Why Does Bad News Increase Volatility and Decrease Leverage?

Abstract

A recent literature shows how an increase in volatility reduces leverage. However, in order to explain pro-cyclical leverage it assumes that bad news increases volatility, that is, it assumes an inverse relationship between first and second moments of asset returns. This paper suggests a reason why bad news is more often than not associated with higher future volatility. We show that, in a model with endogenous leverage and heterogeneous beliefs, agents have the incentive to invest mostly in technologies that become more volatile in bad times. Agents choose these technologies because they can be leveraged more during normal times. Together with the existing literature this explains pro-cyclical leverage. The result also gives a rationale to the pattern of volatility smiles observed in stock options since 1987. Finally, the paper presents for the first time a dynamic model in which an asset is endogenously traded simultaneously at different margin requirements in equilibrium.

Keywords: Collateral, Endogenous leverage, VaR, Volatility, Volatility smile

JEL Classification: D52, D53, E44, G01, G11, G12