Asset Allocation without Unobservable Parameters

Fortunately problem 10 can be modified to accom

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Fortunately, Problem 10 can be modified to accom- modate non-IID returns (Foster and Stutzer 2002). The required formula still involves maximizing over all possible values of a risk-aversion parame- ter, but it is more complicated than Problem 10. Instead, advisors can estimate asset allocation– dependent shortfall-probability curves (like those in Figure 1) directly. To do so, one first fixes asset allocation weights (i.e., a specific rebalanced port- folio); then, one applies a straightforward tech- nique of bootstrapping with moving blocks (e.g., see Hansson and Persson 2000) to simulate numer- ous future return scenarios for the portfolio and the designated benchmark. From the scenarios, one tabulates the fraction of times the portfolio’s cumu- lative return at horizon H falls short of the desig- nated benchmark’s cumulative return. This fraction is the estimate of the portfolio’s shortfall probability at horizon H . By repeating this proce- dure for other portfolios (i.e., other asset allocation weights), a computer program searches for the spe- cific asset allocation weights with the lowest short- fall probability at H . Long-run investors should adopt an asset allocation that minimizes the short- fall probabilities for suitably large values of H . Reexamining the Arguments Given the behavioral evidence favoring target shortfall criteria and the implementational advan- tages of shortfall-probability minimization, a reex- amination of the typical arguments made in favor of the conventional use of expected utility and against the use of shortfall probability will be useful. The normative case for conventional use of expected utility is grounded in the Von Neumann– Morgenstern (1980) axioms for decision making in risky situations. Von Neumann and Morgenstern started from the postulate that a decision maker is able to rank-order the desirability (i.e., from most desirable to least desirable) of different probability distributions of wealth (“wealth lotteries”) result- ing from the various feasible decisions. They posed seemingly sensible axioms that decision makers might adhere to when composing this rank order. They proved that a decision maker acting in accord with those axioms acts as if he or she had adopted some utility function and had then rank-ordered the probability distributions in accord with the size of their respective expected utilities. Hence, the deci- sion maker’s top-ranked decision should be the one that leads to the distribution of wealth with the highest expected utility. The problem with this and other axiomatic “rationalizations” for expected-utility maximiza- tion is that axioms that appear to be reasonable on first examination do not always remain so after R pt w n R nt R Nt ( ) R Nt . + n =1 N –1 = max w 1 , , w N –1 max γ 1 T --- R pt R bt ------- γ t =1 T
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Asset Allocation without Unobservable Parameters September/October 2004 pubs .org 47 closer examination. For example, much reconsider- ation has been given to Von Neumann and Morgen-
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  • Winter '10
  • Acharya,Kandarp
  • Utility, advisor

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