Traditional Beta, Downside Risk Beta and Market Risk Premiums

Abstract

The article develops a downside risk asset-pricing model, which is based on Conditional-VaR (Mean-shortfall) risk measure. As in the traditional model the model leads to a monetary separation and yields a CVaR beta analogous to the traditional beta. An empirical study indicates that CVaR beta, which considers also downside risk, has greater explanatory power than the traditional beta. This is especially true in the case of a bearish market. Moreover, a combined model, which uses both betas, outperforms both the traditional and the CVaR models.

The results indicate that in a bullish economy, risk premiums may be partially explained by the traditional beta. However, in a depressed economy investors are most likely more concerned about downside risk, which is poorly captured by the traditional beta. This downside risk can best be captured by CVaR beta, which is based on historical data and avoids assuming any prior distribution.