By T. Goodall
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Additional resources for Adequate Decision Rules for Portfolio Choice Problems
This insinuates that ‘risk’ was measurable by a single statistical entity. ‘Risk’ thus turns from an undeﬁned characteristic of a decision situation into something inherently tangible and tractable. Expected value and variance become siblings. One sibling serves as an indicator for which ‘return to expect’ on the investment, the other sibling serves as an indicator for the ‘risk’ inherent in it. The intuitive appeal of this dichotomy into ‘return’ and ‘risk’ has proven irresistible. It has become so inﬂuential that many alternatives proposed to Markowitz’s rule are mainly concerned with what statistical entity to use instead of the variance as the measure for ‘risk’.
50 Up to the present day, any discussion of Markowitz’s µ–σ2 rule includes this conclusion on its ‘rationality’. It seems worth emphasising that this entire argument is based on declaring the EU principle the only ‘rational’ one. It is true that there has been a time when the von Neumann–Morgenstern deﬁnition of rationality was irrefutable; and most works on the relationship of the EU principle and Markowitz’s µ–σ2 rule stem from this time. 2, the EU principle’s claim to absolute right cannot be maintained.
It renders results that carry probability one. The link between decisions under Knightian risk and the problem of prediction is thus not self-evident, if inﬁnitely often repeated gambles are in the back of one’s mind. 38 But in the case of investment decisions and problems of portfolio choice, an inﬁnite repetition of the same investment is not the rule. The need to predict the result of an investment is thus inherent. The choice of which parameters to include in any decision rule applied to portfolio choice problems, be it normative or descriptive, may thus be governed by their predictive qualities.