Abstract
A major drawback of Mean-Variance and Stochastic Dominance investment criteria is that they may fail to determine dominance even in situations when all “reasonable” decision-makers would clearly prefer one alternative over another. Leshno and Levy [1] suggest Almost Stochastic Dominance (ASD) as a remedy. This paper develops algorithms for deriving the ASD efficient sets. Empirical application reveals that the improvement to the efficient sets implied by ASD is substantial (64% reduction for FSD). Direct expected utility maximization shows that investment portfolios excluded from the ASD efficient set would not have been chosen by any investors with reasonable preferences.
Highlights
The most popular tool for portfolio optimization and selection is the Mean-Variance (MV) analysis
11It is interesting to note that Equation (8) implies that having a greater mean return is a necessary condition for ε-Almost SSD (ASSD): if EF < EG by (8) we have ε2 > 0.5, i.e. F does not dominate G by ε-ASSD
In order to shed more light on this issue, we ask the following question: we look at the Almost FSD (AFSD) efficient set with ε = 0.06, and we ask what preferences will imply a choice of investments outside of this AFSD efficient set
Summary
The most popular tool for portfolio optimization and selection is the Mean-Variance (MV) analysis. While MV and SD are the most widely used investment criteria, they both suffer from the following drawback Both the MV and SD criteria may fail to determine dominance even in situations where all “reasonable” investors would clearly prefer one investment to another. A serious drawback of the standard investment criteria is that they do not exclude from the efficient set investments which “common sense” tells us that no real-world investor would ever select. The idea of ASD is that if the area between the two cumulative distributions that causes the violation of FSD (area A1 in Figure 1) is very small relative to the total area enclosed between the two distributions (A1 + A2), a dominance relationship holds for all “reasonable” investors. ASD describes dominance for the set of all “reasonable” preferences, excluding extreme preferences that are considered “pathological”.
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