Symmetric Substitution Matrices in Asset Demand Systsems
Working Paper 0574
DOI 10.3386/w0574
Issue Date
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.