Momentum Investing: Skewness-enhanced Momentum Yields Double Alpha

Momentum Investing: Skewness-enhanced Momentum Yields Double Alpha

May 11, 2015 Research Insights, Momentum Investing Research, $mtum
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(Last Updated On: January 18, 2017)

Expected Skewness and Momentum

Abstract:

Motivated by the time-series insights of Daniel and Moskowitz (2014), we investigate the link between expected skewness and momentum in the cross-section. The three factor alpha of skewness-enhanced (-weakened) momentum strategies is about twice (half) as large as the traditional momentum alpha. In fact, skewness is among the most important cross-sectional determinants of momentum. Our findings do not neatly fit within a specific prominent theory of momentum. Due to the simplicity of the approach, its economic magnitude, and its existence among large stocks and in the recent past, the results appear difficult to reconcile with the efficient market hypothesis.

Alpha Highlight:

Daniel and Moskowitz (2014) and Barroso and Santa-Clara (2015) showed that the returns of momentum investing are negatively skewed. Specifically, the return distribution of momentum is largely concentrated on the right side with fat tails, i.e., momentum strategies yield positive returns but can also experience infrequent but significant negative returns. Thus, when pursuing high returns of momentum, investors are often reminded about the risks of momentum crashes.

Inspired by their work, this paper proposes skewness-enhanced momentum strategies, which double-sort stocks based on both skewness and past performance. The outcomes are eye-catching: the alpha of enhanced momentum strategies is about twice as large as traditional momentum (Jegadeesh and Titman, 1993) alpha.

The paper hypothesizes that the outperformance of winners is partly driven by negative skewness, and the underperformance of losers is partly driven by positive skewness. If you are not familiar with the concept of skewness, click here to learn more from Wikipedia.

Based on their conjectures, the authors come up with an enhanced long-short momentum strategy that focuses on negatively skewed winners and positively skewed losers. Below are the details:

  • Step 1: Every month, first sort stocks into five equally sized portfolios based on the skewness measure of Bali et al (2011);
  • Step 2: Within each quintile based on skewness, sort stocks into quintiles based on their past cumulative returns. In this paper, the authors choose a formation period of twelve months, a holding period of one month and skip one month in between (during which skewness is measured).
  • Step 3: Long the stocks in the lowest skewness quintile (negative skew) and highest past performance; Short the stocks in the highest skewness quintile (positive skew) with the lowest past performance. Repeat this procedure every month.

Performance Highlights:

The paper examines results from 1927 to 2011. Below, Panel A of Table 1 shows the results to equal-weight portfolios. Enhanced momentum strategy yields an monthly 3-factor alpha of 2.55%, while the traditional momentum strategy (quintile 3 on skewness — winners minus losers) has a raw monthly 3-factor alpha of only 1.24%. Adding the skewness variable can double the alpha! The weakened momentum portfolio focus on positively skewed winners and negatively skewed losers. If the hypothesis is true that the momentum profits are driven by the negative skewness of winners and positive skewness of losers, then such premiums should be diminished after controlling for skewness. The results back the paper’s hypothesis: the monthly 3-factor alpha of weakened momentum is an insignificant 0.12%.

Expected Skewness and Momentum 3
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.

 

Table 1, Panel C (show below) reports the equally-weighted raw returns of winners and losers in each skewness quintile. It shows no clear pattern for winners, but loser returns decline monotonically. The results show the skewness effect is mainly attributed to the short leg.

Table 1 Panel C
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.

Enhanced Momentum with Risk Management 

Figure 1 below shows the invested growth of several strategies. First, one notices that the regular momentum strategy turns $1 into $29,706 from 1927-2011, a large increase from a simple market return B&H portfolio ($2,107). The enhanced momentum strategy turns a $1 investment in 1927 into$9,685,301 in 2011, which is more than 325-fold the traditional momentum strategy. However, the enhanced momentum has relatively higher volatility than the traditional momentum (as sown in the Table 3 below). To address this issue the authors apply risk management methods by Daniel and Moskowitz (2014) and Barroso and Santa-Clara (2015), which generate even better performances. These techniques are described below:

  • Barroso and Santa-Clara (2015): scale the exposure of momentum to have constant risk/ target level of volatility over time. In their paper, the authors pick a target of an annualized volatility of 12%. This is labeled Enhanced Momentum*.
  • Daniel and Moskowitz (2014): use the projected momentum premium and volatility to generate dynamic weights. This is labeled Enhanced Momentum**.

As we can see, using the risk management rules turns a $1 investment in 1927 into $69 million for Enhanced Momentum* and $116 million for Enhanced Momentum**. Not bad!

Expected Skewness and Momentum
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.

Table 3 (shown below) documents some summary statistics for the various strategies. Sharpe ratios (risk-adjusted) of three enhanced momentum strategies are all higher than the regular/traditional momentum strategy. The risk management helps reduce left-skewness, volatility, drawdowns and thus increase Sharpe ratios.

Expected Skewness and Momentum Sharpe ratio
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.

This paper spends the rest of the time on robustness. It shows that such premiums have long-run persistence and also exist in international markets. It concludes that the relation between expected skewness and momentum returns is significant, even after controlling for virtually all firm characteristics (e.g. past returns, volatility, continuously arriving information/frog in pan effect, credit rating, the 52-week high or unrealized capital gains.)

Summary

This paper documents some interesting findings. However, as the paper points out, the skewness measure has no impact on the long leg of the portfolio. Thus, the results are driven by the short leg, which can have much higher costs.


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




About the Author

Jack Vogel, Ph.D.

Jack Vogel, Ph.D., conducts research in empirical asset pricing and behavioral finance, and is a co-author of DIY FINANCIAL ADVISOR: A Simple Solution to Build and Protect Your Wealth. His dissertation investigates how behavioral biases affect the value anomaly. His academic background includes experience as an instructor and research assistant at Drexel University in both the Finance and Mathematics departments, as well as a Finance instructor at Villanova University. Dr. Vogel is currently a Managing Member of Alpha Architect, LLC, an SEC-Registered Investment Advisor, where he heads the research department and serves as the Chief Financial Officer. He has a PhD in Finance and a MS in Mathematics from Drexel University, and graduated summa cum laude with a BS in Mathematics and Education from The University of Scranton.


  • Steve

    Thanks so much for going into this paper in detail. I’d had a look at it when it was posted in the Quant Geek Weekend Homework (should I actually admit to reading those posts?). I’d come to the conclusion that this was all from the short side and not the long side, but am happy to have that confirmed, as I found that particular paper a little hard going…and it seemed important enough to know about.

  • dph

    Jack, eye popping results to be sure. However it seems that there are many academic strategies that show 25% long term annual returns in back tests. But is there anything in the real world that approaches this? Can the transaction costs and shorting costs ever be overcome to where one can even get within 5% annually of replicating this type of strategy or similar?

  • Michael Milburn

    Hi Jack, I’m getting ready to ask some really dumb questions (seriously!). I’m trying to get my head around skewness and break it down to something I can understand maybe a little bit intuitively. I’d appreciate if you could tell me if I am interpreting correctly:

    Can low skewness be interpreted as relatively more and bigger better-than-avg days than less-than-avg days? (on a monthly basis) (If I’m reading correctly I’m interpreting _low skew_ to actually be stocks have higher number of and bigger above average days?)

    I’m looking at the formula on pg 20-22 of the Bali paper, and would it be right to to say the we might tend to see more volatile stocks that are going up in the long category?

    Is this saying that maybe even though we might use a momentum (from say t12 to t2) and tend to throw out the most recent month’s performance for momentum, we still have valuable information in the prior month’s performance from this skewness measure? If the above is correct way of thinking, I’d think a low skew stock on a monthly basis that goes into the “long” pool would also would tend to have a positive momentum on the prior month basis (but this month’s data tends to be excluded from the momentum calc?). Am I thinking about this wrong? It seems desired skewness may be in conflict w/ the reason prior month data is often excluded from momentum calc.

    Thanks, I appreciate the thoughts. I’m kindof slow to catch on and not familiar with thinking about this idea. If I’m totally confused you can just say “you’re totally wrong – read more” and save time on any reply. Am I thinking about this in somewhat right way?

  • Jack Vogel, PhD

    It appears the skewness has an effect on the short book. So if there is causation, it would be evidence of selling pressure.

  • Jack Vogel, PhD

    The paper claims the results hold after transaction costs (which they estimate). Not sure how it would work in live trading however.

  • Jack Vogel, PhD

    The results are too eye-popping to ignore! We had to investigate, and as you point out, find out the results are driven by the short book.

  • portfoliologic

    Hi, hoping you can clarify something for me. It appears from reading the paper that an algo would process:

    1. rank your universe on skew into 5 different portfolios.

    2. take each portfolio and then rank it’s components on momemtum.

    At this point it is not clear to me what positions to establish as the text could be read to mean to go long the stocks in the top quintile of each quintile, or should I read it as just take positions in the top quintile of the top quintile (Confused because why bother ranking the other quintiles at all if only ranking momentum of the top skew quintile)?

    Thanks for your help,

    Alex

  • Jack Vogel, PhD

    Yes, you basically form 25 portfolios by first sorting into 5 buckets based on skewness, and then (within each bucket) by sorting into another 5 buckets on momentum. The paper recommends the following:

    Long the stocks in the lowest skewness quintile (negative skew) and highest past performance; Short the stocks in the highest skewness quintile (positive skew) with the lowest past performance. Repeat this procedure every month.

    I hope that helps!

  • portfoliologic

    Jack,

    Thanks, but I am still a bit confused. If the final long portfolio will only be made up only of the lowest quintile skewness stocks, and the short portfolio the high skew stocks, then why bother ranking the momentum for the skew quintiles #2, 3,& 4? My concern is that I am somehow missing something here….

    Thanks,

    Alex

  • Jack Vogel, PhD

    Alex,

    This is a double-sort procedure. The authors create 25 portfolios (sorting 5×5 on both skewness and momentum). So if there are 1,000 stocks, there would be 40 stocks in each portfolio. You then go long one 40 stock portfolio, and short another 40 stock portfolio.

    Jack