicts a 1.29 percent decrease in the monthly momentum return after controlling for existing predictors. The momentum gap remains a significant predictor in out-of-sample tests. Conditional momentum strategies using the momentum gap yield substantially higher Sharpe ratios and lower skewness than the unconditional strategy. These findings are less consistent with the notion that past return proxies for the loading on a priced risk factor. I find evidence to support the alternative hypothesis that momentum is a mispricing phenomenon and that the momentum gap measures momentum arbitrage activity.

Alpha Highlight: 

Momentum strategies, which go long past winners and short past losers, have historically outperformed. This paper extends the momentum research and finds that there is a negative relationship between momentum returns and the formation period return difference, or “gap,” between past winners and losers. The term for their enhanced momentum factor is Momentum Gapdefined here:

  • Momentum Gap is defined as the difference between 75th and 25th percentiles of the distribution of cumulative stock returns from month t-12 to t-2. (Paper also use 90th and 10th percentiles in their back tests.)

For example, let’s say you looked at stock returns from some year, say, 1991, and sorted them into quartiles based on momentum. You might find that at the 75th percentile, these relatively high momentum stocks returned, say, 12%, while at the 25th percentile, these relatively lower momentum stocks returned, say, 10%. In this case, the momentum “gap” between high/low momentum would be 2%. It turns out this gap changes over time (shows “time variation”).

The figure below plots the Momentum Gap based on the CRSP universe from 1926 to 2012.

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 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.

Key Findings: 

  1. The Momentum Gap is negatively related to momentum returns. That is, if the lagged momentum gap is small, subsequent long/short momentum returns are high; if the lagged momentum gap is large, subsequent long/short momentum returns are low.
  2. A one standard deviation increase in Momentum Gap is associated with a 1.29% decrease in the monthly momentum returns. (Details see Table 3). This new predictor is quite significant in out-of-sample tests.
  3. Conditional Momentum Strategies using the Momentum Gap yield substantially higher Sharpe Ratios and lower skewness than unconditional strategies.

The table below shows the relationship between the gap and subsequent momentum returns; when momentum gap is small (23.26% average gap), momentum earns large alphas of 2.23% per month, while when the momentum gap is large (52.17% average gap), momentum loses 0.13% a month.

2014-08-27 12_17_58-The momentum Gap and Return Predictability.pdf - Adobe Reader
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.

Since long/short momentum strategies work very well when the Momentum Gap is small, can one use this to time when to be in a momentum long/short strategy? The answer is yes, a conditional momentum strategy yields higher Sharpe ratios with lower skewness, as shown 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.
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 paper proposes 3 hypothesis to explain the Momentum Gap finding:

  • Hypothesis 1: The empirical relation is spurious and related to data-mining.
  • Hypothesis 2: The Momentum Gap’s predictive power is driven by its relationship to the business cycle.
  • Hypothesis 3:  The Momentum Gap reflects the degree to which arbitrageurs are trading the strategy, and thus momentum is a mispricing phenomenon.

The paper finds no evidence to support first 2 hypothesis, but does find evidence for hypothesis 3 (mispricing).

Overall, this is an interesting paper with an idea that appears to add value to a momentum strategy, by providing a timing mechanism (Momentum Gap). The only downside to such a strategy, is that one would not always be invested in the momentum long/short strategy (which may be an issue for institutional investors).


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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.


  • IlyaKipnis

    What I don’t like about these sorts of findings is that the universes aren’t comparable. EG if you’re trading some subset of securities (EG the 9 sector spiders), does the cumulative return of some other stock you’re not trading make any difference to you? To me, it seems this computation is based off of looking over an entire universe, only a subset of which is actually traded.

  • Doug

    So you trade the equity curve of a momentum fund. There has been a similar strand of research in the trendfollowing CTA world, where the old nugget of wisdom has always been “don’t invest in a CTA until they’ve had a bad year.” People have developed strategies to trade another strategy’s equity curve.
    I think this is the natural result of markets getting more efficient – people start looking at 2nd and 3rd order effects after the primary driver gets too much publicity.
    I also find it ironic that you are using a mean reversion strategy on top of a momentum strategy.

  • Jack Vogel, PhD

    Doug, just to clarify, this is a recap of a research paper by Simon Huang.

  • Jack Vogel, PhD

    Yes, the computation is based off the entire universe (not sure how the results would change if you split the universe up).

  • IlyaKipnis

    Trading the equity curve is far from a panacea. I tried it with a SeekingAlpha strategy replication, and even with a 200-day SMA filter, you’re still taking some heavy pain. It’s definitely something worth looking into, however.

  • Doug

    @ilya. Not promoting the efficacy of trading an equity curve, just making an observation that this looks a lot like that. I wonder if we’ll see a paper with a strategy to “trade the equity curve of someone trading the equity curve,” and so on. Turtles all the way down.
    @Jack Understood. Sorry for the vague use of “you.”

  • Jack Vogel, PhD

    No problem, thanks for the comments.

  • Steve

    Haven’t had a chance to read the paper yet…and this might be considered away from the topic of the paper anyway…but were you able to obtain (from the paper) whether the gap was useful to long only momentum?

  • Check out table 2 in paper…useful for long and short…we haven’t done an in-house replication and investigation, but certainly looks interesting

  • Steve

    cool, i’ll look forward to if you share your own results…so many ways these studies can go wrong.
    I’m wracking my brain trying to think if I’ve ever seen anything similar looked at with value. I don’t take good notes and I can’t remember any off hand.
    It’d be an interesting next step: does the value gap tell us anything?

  • Aaron

    I agree Doug. What used to be a persistent anomaly, now becomes an anomaly only when a few people are using the strategy. Everybody piles on and the returns aren’t attractive anymore. So everyone leaves, and the returns come back for a time.

    I think it’s possible to switch between historically outperforming strategies that keep coming back after getting knocked down – like value and momentum. Just look at the ones that have performed the worst, and go with that. You know that most people don’t have the emotional capacity to buy when everyone else is selling, and if it’s a strategy that most likely will have some outperformance in the future, you should be in a decent contrarian position.

  • Denys Glushkov

    Interesting paper, however, benefits of betting on mean reversion in factor premiums due to the arbitrage activity have already been extensively documented in the literature. For example, Lou and Polk (2012) show that during periods of low comomentum (proxy for periods when arbitrage trades are less crowded), momentum strategies are profitable and stabilizing, whereas following periods of high comomentum, momentum strategies become unprofitable and tend to crash.

    More generally, betting on mean reversion in factor premium should not be confined only to momentum. As Hsu (2014) shows in “Value Investing: Smart Beta vs. Style Indices”, smart beta strategies profit from mean reversion in the value premium by effectively implementing a dollar cost averaging program.

    My guess would be that performance of any theoretically sound return predictive signal can be potentially enhanced by conditioning it on the magnitude of the most recent factor premium relative to its long-run mean. Good paper, yes, novel, far from it.

  • Arjun K

    Did you guys ever end up doing an in-depth investigation of the paper? Maybe I’m doing something wrong, but when I attempted to recreate it, my numbers didn’t line up with figure 1 in the paper. Granted I’m only able to access pricing data from 1984-present day through Compustat, not CRSP, but my calculations found the momentum gap peaks in 2010, not 2009 like the paper states. Hoping you guys have taken a look and would be willing to discuss.

  • We looked at it a while ago and I know the author. We were having some issues replicating some of the results as well and questioned their robustness at a high level. That said, the idea is definitely interesting and worthy of further investigation, but we’ve been so buried in other projects we haven’t done a massive deep dive.

  • Arjun K

    Makes sense, thanks for the response. I tried emailing the author a while ago but got no response unfortunately (which wasn’t unexpected). Hopefully you guys get around to it since the idea sounds interesting if the data lines up.

  • Grant Colthup

    I am currently completing a PhD and have also had issues with replication. I also note that in Table 1 – Summary Statistics that the Market Return has a negative minimum value in excess of 100%. I can produce a correlation table that is consistent with that shown in Table 1, except for the correlation between Momentum Gap & Market Return.

  • Thanks for sharing, Grant. If you want to highlight your replication results on the blog, please post or let us know

  • Grant Colthup

    Hi Wesley,

    As you can see the standardized momentum gap computed using my data (from CRSP) and Ken French data (from his website differs quite considerably from that presented in Huang). The difference is particularly stark, fro 2009 when the authors claims there to be another spike, whereas using both other data sets, I find the spike in the later sample to occur in 2010.

    I also attach my attempt at replicating Table 2. I use both raw and “adjusted” returns (again I use returns and MG computed by myself and data from Prof. French) and struggle to replicate similar results. I attach a table, that shows the levels of momentum gap (MG) are roughly approximate by quintile. I also note that there is potential for difference between my results and Prof French as I do not use NYSE Breakpoints (Daniel & Moskowitz (2014) – NBER WP outline the impacts), there is no difference until 1963. Huang also uses NYSE Breakpoints.

    I note you mention you have had trouble replicating. I have further research that I can share if you would like to contact me privately.

    https://uploads.disquscdn.com/images/630d7445b6c557635e1482435ebe252f3c1750e5d321e28bc75a276d675be1f3.png

    https://uploads.disquscdn.com/images/1e96ee4d9d79ea157644759a0b5b717dcb313c39f613ba993a0de67481c7261f.png https://uploads.disquscdn.com/images/fed3132a7e6215205ce796f7b04c885f50b9399012f999eced2b4c8c3de1dfca.png

    https://uploads.disquscdn.com/images/3fde251874d152c18c09d354104a77c539ecad9f42e57860a132a09bf9add67d.png

  • thx for sharing. will dig in this summer when I have a bit more time