Fousseni Chabi-Yo

Pricing Kernels with Stochastic Skewness and Volatility Risk

I derive pricing kernels in which the market volatility is endogenously determined. Using the Taylor expansion series of the representative investors marginal utility, I show that the price of market volatility risk is restricted by the investors risk aversion and skewness preference. The risk aversion is estimated to be between two and five and is significant. The price of the market volatility is negative. Consistent with economic theory, I find that the pricing kernel decreases in the market index return and increases in market volatility. The projection of the estimated pricing kernel onto a polynomial function of the market return produces puzzling behaviors, which can be observed in the pricing kernel and absolute risk aversion functions. The inclusion of additional terms in the Taylor expansion series of the investors marginal utility produces a pricing kernel function of market stochastic volatility, stochastic skewness, and stochastic kurtosis. The prices of risk of these moments are restricted by the investors risk aversion, skewness preference, and kurtosis preference. The prices of risk of these moments should not be confused with the price of risk of powers of the market return, such as coskewness and cokurtosis. This paper was accepted by Wei Xiong, finance.

Variance Bounds on the Permanent and Transitory Components Of Stochastic Discount Factors

In this paper, we develop lower bounds on the variance of the permanent component and the transitory component, and on the variance of the ratio of the permanent to the transitory components of SDFs. Exactly solved eigenfunction problems are then used to study the empirical attributes of asset pricing models that incorporate long-run risk, external habit persistence, and rare disasters. Specific quantitative implications are developed for the variance of the permanent and the transitory components, the return behavior of the long-term bond, and the comovement between the transitory and the permanent components of SDFs.

A Recovery that We Can Trust? Deducing and Testing the Restrictions of the Recovery Theorem

How reliable is the recovery theorem of Ross (2015)? We explore this question in the context of options on the 30-year Treasury bond futures, allowing us to deduce restrictions that link the physical and risk-neutral return distributions. Our empirical results undermine the implications of the recovery theorem. First, we reject an implicit assumption of the recovery theorem that the martingale component of the stochastic discount factor is identical to unity. Second, we consider the restrictions between the physical and risk-neutral return moments when the recovery theorem holds, and reject them in both forecasting regressions and generalized method of moments estimations. Received November 7, 2016; editorial decision July 24, 2017 by Editor Stijn Van Nieuwerburgh. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

Aggregation of preferences for skewed asset returns

This paper characterizes the equilibrium demand and risk premiums in the presence of skewness risk. We extend the classical mean-variance two-fund separation theorem to a three-fund separation theorem. The additional fund is the skewness portfolio, i.e. a portfolio that gives the optimal hedge of the squared market return; it contributes to the skewness risk premium through co-variation with the squared market return and supports a stochastic discount factor that is quadratic in the market return. When the skewness portfolio does not replicate the squared market return, a tracking error appears; this tracking error contributes to risk premiums through kurtosis and pentosis risk if and only if preferences for skewness are heterogeneous. In addition to the common powers of market returns, this tracking error shows up in stochastic discount factors as priced factors that are products of the tracking error and market returns.

A New Approach to Measuring Riskiness in the Equity Market: Implications for the Risk Premium

We introduce a new approach to measuring riskiness in the equity market. We propose option implied and physical measures of riskiness and investigate their performance in predicting future market returns. The predictive regressions indicate a positive and significant relation between time-varying riskiness and expected market returns. The significantly positive link between aggregate riskiness and market risk premium remains intact after controlling for the S&P 500 index option implied volatility (VIX), aggregate idiosyncratic volatility, and a large set of macroeconomic variables. We also provide alternative explanations for the positive relation by showing that aggregate riskiness is higher during economic downturns characterized by high aggregate risk aversion and high expected returns.

The Term Structures of Coentropy in International Financial Markets

We propose a new entropy-based correlation measure (co-entropy) to evaluate the performance of international asset pricing models. Co-entropy summarizes in a single number the extent of co-dependence between two variables beyond normality. We document that the co-entropy of international stochastic discount factors (SDFs) can be decomposed into a series of entropy-based correlations of permanent and transitory components of the SDFs. We derive bounds and restrictions on co-entropies of these components, which we then use to analyze the composition of co-dependence of international SDFs. A large cross-section of countries is employed to provide empirical evidence on the entropy-based correlations at various horizons. We find that the co-entropy of the transitory components is always sizably smaller than the co-entropy of the permanent components, with the latter usually being very close to one. Furthermore, the entropy based correlation of transitory components of SDFs increases with the investment horizon, which features an upward sloping term structure of co-entropies. We confront several state-of-the-art international finance models with these empirical regularities, and find that existing models cannot account for the composition of codependence at all horizons.

An Inquiry into the Nature and Sources of Variation in the Expected Excess Return of a Long-Term Bond

This paper proposes an approach to study the expected excess return of a long-term bond and focuses on a lower bound. This lower bound is a crucial number, as it represents the minimum expected excess return demanded by investors. The derived bound is model-independent and can be extracted from options on the 30-year Treasury bond futures. Our implementation reveals that the annualized lower bound ranges from 0.22 to 6.07, with an unconditional average of 1.18%. The ideas and developed results are useful for thinking about cost of debt, allocation between equities and bonds, and measuring investor reaction to monetary policy shocks.

Riskiness Measures and Expected Returns

Inspired by Aumann and Serrano (2008) and Foster and Hart (2009), we propose risk-neutral options’ implied measures of riskiness and investigate their significance in predicting the cross section of expected returns per unit of risk. The empirical analyses indicate a negative and significant link between the forward looking options’ implied measures of riskiness and future stock returns. Stocks in the lowest riskiness portfolio have economically and statistically higher risk-adjusted returns than those in the highest riskiness portfolio. These results are robust to controls for market beta, size, book-to-market, momentum, short-term reversal, and liquidity of individual stocks. Controlling for the risk-neutral measure of skewness and the widely used measures of volatility and downside risk (value-at-risk and expected shortfall) does not affect the significant predictive power of riskiness. The paper also introduces alternative measures of riskiness for the aggregate stock market and shows that aggregate riskiness successfully predicts future economic downturns.

Default Risk, Idiosyncratic Coskewness and Equity Returns

In this paper, we intend to explain an empirical finding that distressed stocks delivered anomalously low returns. We show that in a model with heterogeneous investors where idiosyncratic skewness is priced, the expected return of risky assets depends on idiosyncratic coskewness betas, which measure the covariance between idiosyncratic variance and the market return. We find that there is a negative (positive) relation between idiosyncratic coskewness and equity returns when idiosyncratic coskewness betas are positive (negative). We construct two idiosyncratic coskewness factors to capture market-wide effect of idiosyncratic coskewness betas. When we control for these two idiosyncratic coskewness factors, the return difference for distress-sorted portfolios becomes insignificant. High stressed firms earn low returns because high stressed firms have high (low) idiosyncratic coskewness betas when idiosyncratic coskewness betas are positive (negative).

New Entropy Restrictions and the Quest for Better Specified Asset Pricing Models

Under the setting that stochastic discount factors (SDFs) jointly price a vector of returns, this paper features entropy-based restrictions on SDFs, and its correlated multiplicative components, to evaluate asset pricing models. Specifically, our entropy bound on the square of the SDFs is intended to capture the time-variation in the conditional volatility of the log SDF as well as distributional non-normalities. Each entropy bound can be inferred from the mean and the variance-covariance matrix of the vector of asset returns. Extending extant treatments, we develop entropy codependence measures and our bounds generalize to multi-period SDFs. Our approach offer ways to improve model performance.