Increases in risk aversion and the distribution of portfolio payoffs

In a mean-variance world, a less risk averse agent accepts additional variance in exchange for higher expected return. This is not true in all complete markets, but we show that a similar result holds with risk and return defined as in stochastic dominance. Specifically, an agent is less risk averse than another if and only if the agent chooses a payoff that is distributed as the other’s payoff plus a nonnegative random variable plus conditional-mean-zero noise for all state-price-density distributions. Additionally, if either agent has non-increasing absolute risk aversion, the non-negative random variable can be chosen to be constant. This main result also holds in some special incomplete markets with two assets or two-fund separation. In multiple periods, increasing risk aversion has an ambiguous impact at a point in time, but there is a natural mixture of distributions over time that preserves our results. JEL Classification Codes: D33, G11.