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A New Example of a Closed Form Mean-Variance Representation

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  • Keith R. McLaren

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Abstract

In most finance papers and textbooks mean-variance preferences are usually introduced and motivated as a special case of expected utility theory. In general, the two sufficient conditions to allow this are either quadratic preferences with an arbitrary distribution of stochastic assets, or arbitrary preferences with Normally distributed assets. In the first case, the specific functional form of mean-variance preferences follows naturally. In the second case, the only specific functional form usually provided is the case of negative exponential preferences. In this note, the specific functional form for mean-variance preferences is derived for the much more realistic example of lognormally distributed assets, and constant relative risk aversion (CRRA) preferences.

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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 1/09.

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Length: 6 pages
Date of creation: Feb 2009
Date of revision:
Handle: RePEc:msh:ebswps:2009-1

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Keywords: Mean-variance preferences; expected utility; lognormal assets; risk aversion;

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  1. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
  2. Courakis, Anthony S, 1989. "Does Constant Relative Risk Aversion Imply Asset Demands That Are Linear in Expected Returns?," Oxford Economic Papers, Oxford University Press, vol. 41(3), pages 553-66, July.
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