Downside risk asset pricing revisited: a new non-linear threshold model

ABSTRACT We derive an asset pricing equilibrium formula in which the risk premium on a risky asset is given by a weighted sum of the regular beta capital asset pricing model and a market portfolio downside risk beta. The equilibrium model is obtained from a new utility function that builds on the class of downside risk functions introduced in Bawa (1975, 1978) and that can be interpreted as an alternative to the disappointment utility functions of Dekel (1986) and Gul (1991), and the loss aversion utility functions as in Tversky and Kahneman (1991, 1992). This equilibrium model is econometrically represented by a non-linear threshold model that depends on a target return indicating market downturns. In the case where the target return is unknown we introduce an estimator of this threshold and a hypothesis test to assess statistically the significance of the downside risk parameter in the risk premium of the risky asset. An empirical exercise to industry, size and book-to-market portfolios uncovers a strong relationship between the risk premium and market portfolio downside risk.