By T. Goodall
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Extra info for Adequate Decision Rules for Portfolio Choice Problems
What the discussion will bring forth are arguments for and against all decision rules that make use of expected values. 16 The same is true for the ‘expected utility’ principle, designed by von Neumann and Morgenstern in 1944. Their work’s inﬂuence on decision theory in general and on portfolio choice theory in particular has been, and continues to be, overwhelming. Expected utility analysis has established two major lines of research. 7 Its inﬂuence was such that for a long time a decision rule could only be declared ‘rational’ by its proponents, if it complied with the expected utility’s axioms.
Serving both normative and descriptive analysis has undoubtedly contributed to its predominant role. On the other hand, its serving two masters has caused the expected utility principle to become a prime example of the continuing blurring of normative and descriptive decision theory. Discussing it will thus not only illuminate the predominant definition of ‘rationality’. It will also illustrate how to separate justiﬁed from unjustiﬁed criticism. There do exist direct applications of the expected utility principle to portfolio choice theory.
Thus, a measure is needed of how likely returns other than the expected value are, and how much conﬁdence an investor may thus have in the guiding quality of the expected value. Markowitz interprets the variance of the returns as such a measure. More specifically, he interprets the variance as a measure of the possibility of unfavourable results. This may be justiﬁable, at least for some decision situations. If the situation is characterised by normally distributed gambles, variance and standard deviation may well be used to calculate probabilities and conﬁdence ranges for results around the expected value.