Dependence and Risk Attitudes: Neutrality and Aversion

Abstract

Suppose that a decision maker faces a random outcome which is the sum of several risky components. If she is indifferent to the dependence structure of the risky components, then we say that she (or her preference) is dependence neutral. Obviously, if the decision maker is risk neutral, i.e., her preference is numerically represented by the expectation, then she is dependence neutral. We show the converse direction is also true: dependence neutrality and risk neutrality are indeed equivalent. Moreover, the decision maker may be averse to strong positive dependence representing extreme comovement (comovement aversion), and she may prefer less to more positive dependence (dependence monotonicity). Under a continuity assumption on the preference, we show that comovement aversion, dependence monotonicity, and strong risk aversion are all equivalent. Our results bridge the gap between dependence and risk attitudes, connecting two prominent concepts in statistics and decision theory.