Compound-Return Mean-Variance Efficient Portfolios Never Risk Ruin

Nils H. Hakansson and Bruce L. Miller
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Nils H. Hakansson: Graduate School of Business Administration, University of California, Berkeley
Bruce L. Miller: Department of Engineering Systems, University of California, Los Angeles

Management Science, 1975, vol. 22, issue 4, 391-400

Abstract: The implications of concentrating on the lowest moment(s) of average compound return over N periods in making investment decisions have recently been examined. In particular, maximization of expected average compound return has been shown to imply the existence of a utility of wealth function in each period with the "right" properties for all finite N \ge 2 as well as in the limit. More importantly, for large N a close (or exact) approximation to the set of mean-variance efficient portfolios (with respect to average compound return) is obtainable via a subset of the isoelastic class of utility of wealth functions. The properties of this class render it both empirically plausible and highly attractive analytically: among them are monotonicity, strict concavity, and decreasing risk aversion; moreover, the optimal mix of risky assets is independent of initial wealth (providing a basis for the formation of mutual funds) and the optimal investment policy is myopic. The purpose of this paper is to extend the class of return distributions for which the preceding results hold and to demonstrate that portfolios which are efficient with respect to average compound return, at least for large N, do not risk ruin either in a short-run or a long-run sense.

Date: 1975
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