By T. Goodall
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Extra info for Adequate Decision Rules for Portfolio Choice Problems
It is depicted as that part of the boundary that lies between points A and B, with A being the ‘minimum variance portfolio’. The boundary of the feasible set does not simply connect those assets that offer superior expected value-to-variance ratios. 1 Portfolio choice in Markowitz’s model 32 offer better risk–return ratios than the single assets of the feasible set. This is so because the expected value of a sum of random variables is a linear combination of the random variables’ expected values, whereas the standard deviation of a sum of random variables is smaller than the linear combination of the random variables’ standard deviations.
Only under very special assumptions are the two identical in form and spirit. 26 But this means depriving the EU principle of much of its appeal and generality. The other such assumption is that all individuals again evaluate all possible results at face value, that is, omit the function u(r) altogether by setting u(r) = r, which amounts to setting ω(r) = ϕ(u). But the subjective character of all decision situations of Knightian risk calls for allowing individual evaluations of results. Thus, the EU principle and Bayes’s rule should not be considered equivalent.
Decision rules differ with respect to how much they utilise the information provided by the gambles’ distributions. The kind of information used reveals something about the proposed or assumed evaluation of a decision situation. Decision rules may be characterised accordingly. 2 Rather than utilising all information provided by the entire distribution of a gamble, classical decision rules utilise only some distribution parameters, like the mean, the median or the variance. The parameters alone determine which alternative to 15 A D E Q U AT E D E C I S I O N R U L E S F O R PORTFOLIO CHOICE PROBLEMS choose.