Portfolio Dominance, Lower Conditional Expectation And The Monotone Likelihood Ratio Order

In the standard portfolio problem, a shift in the distribution of the risky asset is ``portfolio-dominated'' if it reduces the demand for the risky asset by all risk-averse agents, whatever the riskfree rate. We show that the condition obtained by Landsberger and Meilijson [1993] (while necessary) is not sufficient for portfolio dominance and we present the exact necessary and sufficient condition for portfolio dominance. It is shown that, if the comparative statics property holds for any concave utility functions that are piecewise linear with two kinks, it also holds for the set of all concave utility functions. Portfolio dominance is stronger than second-degree stochastic dominance, but weaker than the monotone likelihood ratio order. We also show that the monotone likelihood ratio order is necessary and sufficient to yield the same unambiguous comparative statics property for a larger class of (nonlinear) payoff functions.