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By Paul Borochin and Yanhui Zhao
Option-Implied Skewness Can Predict Market and Individual Stock Bottoms
Was mid-March of this year a bottom in the market? And, what is the next time we will hit bottom?
The options market, and implied volatility (IV) and the VIX, in particular, are getting a lot of attention for their ability to offer meaningful insights into the market’s expectations for future stock price outcomes. But the third moment of the option-implied distribution of underlying returns might also offer important information. This moment, defining the asymmetry of the distribution, is known as skewness.
Research suggests that positive option-implied risk-neutral skewness (RNS) can be applied to optionable assets to help predict next-month abnormal underlying stock returns, such as when a stock, or the market, might start to have an upturn.
However, some uncertainty exists when it comes to what exactly option implied skewness represents and speculates on. For instance, some research has found a positive relationship between skewness and future stock returns. Still, other research has indicated a negative relationship between skewness and future stock returns.
What, exactly, then can risk-neutral skewness tell us when it comes to future returns on stocks?
Our recent research, entitled “Risk Neutral Skewness Predicts Price Rebounds and so can Improve Momentum Performance,” using options data from OptionMetrics, takes a look at the relation between option-implied skew and equity performance in a way that people have been wondering about for years.
Looking at what happens to very negatively or positively skewed stocks, we find that:
- Skewness is, indeed, related to rebound behaviors both at the macroeconomic and individual stock level, and
- This factor can also be used to improve strategies sensitive to rebound behavior to avoid rebounds that are bad for the trading strategy.
Speculation on the Skew
Past research from Conrad, Dittmar, and Ghysels in 2013 suggests that high positive RNS has a negative relationship to returns with investors preferring lottery stocks. Later, Stilger, Kostakis, and Poon suggested in 2016 that RNS has a positive relationship due to low RNS proxying for overvaluation, such as with the presence of short-sale constraints. Bali, Hu, and Murray later indicated in 2018 that RNS has a positive relationship due to price pressure. Further, unpublished research from Rehman and Vilkov from 2012 indicates the RNS relationship may relate to under- and overvaluation of underlying assets.
We sought to build on these findings to show what happens to very positively or negatively skewed stocks over time. We confirm the historical rebound behavior in stock performance: that negatively skewed stocks have recent superior performance and then in the next month, have the worst downward reversal. Conversely, stocks with the highest skewness, have the worst performance, and in the next month empirically are observed to have a positive rebound.
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 RNS terciles and finding significant differences in its performance across them.
We look at stocks with traded options first. To extract option-implied risk neutral skewness for each stock, we use the volatility surface at the 30 day maturity from IvyDB US from OptionMetrics.
We used OptionMetrics data because it is the industry standard in options research. It’s a good, comprehensive, timely, well-respected data set that pretty much all economic research in options is based on. We also used returns data for stocks from CRSPR and some stock characteristic, regressions, and firm book value from Compustat.
We find that 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.
With RNS calculated on optionable securities, we next construct a RNS factor, or characteristic-mimicking portfolio (which we refer to as SKEW), to generalize findings to stocks that do not have traded options. 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.
One Anomaly Amplifies Another: Leveraging Skew in Trading Strategies
With this information that momentum crashes might be identified and avoided (and that negatively skewed stocks experience recent superior performance and then in the next month, the worst downward reversal, and stocks with the highest skewness have had the worst performance, and in the next month empirically are observed to have a big upward rebound), we seek to show how leveraging this rebound behavior might help traders to avoid rebounds that could be bad for trading strategies that rely on continuation of trends and suffer during trend reversals, such as the momentum strategy.
We cite existing research (at the macro level) from Daniel and Moskowitz on momentum crashes to help make the connection with skew to the momentum trading strategy, given sensitivity to least performance rebounds. Research by Daniel and Moskowitz reveals that when the economy is going to rebound after some period of negative performance, is when momentum has a negative beta on this rebound. In this case, momentum does badly as the economy picks up, because the momentum trade had expected that whatever was going down would keep going down. However, since it goes up, investors and traders who were short, are making losses.
Since skewness can inform traders of the rebound behavior at the firm level (rather than at the macro level), we conjecture that it should have a similar relation to momentum performance. To do this, we look at stocks that are least exposed to skewness, using a factor mimicking portfolio.
We go long on high skew stocks and short low skew stocks to create a time series of factor mimicking returns that represent returns one might get on positively skewed stocks. We then estimate the beta (or how sensitive the stock is to movements in the stock market, with stocks with a high beta considered risky, and those with a low beta, considered less risky) on this factor mimicking portfolio for any stock (based on its time series of returns) to determine how sensitive even non optionable stocks are.
We find that, similar to the high beta stock that has a strong relationship to the market, a stock with a strong beta on the skewness portfolio, has a strong relationship to skewness.
We then estimate the skewness beta for all stocks and run a momentum strategy (low recent winners, short recent losers) in quintiles by the skewness exposure.
We find that the momentum strategy behaves the strongest/has the strongest performance (recent winners outperform recent losers the most) in the lowest beta quintile by the skewness data (the 20% of stocks with the lowest exposure to skewness momentum is strongest here).
A visualization of the extent to which using the SKEW factor-mimicking portfolio to isolate stocks with low likelihood of rebounds, and therefore low risk of momentum crashes, improves momentum performance. The momentum strategy in stocks within the lowest quintile of SKEW beta has the highest cumulative log return relative to other recently proposed momentum improvements.
Our findings are consistent with the idea that stocks that have an upcoming rebound have the highest exposure to skewness. We also tabulate the frequency of rebounds and show that it is monotonically decreasing in exposure to the skewness factor. This supports the idea that skewness factor predicts rebounds and that it has economic meaning. If one has a trading strategy that is sensitive to rebounds, as momentum is, then he/she can observe that it does much better in the assets that are less likely to have rebounds using skewness as a predictor. In other words: skewness does seem to predict rebounds, and it does predict them economically significantly because a strategy sensitive to these rebounds does much better in a sub sample that is predicted to have the fewest of them.
The negative reversal experienced by the Q1 (low RNS) stocks is consistent with the short-sale constraint explanation of the RNS anomaly. However, the reversal of the Q5 (high RNS) stocks cannot be explained by short-sale constraints.
Leveraging Skew in Trading Strategies
Could skewness have predicted the dip in March? That is exactly the situation that skewness could help traders and institutional investors avoid.
Generally, the ideas of the options market may be better informed than the stock market. If we can use skewness to see a rebound coming, like the one in mid-March, then we should expect skewness for the whole index and all of the individual firms, as well, to have become positive in mid-March. And that would be a signal that we are about to rebound. Then one could get out of a momentum trade that had become short recent losers, because those losers were about to become winners and, actually, exposed in hindsight did.
What do these insights mean for institutional investors and traders?
Investors will again begin to wonder, how low is the market going to go? When should we get back in? And that is the sort of thing skewness can tell you. If you can predict the bottom, you can predict the upturn. Going forward, this rally will end and there will be a downward rebound. And one might find oneself shorting stocks again, and if one wants to look for a good place to get out of that short position, looking at skewness and a predictor of rebounds would be good there as well.
Also interesting about the research is how one strategy can amplify another one. The process of combining alphas, each known to predict returns to attempt to gain a sum greater than the parts, is a growing trend, with WorldQuant funds, an example.
Regarding combining momentum anomaly and skewness anomaly in his research, the magnitude of returns is even stronger in the momentum anomaly than if one were just to trade skews by itself. An investor could trade positive skew stocks and be short negative skew stocks, and that could earn them a little bit less than 1% a year, based on our data. However, if one were to instead to look at really low skew stocks (that are least likely to rebound upward) and to run the momentum strategy with them closed along with winners, short losers, that could earn them 1½% per month. So investors are better off using skewness as a signal to improve momentum than in trading skewness by itself. By combining them, investors and traders could get something greater than just the sum of the parts.
Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.
Additional disclosure: This article is based on a joint academic research paper with Yanhui Zhao, forthcoming at the Critical Finance Review