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APE-6: Cross-section of stock returns: higher-order moments and mis-specification
Correcting Misspecified Stochastic Discount Factors
1EDHEC Business School, United Kingdom; 2Imperial College London; 3Stockholm School of Economics
We show how, given a misspecified stochastic discount factor (SDF), one can construct an admissible SDF, namely an SDF that prices assets correctly. We first extend the traditional Arbitrage Pricing Theory (APT) to capture misspecification from both pervasive (systematic) pricing errors and idiosyncratic pricing errors. The constructed admissible SDF, which uses the extended APT as its foundation, satisfies the Hansen and Jagannathan (1991) bound exactly.* If the number of assets N is large, the admissible SDF recovers the contribution of the missing pervasive factors completely without requiring one to identify the missing factors. Indeed, projecting the correction term of the SDF on the space spanned by the candidate missing factors, achieves an R-squared that converges to one as N increases. Our approach applies also to nonlinear SDFs that typically characterize equilibrium asset-pricing models, where our correction fully accounts for the nonlinear components. Simulations demonstrate that the theory we develop is remarkably effective in correcting various sources of misspecification.
1Bocconi University; 2University of Chicago, Booth School of Business
We estimate and analyze the ex ante higher order moments of stock market returns. We document that even and odd higher-order moments are strongly negatively correlated, creating periods where the return distribution is riskier because it is more left-skewed and fat tailed. Such higher-moment risk is negatively correlated with variance and past returns, meaning that it peaks during calm periods. The variation in higher-moment risk is large and causes the probability of a two-sigma loss on the market portfolio to vary from 3.3% to 11% percent over the sample, peaking in calm periods such as just before the onset of the financial crisis. In addition, we argue that an increase in higher-moment risk works as an "uncertainty shock" that deters firms from investing. Consistent with this argument, more higher-moment risk predicts lower future industrial production.
Crash Risk in Individual Stocks
University of Houston, United States of America
In this paper I study and implement skewness swaps in individual stocks, which are trading strategies closely related to the more familiar variance swaps. Just as variance swap returns measure the variance risk premium, skewness swap returns measure the skewness risk premium. I document that (i) the returns of the skewness swaps in individual stocks are positive and significant (ii) after the 2008/2009 financial crisis the returns of the skewness swaps on individual stocks increase substantially while the return of the skewness swap on the market index does not change. The result is robust for different measures of skewness and it is not driven by the difference in option data availability and liquidity between the index and individual stocks. This result provides evidence of a new idiosyncratic skewness risk priced in individual stock. I finally discuss different possible explanations for this pattern.
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