Portfolio Efficiency Tests based on Stochastic Dominance Criteria
Speaker
Abstract
| Existing approaches to testing for the efficiency of a given portfolio make strong parametric assumptions about investor preferences and return distributions. Stochastic dominance based procedures promise a useful non-parametric alternative. However, these procedures have been limited to considering binary choices. We consider a new approach that considers all diversified portfolios, and thereby introduce a new concept of first-order stochastic dominance (FSD) optimality of a given portfolio relative to all possible portfolios. The scenario approach for distribution of outcomes is assumed. We develop an algorithm to test FSD optimality of a given portfolio. We show that the US stock market portfolio is significantly FSD non-optimal relative to benchmark portfolios formed on market capitalization and book-to-market equity ratios. Without appealing to parametric assumptions about the return distribution, we conclude that no non-satiable investor would hold the market portfolio in the face of the attractive premia of small caps and value stocks.For a risk averse decision maker a linear programming second-order stochastic dominance (SSD) portfolio efficiency test is derived. It is based on the relationship between CVaR and dual second-order stochastic dominance. If a given portfolio is SSD inefficient, our test, contrary to Post test and Kuosmanen test, detects a dominating portfolio which is SSD efficient. Moreover, using convexity of CVaR, a necessary condition for SSD efficiency is presented. A new SSD portfolio inefficiency measure is introduced. It is consistent with the second-order stochastic dominance relation. This measure is represented by a distance between the tested portfolio and its dominating SSD efficient portfolio. If there exist more dominating SSD efficient portfolios then the least risky portfolio is considered. |
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| Erik Kole |
