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Symmetric Substitution Matrices in Asset Demand Systsems

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  • 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.

Suggested Citation

  • David S. Jones, 1980. "Symmetric Substitution Matrices in Asset Demand Systsems," NBER Working Papers 0574, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:0574
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    1. Edward M. Gramlich & John H. Kalchbrenner, 1970. "A constrained estimation approach to the demand for liquid assets," Special Studies Papers 3, Board of Governors of the Federal Reserve System (U.S.).
    2. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
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