Entropy and entropy-like measures of pricing kernel dispersion emerge as useful tools in asset pricing research. We develop a systematic approach to bounding entropy by incorporating conditioning information. Our bounds feature a fixed-point solution to a dynamic asset allocation problem....

Current factor models do not identify risks that matter to investors. To address this issue, we provide a factor model implementation of the ICAPM, which captures market risk and intertemporal risk (i.e., changes in long-term expected returns and volatility). We build our intertemporal risk...

This paper examines whether investors receive compensation for holding crash-sensitive stocks. We capture the crash sensitivity of stocks by their lower tail dependence (LTD) with the market based on copulas. We find that stocks with strong LTD have higher average future returns than stocks with...

We develop a new approach to determine investors' risk compensations for all distributional moments of a security. Using the concept of entropy, a summary of all moments of a risky security, we derive the relationship between expected returns and their compensation for entropy risk. Entropy risk...

We derive lower and upper bounds on the conditional expected excess market return that are related to risk-neutral volatility, skewness, and kurtosis indexes. The bounds can be calculated in real time using a cross section of option prices. The bounds require a no-arbitrage assumption, but do...

We derive lower and upper bounds on the conditional market autocorrelation index at various investment horizons without using the precise form of the utility function. The bounds are derived in terms of option prices and can be computed at daily frequency for any given horizon. The bounds...

I derive pricing kernels in which the market volatility is endogenously determined. Using the Taylor expansion series of the representative investor's marginal utility, I show that the price of market volatility risk is restricted by the investor's risk aversion and skewness preference. The risk...

This paper investigates whether multivariate crash risk (MCRASH), defined as exposure to extreme realizations of multiple systematic factors, is priced in the cross-section of expected stock returns. We derive an extended linear model with a positive premium for MCRASH and we empirically confirm...

We develop a methodology to decompose the conditional market risk premium and risk premia on higher-order moments of excess market returns into components related to contingent claims on down, up, and moderate market returns. The decompositions do not depend on assumptions about investor...