How does a change in downside risk affect optimal demand for a risky asset?: Comparative statics on Tail Conditional Expectation

Abstract

This paper explains how changes in the return distribution of a risky asset, which alters Tail Conditional Expectation (TCE), impact the agent’s portfolio selection. We establish sufficient conditions for distribution changes, leading to a TCE reduction, to increase optimal demand for the risky asset. These results imply that risk-averse agents may increase their optimal demand for the risky asset when the downside risk premium increases. Furthermore, evaluating TCE, or downside risk premium, is compatible with second-degree stochastic dominance. This suggests that such an order of downside risk measures can provide additional insight into an agent’s portfolio selection, as identified by the stochastic dominance criteria.