Abstract
Joram Mayshar's [3] note is a valuable contribution to the theory of mean-variance portfolio analysis. His two points are correctly and carefully stated. It is important, however, that these results should not be overinterpreted. Mayshar shows first that when the outcome of a portfolio mix can be represented in >u space, these preferences will be quasi-concave for a risk-averse investor. The lognormal distribution that I used [2] as a counter-example to Tobin's [4] conclusion is not quasi-concave but is excluded by Mayshar because such a distribution is not the result of a portfolio mix. Although Mayshar is correct to emphasize the importance of results that are restricted to the distributions generated by portfolio mix problems, this class of distributions is quite limited. Readers may recall that Tobin's original article stated preferences and subjective probabilities in terms of rates of return and therefore, like my comment on it, was not set as a problem of portfolio choice in Mayshar's sense. Mayshar's second point is that a I a representation of preferences always exists when one asset is safe and the other has a given distribution. There can obviously be no quarrel about this conclusion when the form of the given distribution is known. But more generally it remains true that if theform of the two-parameter distribution of the risky asset is unknown, a knowledge of these two parameters is not sufficient to rank the portfolio combinations that result from combining this risky asset with a safe asset. Developments in portfolio theory during the past decade have gone beyond the meanvariance framework to study the portfolio behaviour of risk-averse investors facing general probability distributions (e.g. Arrow [1]). The results of these investigations confirm that I-au analyses may be heuristically useful but should always be regarded as only illustrative of a possible special case.
Published Version
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