Working Paper: NBER ID: w0574
Authors: David S. Jones
Abstract: In this paper, necessary and sufficient conditions for an asset substitution matrix to be symmetric for all distributions of rates of return are derived. It is found that symmetry in this context is essentially equivalent to the proposition that the von Neumann-Morgenstern utility function displays either constant absolute or constant relative risk aversion, depending upon whether the substitution matrix is defined in terms of arithmetic or geometric rates of return.
Keywords: Asset Demand; Substitution Matrices; Risk Aversion
JEL Codes: D81; G11
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Utility function displays CARA (R29) | Substitution matrix is symmetric (C65) |
| Utility function displays CRRA (D11) | Substitution matrix is symmetric (geometric rates of return) (C69) |