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**The Information Content of the Term Structure of Risk-Neutral Skewness**

Can the term structure of risk-neutral skewness (RNS), the asymmetry of the risk-neutral distribution of underlying returns estimated from option prices, help us better understand what investor general attitudes toward skewness are?

Our study, forthcoming in the Journal of Empirical Finance, suggests that time horizon plays an important role in the relation between RNS and future stock returns. We find evidence consistent with informed traders decreasing demand for option contracts with increasing maturity due to increasingly unfavorable timing, exposure, and liquidity characteristics.

The price effect of RNS across maturity horizons is thus driven both by informed option traders’ hedging/speculative demand and the equity market’s baseline expectations about the skewness of the underlying stock.

Behavioral and rational models of investor attitudes to skewness, in which investors exhibit a preference for securities with positive skewness, have motivated a large empirical literature on whether positively skewed securities are overpriced and earn negative average excess returns. As most historical estimates of skewness provide poor forecasts of future skewness (see Boyer, Mitton, and Vorkink, 2010), empirical studies commonly use option data to estimate investor expectations of skewness.

To date, existing studies have produced mixed evidence for whether option-implied risk-neutral skewness carries a positive or negative premium in the cross-section of equity returns. Consistent with skewness preference theory, Conrad, Dittmar, and Ghysels (2013) find a negative relation between RNS and future equity returns.

This approach implicitly assumes that option and stock markets reflect the same information and that option-implied skewness proxies for expected underlying skewness. Thus, positive option-implied skewness combined with skewness preference among investors in the underlying asset leads to low realized returns.

This assumption is challenged by findings of information differences between the option and equity markets.

Ait-Sahalia, Wang, and Yared (2001) demonstrate that the risk-neutral density estimated from the S&P 500 options is different from a density inferred from historical index returns, suggesting that the option market includes a ”peso problem” due to unobserved jump dynamics in the underlying asset.

Consistent with an information difference between two markets, other studies contradict Conrad et al. (2013) by demonstrating that RNS can positively predict future stock returns. While Bali and Murray (2013) focus on the returns of a hedged asset with skewness exposure, part of their analysis confirms a positive relationship between RNS and the underlying asset.

Stilger et al. (2017) suggest that the difference between the Conrad et al. (2013) results and others are driven by the aggregation of RNS across monthly versus quarterly time periods. In this study, we consider the role of the option maturity horizon in defining the relationship of RNS with the cross-section of underlying returns.

Xing et al. (2010) suggest that informed option traders purchase out-of-the-money (OTM) put options before downward jumps in the underlying, which drives up the volatility of OTM puts and consequently leads to a steeper slope of the implied volatility function.

This is analogous to a more negative RNS that would be estimated from the same data following Bakshi, Kapadia, and Madan (2003). Furthermore, Stilger et al. (2017) find this trading activity mainly focuses on stocks that are perceived as relatively overpriced by investors and costly to sell short.

Therefore, hedging demand for underlying positions or speculation on pessimistic expectations causes informed investors to buy OTM puts or sell OTM calls, also making RNS more negative. As information is transmitted from the option market to the stock market these relatively overpriced stocks with low RNS subsequently underperform, producing a positive relation between RNS and future realized equity returns.

Our study contributes to this ongoing debate between two empirical views on RNS by considering its term structure: we find that short-term options attract more informed traders, supporting the view that positive RNS predicts positive underlying returns because it reflects market beliefs.

We also find evidence consistent with long-term options attracting more uninformed hedgers consistent with the skewness preference view that positive RNS predicts negative underlying returns because it results in overbidding. We build the intuition for the potential to reconcile informed trading and skewness preference using a multi-period equilibrium model where investors have heterogeneous skewness preferences and information sets.

Importantly, our theoretical results show that when there is a small proportion of informed investors that have a signal about the true skewness of risk assets, the risk premium for RNS is negative. In this case, RNS is predominantly determined by uninformed investors’ expected skewness for assets.

Uninformed investor preferences thus result in more demand and lower subsequent return for positively-skewed assets.

Conversely, when the proportion of skewness-informed traders increases, the RNS risk premium turns positive. In this case, RNS reflects informed traders’ superior information about the true skewness of assets.

Thus, for a stock with higher RNS, its true skewness should be higher than what uninformed investors expect. When the information becomes public afterwards, the demand for the stock increases, pushing up its price and generating a positive relation between RNS and subsequent return.

We empirically test whether the direction of RNS return predictability varies with the maturity of the options used to compute it.

In other words, we test the predictability of the underlying returns across the term structure of RNS, as we hypothesize that the proportion of informed traders varies across options with different maturities.

If differently informed investor types have different maturity preferences and thereby produce market segmentation across option maturities, the resulting RNS estimated across different maturity horizons will contain distinct information sets consistent with our model.

While we cannot empirically map trades to investor types, consistent with our model we conjecture that informed traders may prefer to use short term options due to lower cost and higher liquidity while hedgers may need longer-maturity contracts. Our findings confirm this conjecture.

We use the OptionMetrics Volatility Surface file from 1996 to 2015 to calculate monthly RNS at the 1-, 3-, 6-, 9-, and 12- month maturities for a large sample of U.S. stocks.

We estimate RNS for each security at each time horizon using the model-free method of Bakshi et al. (2003) and analyze the cross-sectional predictive relationship between the RNS at different maturities with subsequent monthly underlying returns.

The results indicate that this relationship exhibits a monotonic pattern, which is significantly positive for the short-term (1 month), insignificant for the middle-term (6 months), and significantly negative for the long-term (12 months).

In particular, a strategy that is long the equal-weighted quintile portfolio with the highest 1-month RNS and short the equal-weighted quintile portfolio with the lowest 1-month RNS yields a risk-adjusted return (alpha) of 0.95% per month with a t-statistic of 5.78, while the same strategy based on 12-month RNS produces a corresponding alpha of -0.56% per month with a t-statistic of -2.52.

The positive predictability of future equity returns from short-term RNS is consistent with informed trading (Xing et al., 2010) and hedging (Stilger et al., 2017) interpretations, while the negative predictability from the long-term RNS is consistent with skewness preference (Bali and Murray, 2013; Conrad et al., 2013).

Since the short-term RNS has positive predictive power for returns while long-term RNShas the opposite, we capture the different information sets on the two ends of the RNS term structure by constructing a term spread of RNS defined as 12-month RNS minus 1-month RNS.

We demonstrate that this spread effectively combines the two information sources and yields even stronger negative return predictability for the underlying asset using a portfolio sorting approach.

A trading strategy that is long the equal-weighted quintile portfolio with the highest term spread and short the equal-weighted quintile portfolio with the lowest term spread yields an alpha of -1.22% per month with a t-statistic of -6.61 after controlling for the Fama and French 3 factors, Carhart momentum factor, and a liquidity factor. We confirm these results with a Fama and MacBeth (1973) cross-sectional regression.

To further explore the extent of the information impounded in the term structure of RNS, we test whether short- and long-term RNS have differing predictive power for firms’ standardized unexpected earnings (SUE) using a Fama and MacBeth (1973) regression.

We find that the short-term RNS is a positive predictor of SUE, suggesting that it captures option traders’ superior information about earnings.

Simultaneously, we find that long-term RNS is a negative predictor of SUE, consistent with overvaluation due to skewness preference.

As a robustness check for the information content of RNS across different maturities, we also test its ability to predict future stock price crashes.

Consistent with the previous results, we find a significantly negative (positive) relationship between the short-term (long-term) RNS and future price crashes.

Notably, the predictive power of short-term RNS persists for at least 6 months.

Furthermore, consistent with Stilger et al. (2017), we demonstrate that the positive predictability of future equity returns from short-term RNS is strongest for overpriced and short-sale constrained underlying stocks, indicating that the short-term RNS reflects hedging demand.

In addition, we provide some direct evidence showing that the long-term RNS reflects skewness preference.

We compare long-term RNS with two recent well known physical skewness measures exhibiting negative predictive power for equity returns consistent with the skewness preference literature, maximum daily return over the previous month (MAX) (Bali, Cakici, and Whitelaw, 2011) and expected idiosyncratic skewness (EIS) (Boyer et al., 2010).

We find that our long-term RNS measure not only has strong positive correlation with these physical skewness proxies, but also complements them in identifying low expected return stocks with lottery-like payoffs.

We find that the term structure of RNS is largely explained by two principal factors, a level and a slope, similar to prior findings for the bond yield term structure (see Figure 1).

The RNS term structure slope factor, which is most significantly related to both cross-sectional and time-series stock returns, is significantly related to the Welch and Goyal (2008) macroeconomic state variables for the equity premium in vector autoregressive models.

We help to reconcile the ongoing debate about the direction of the skewness anomaly by demonstrating the existence of a term structure of RNS and its differential information content across option maturities. We find evidence consistent with informed trader preference for hedging underlying stock positions or speculating by trading short-term options.

This interpretation is intuitive for several reasons. First, mispricing in the stock market can be corrected over a short time horizon (Bali et al., 2011).

Second, short-term options are more sensitive to the variation of the underlying stock’s price, thus providing more protection to hedgers or a more leveraged position to speculators.

Third, the short-term option market is usually more liquid and thus imposes lower trading costs.

The RNS implied by short-term options deviates away from the expected skewness of the

underlying stock due to informed trading.

As the option term increases, informed traders have monotonically decreasing hedging/speculating demand for the corresponding option contracts due to increasingly unfavorable timing, exposure, and liquidity characteristics.

Being increasingly less affected by informed trading, these longer-term options more closely

mirror the distribution of the underlying stock.

As a consequence, the skewness implied by the long-term options tend to reflect the equity market’s expected skewness of the underlying stock and carries a negative risk premium.

These patterns are consistent with Holowczak, Simaan, and Wu (2006), who find that the informativeness of option prices increases when option trading activity generates net sell or buy pressure on the underlying stock and even more so when the pressure coincides with deviations between the stock and options prices.

Thus, the price effect of RNS across its term structure is determined by a combination of informed option traders’ hedging/speculative demand and the equity market’s expectations about the skewness of the underlying stock.

**Written by Paul Borochin, Hao Chang, Yangru Wu**

The full text of the paper may be found at:

Figure 1

**References**

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

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Fama, E. F., and J. D. MacBeth. 1973. Risk, return, and equilibrium: Empirical tests.

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Holowczak, R., Y. E. Simaan, and L. Wu. 2006. Price discovery in the US stock and stock

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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.

Xing, Y., X. Zhang, and R. Zhao. 2010. What does the individual option volatility smirk tell

us about future equity returns? Journal of Financial Quantitative Analysis 45:641-662.

Welch, I., and A. Goyal. 2008. A comprehensive look at the empirical performance of equity premium prediction. Review of Financial Studies 21:1455-1508.

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