# SFB 303 Discussion Paper No. A - 373

**Author**: Werner, Jan, and Zhenyu Wang

**Title**: Portfolio Characterization of Risk Aversion

**Abstract**: The purpose of this note is to clarify the nature of the equivalence of the Arrow-Pratt measure of risk
aversion and the demand for risky asset. We shall state and prove three theorems and provide examples which
illustrate necessity of the assumptions. The proofs are relegated to the Appendix. The main result is Theorem 3
which shows that one investor is more risk averse (in the global sense) than the other, if and only if her portfolio
demand for risky asset with short-sales restrictions for both assets is lower than the demand of the other investor,
for every level of initial wealth, and every random return of the risky asset. This result holds for arbitrary (not
necessarily concave) utility functions.

**Keywords**:

**JEL-Classification-Number**:

**Creation-Date**: June 1992

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