Practical analysis for investment professionals
22 February 2019

Option-Implied Skewness and the Momentum Anomaly

What information does option-implied skewness contain, and how is it related to the momentum anomaly?

Gurdip Bakshi, Nikunj Kapadia, and Dilip B. Madan created estimators for option-implied moments of the distribution of the returns to the underlying asset, and launched a broad and ongoing investigation of this distribution’s information content that focuses on the asymmetric third moment of skewness.

So far, these explorations find at times contradictory evidence about the information content of option-implied risk-neutral skewness (RNS), the third moment of this distribution. High positive RNS has been said to have a negative relationship with returns due to behavioral preferences for lottery stocks and a positive relationship due to low RNS proxying for overvaluation, particularly in the presence of short-sale constraints.

To shed additional light on this issue, help resolve potentially contradictory findings, and better understand the information channel, we examined the relationship of RNS to both the past and future price path of stocks.

We find that contemporaneous RNS estimated at the end of the month has a positive correlation with returns for the underlying stock over the following month. An equal-weighted zero-cost portfolio sort on high (i.e., most positive) minus low (most negative) RNS exhibits significant abnormal returns of 94 bps, of which 39 bps is due to the short leg. This result is consistent with the overvaluation explanation advanced by prior research.

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However, the remaining 55 bps is due to the long leg, which doesn’t fit the explanation. Furthermore, a value-weighted equivalent high minus low RNS portfolio has abnormal returns of approximately 70 bps, with 48 bps due to the long and 21 bps due to the short leg. Across both portfolio weightings, the greater magnitude of the excess and abnormal return contribution of the high-RNS long leg suggests that there is more to the RNS anomaly than the extant overvaluation explanation of the RNS anomaly that focuses on the short leg. Indeed, we find that the valuation channel proposed for low-RNS stocks works both ways, and that high-RNS stocks are relatively undervalued, explaining their upward price rebounds in the figure below. Furthermore, we find that the long leg of the zero-cost high-low RNS portfolio has a positive and significant conditional beta during market rebounds while the short leg does not, suggesting a dynamic that overvaluation under short-sale constraints does not capture.

Based on these findings, we propose an alternative explanation to the RNS anomaly as an indicator of stock price rebounds, directly tying it to the momentum crash phenomenon in which a reversal of trends causes a reversal in the momentum anomaly.


Path-Dependent Relationship between RNS and Underlying Monthly Returns

Path-Dependent Relationship between RNS and Underlying Monthly Returns

Path-dependent relationship between RNS and underlying monthly returns. The Quintile 5 portfolio contains stocks with the most positive option-implied skewness at the end of month 0, whereas Quintile 1 contains the lowest.


The above graphic demonstrates the path-dependence of RNS with respect to the past and future performance of the underlying stock. At the end of each portfolio formation month (t=0), we rank stocks into RNS quintiles, form portfolios, and plot the portfolio’s past and future equal-weighted excess returns for low RNS Q1 and high RNS Q5.

The chart shows that both high and low RNS stocks experience reversals in their performance. The Q1 stocks have good historical performance before portfolio formation and poor performance after. Conversely, the Q5 stocks exhibit negative performance before portfolio formation and a positive rebound afterward. The Q1 portfolio’s behavior is consistent with the explanation of worse future performance by overvalued and short-sale–constrained stocks. But the Q5 portfolio’s positive rebound is not.

Consistent with the trend reversal of negative momentum stocks observed in the RNS Q5 portfolio, we find that the RNS anomaly isolates the effect of momentum crashes. Daniel and Moskowitz show that momentum strategies suffer infrequent negative returns that are persistent, especially at the end of market recessions, and high market volatility periods as low-momentum stocks rebound. The market beta of the momentum strategy becomes more negative in high market stress periods, giving it asymmetric negative exposure to the rebound. We find that the RNS anomaly has a positive beta during market-wide rebounds, giving it an opposite asymmetric positive exposure.

Based on its negative relationship with momentum returns, we theorize that the RNS anomaly picks up momentum crashes. We demonstrate this by forming a winner minus loser momentum strategy within RNS terciles and finding significant differences in its performance across them.

The momentum strategy in the high RNS tercile experiences the most severe crashes around market rebounds following recessionary periods. Controlling for size, we find that for all but the smallest tercile of stocks, the momentum strategy earns the lowest returns in recessions and periods of high market volatility in the highest RNS tercile. Conversely, the lowest RNS tercile yields the strongest momentum performance (the fewest momentum crashes) for both median and large firms.

To generalize this finding to stocks without traded options necessary to compute the RNS characteristic, we construct a characteristic-mimicking portfolio using optionable stocks. This allows us to address a larger universe of tradeable assets, which both increases the economic significance of our finding as well as its robustness.

By eliminating the requirement that stocks have the traded options necessary to compute the RNS characteristic, we remove a potential selection bias in our results. We hypothesize that non-optionable stocks with similar price rebound patterns will have exposure to this factor-mimicking portfolio constructed from optionable stocks predicted to have price rebounds from a sort on the RNS characteristic, and find evidence consistent with this hypothesis.

Stocks with a high RNS characteristic, as well as those with a high skewness characteristic-mimicking portfolio loading, have substantially more frequent positive performance reversals at the individual firm level driven by a reaction to past undervaluation. Loadings on the skewness factor-mimicking portfolio predict future realized skewness, consistent with its effectiveness as a proxy for RNS. Furthermore, a momentum strategy on stocks with the lowest skewness factor-mimicking portfolio loadings has significantly improved performance, confirming the RNS characteristic’s ability to identify and avoid the momentum crash phenomenon as shown in the table below:


Excess Return Momentum Decile

Excess Return Momentum Decile

Performance of the momentum strategy across quintiles of exposure to the option-implied skewness factor-mimicking portfolio SKEW. Momentum is defined following Robert Novy-Marx but is robust to alternative specifications.


These results are not driven by small, illiquid, or high trading cost stocks. The improvement in the risk-return tradeoff of the momentum strategy introduced by avoiding momentum crashes with low-RNS stocks is more significant than that of the risk-managed momentum strategy suggested by Pedro Barroso and Pedro Santa-Clara. This implies the performance reversal information captured in the RNS characteristic has meaningful economic value.

It also demonstrates that momentum crashes can be identified and avoided, significantly improving the strategy’s performance. We demonstrate that high RNS stocks predict positive stock performance, particularly after a period of underperformance, and this reversal has a relationship with the momentum crash phenomenon documented by Daniel and Moskowitz. We observe this behavior using both the RNS characteristics in optionable stocks as well as all CRSP stocks regardless of optionability using stock loadings on our novel constructed risk-neutral skewness factor.

Risk-neutral skewness factor loadings provide a simple strategy to avoid momentum crashes in an economically significant way and demonstrate the RNS anomaly’s relationship with price rebounds and momentum crash risk. These findings bolster our understanding of the information content of the option-implied skewness of the distribution of underlying stock returns.

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All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.

Image credit: ©Getty Images/Ralf Hiemisch


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About the Author(s)
Paul Borochin, PhD, CFA

Paul Borochin, PhD, CFA, is an assistant professor of finance at the University of Connecticut. He earned a PhD in finance from the Fuqua School at Duke University and a BS in finance and statistics from the Wharton School at the University of Pennsylvania. His research interests are institutional ownership and applications of asset pricing theory to extract information about corporate events and policies, with sub-specializations in corporate governance, information asymmetry, and M&A. He teaches a graduate seminar in asset pricing theory and undergraduate courses in corporate finance.

Yanhui Zhao, PhD

Yanhui Zhao, PhD, is an assistant professor of finance at the University of Wisconsin – Whitewater. She earned a PhD in finance from the University of Connecticut and a masters degree in quantitative finance from Rutgers University in 2012. Her research focuses on two streams: eliciting information about underlying assets from the equity options markets, and improving our understanding of the term structure of the cost of equity.

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