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The Variance Risk Premium in Equilibrium Models

Review of Finance 2023 27(6), 1977-2014 open access
Abstract The equity variance risk premium is the expected compensation earned for selling variance risk in equity markets. The variance risk premium is positive and shows only moderate persistence. High variance risk premiums coincide with the left tail of the consumption growth distribution shifting down. These facts, together with risk-neutral skewness being substantially more negative than physical return skewness, refute the bulk of the extant consumption-based asset pricing models. We introduce a tractable habit model that does fit the data. In the model, the variance risk premium depends positively (or negatively) on “bad” (or “good”) consumption growth uncertainty.

Asset Return Dynamics under Habits and Bad Environment–Good Environment Fundamentals

Journal of Political Economy 2017 125(3), 713-760
We introduce a “bad environment–good environment” (BEGE) technology for consumption growth in a consumption-based asset pricing model with external habit formation. The model generates realistic non-Gaussian features of consumption growth and fits standard salient features of asset prices including the means and volatilities of equity returns and a low risk-free rate. BEGE dynamics additionally allow the model to generate realistic properties of equity index options prices and their comovements with the macroeconomic outlook. In particular, when option-implied volatility is high—as measured, for instance, by the VIX index—the distribution of consumption growth is more negatively skewed.

Macro risks and the term structure of interest rates

Journal of Financial Economics 2021 141(2), 479-504
We use non-Gaussian features in U.S. macroeconomic data to identify aggregate supply and demand shocks while imposing minimal economic assumptions. Macro risks represent the variables that govern the time-varying variance, skewness, and higher-order moments of these two shocks, with ”good” (”bad”) variance associated with positive (negative) skewness. We document that macro risks significantly contribute to the variation of yields and risk premiums for nominal bonds. While overall bond risk premiums are countercyclical, an increase in aggregate demand variance significantly lowers risk premiums. Macro risks also significantly predict future realized bond return variances.

Risk, uncertainty, and asset prices

Journal of Financial Economics 2009 91(1), 59-82
We identify the relative importance of changes in the conditional variance of fundamentals (which we call “uncertainty”) and changes in risk aversion in the determination of the term structure, equity prices, and risk premiums. Theoretically, we introduce persistent time-varying uncertainty about the fundamentals in an external habit model. The model matches the dynamics of dividend and consumption growth, including their volatility dynamics and many salient asset market phenomena. While the variation in price–dividend ratios and the equity risk premium is primarily driven by risk aversion, uncertainty plays a large role in the term structure and is the driver of countercyclical volatility of asset returns.