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Options Wealth Machine : Risk Neutral Skewness Predicts Price Rebounds and so Can Improve Momentum Performance

Options Wealth Machine : Can option data be used to improve the momentum strategy, and if so, how?

Our study, in the Critical Finance Review, suggests that option-implied risk-neutral skewness (RNS) can predict stock rebounds and thereby help avoid momentum crashes.

High positive RNS has been argued to have a negative relationship with returns due to behavioral preferences for lottery stocks (Conrad, Dittmar, and Ghysels, 2013), a positive relationship due to low RNS proxying for overvaluation, particularly in the presence of short-sale constraints (Stilger, Kostakis, and Poon, 2017), and a positive relationship due to price pressure (Bali, Hu, and Murray, 2018).

Notably, the unpublished work by Rehman and Vilkov (2012) suggests that RNS may more generally relate to undervaluation as well as overvaluation. Building on this insight, we consider the relationship of RNS to both the past and future price path of stocks to shed additional light on this issue, help resolve potentially contradictory findings, and better understand the information channel for the relationship between RNS and future underlying returns.

Contemporaneous RNS estimated at the end of the month has a positive correlation with returns for the underlying stock over the following month, and we find evidence consistent with relative undervaluation as the driver of this positive performance.

An equal-weighted zero-cost portfolio sorted on high (ie, most positive) minus low (most negative) RNS exhibits significant abnormal monthly returns of 94 bp, of which 39 bp is due to the short leg consistent with an overvaluation explanation advanced by prior literature (Stilger, Kostakis, and Poon, 2017).

However, the remaining 55 bp is due to the long leg, contrary to an overvaluation explanation, consistent with evidence that RNS can reflect undervaluation also (Rehman and Vilkov, 2012). Furthermore, a value-weighted equivalent high minus low RNS portfolio has abnormal returns of approximately 70 bp with 48 bp due to the long leg and only 21 bp due to the short leg.

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Across both portfolio weightings, the observed greater magnitude of the excess and abnormal return contributions of the high-RNS long leg is contrary to the overvaluation explanation that assumes information is contained in the low-RNS short leg.

Furthermore, we show 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 not captured by overvaluation under short-sale constraints. We, therefore, consider an alternative explanation to the RNS anomaly as an indicator of stock price rebounds.

Figure 1 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 Q1 (low RNS) and Q5 (high RNS).

The Figure shows that both high and low RNS stocks experience reversals in their performance. The Q1 (low RNS) stocks have higher historical performance before portfolio formation and lower, though still positive, performance after. Conversely, the Q5 (high RNS) stocks exhibit negative performance before portfolio formation and a positive rebound afterward.

The behavior of the RNS Q1 portfolio is consistent with the explanation of worse future performance by overvalued and short-sale-constrained stocks. However, the positive rebound observed in the RNS Q5 portfolio is not consistent with this explanation. Value-weighted portfolios produce very similar results which we suppress for brevity.

Consistent with the trend reversal of negative momentum stocks observed in the RNS Q5 portfolio in Figure 1, we find that the RNS anomaly is related to the momentum crash phenomenon in which a reversal of trends causes a reversal in the momentum anomaly (Daniel and Moskowitz, 2016). The authors show that momentum strategies can experience infrequent negative returns, especially at the end of market recessions and high market volatility periods as low-momentum stocks rebound.

They demonstrate that the market beta of the momentum strategy becomes more negative during these 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.

Due to its predictive power for firm-specific rebounds and its negative relationship with momentum returns, we conjecture that RNS can be used to identify upward rebounds and improve the performance of momentum by avoiding rebound-driven crashes. We demonstrate this by forming a winner minus loser momentum strategy within the RNS tercile and finding significant differences in its performance across them.

The momentum strategy in the high RNS tercile experiences the worst performance around market rebounds following recessionary periods. This effect is not driven by small firms, as we find that the momentum strategy earns the lowest returns in recessions and periods of high market volatility in the highest RNS tercile for both middle and high size terciles. Conversely, the lowest RNS tercile yields the strongest momentum performance for both middle and high firm size terciles.

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

By relaxing the requirement of stocks having the traded options necessary to compute the RNS characteristic, we eliminate 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.

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Stocks with a high RNS characteristic, as well as those with a high skewness characteristic-mimicking portfolio loading, experience substantially more frequent positive performance reversals at the individual firm level and have the lowest firm-specific valuation component using an industry multiples method of decomposing the market to book ratio.

Loadings on the skewness factor mimicking portfolio predict future realized skewness, consistent with its validity 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 ability of the RNS characteristic to identify and avoid the momentum crash phenomenon.

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 the avoidance of momentum crashes using low-RNS stocks is more significant than that of the risk-managed momentum strategy suggested by Barroso and Santa-Clara (2015), suggesting the performance reversal information captured in the RNS characteristic has meaningful economic value.

This study contributes to the asset pricing anomaly literature, to our understanding of the pricing of risk-neutral skewness as a factor and as a characteristic, and to its relationship with future realized outcomes. Bakshi, Kapadia, and Madan (2003) demonstrate that RNS is related to the moments of the physical distribution moderated by the risk aversion parameter.

More recent work by Kozhan, Neuberger, and Schneider (2013) and Harris and Qiao (2018) relates option-implied and historical skewness as a time-varying skewness risk premium.

Notably, Harris and Qiao (2018) find that more than 40% of the skewness risk premium is explained by the prior month’s returns, a reversal pattern similar to the behavior that we find for the relationship between RNS and next month’s price rebounds which drive momentum crashes. In related work, Borochin, Chang, and Wu (2020) demonstrate that the positive relation between RNS and future returns is concentrated in short-maturity options.

It also adds to our understanding of the relationship between measures of the asymmetry of the distribution of underlying assets and its future performance It also demonstrates that momentum crashes can be identified and avoided, significantly improving the anomaly’s performance.

We add to the skewness pricing literature by documenting 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 in Daniel and Moskowitz (2016).

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. We demonstrate this behavior both at the market-wide level and at the individual stock level, and identify undervaluation-driven rebounds as the channel for this relation.

The full text of the paper may be found at


Figure 1


Bakshi, G., N. Kapadia, and D. Madan. 2003. Stock return characteristics, skew laws, and

the differential pricing of individual equity options. Review of Financial Studies 16:101-


Borochin, P., H. Chang, and Y. Wu, 2020. The Information Content of the Term Structure

of Risk-Neutral Skewness, Journal of Empirical Finance forthcoming.

Conrad, J., R. F. Dittmar, and E. Ghysels. 2013. Ex ante skewness and expected stock

returns. Journal of Finance 68:85-124.

Daniel, K., and T. Moskowitz, 2016. Momentum crashes. Journal of Financial Economics,

122(2), 221-247.

Harris, R.D. and Qiao, F., 2018. Moment Risk Premia and the Cross-Section of Stock

Returns. Working paper.

Kozhan, R., Neuberger, A. and Schneider, P., 2013. The skew risk premium in the equity

index market. Review of Financial Studies, 26(9), 2174-2203.

Stilger, P. S., A. Kostakis, and S.-H. Poon. 2017. What does risk-neutral skewness tell us

about future stock returns? Management Science 63:1814-1834.

Rehman, Z., and Vilkov, G., 2012. Risk-Neutral Skewness: Return Predictability and Its

Sources. Working paper.

Written by Paul Borochin, Yanhui Zhao

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