Value at Risk and Expected Stock Returns

This paper provides empirical evidence that firm size, liquidity, and Value-at-Risk (VaR) explain the cross-sectional variation in expected returns, while market beta and total volatility have almost no power to capture the cross-section of expected returns at the firm level. The strong positive relation between average returns and VaR turns out to be robust across different investment horizons and loss probability levels. In addition to the cross-sectional regressions at the firm level, this study tests the empirical performance of VaR at the portfolio level using a time-series approach. The results based on the 25 size/book-to-market portfolios of Fama-French (1993) indicate that VaR has additional explanatory power after controlling for the characteristics of market return, size, book-to-market ratio, and liquidity. Mini-Abstract This paper provides empirical evidence that firm size, liquidity, and Value-at-Risk (VaR) explain the cross-sectional variation in expected returns, while market beta and total volatility have almost no power to capture the cross-section of expected returns at the firm level. The results based on the 25 size/bookto-market portfolios of Fama-French (1993) indicate that VaR has additional explanatory power after controlling for the characteristics of market return, size, book-to-market ratio, and liquidity.