Stochastic Volatility Risk and the Size Anomaly

Abstract

Investors' concerns about systematic volatility risk explain a large portion of the small firm premia in the long run. This novel finding supports the concept of market efficiency and indicates a "flight to quality" during recessions. Investors shift their preferences away from small firms, which are considered as being relatively risky. Instead they use large, "quality" stocks, whose returns co-vary positively with innovations in volatility (a recession-and-distress proxy), and therefore pay off during times of low market returns. This leads to higher hedging demands for large stocks, higher prices and lower expected returns. Using a sample of monthly returns spanning the period January 1927-December 2005, I estimate a statistically significant and negative price for volatility risk. This result is robust to the type of volatility measure used, to the inclusion of traditional risk factors in the model and to different model specifications. Controlling for accounting profitability type, I document a significant volatility premium ranging between 3% and 7% per year, for the Fama-French portfolios.

Keywords: Size anomaly, Volatility premium, Cross-section of stock returns, Griddy-Gibbs sampler, GARCH models

JEL Classification: G12, C11, C23