University of Washington - Department of Statistics
This talk describes some half-baked ideas for improving portfolio performance by making various modifications to classical mean-variance optimal portfolios. We begin by briefly reviewing the classical mean-variance (Markowitz) method of optimizing portfolios. We illustrate the outlier-generating non-Gaussian character of stock returns, and the problem of sensitivity of mean-variance optimal portfolio solutions to outliers. Then we discuss two distinct and potentially complementary approaches to dealing with the problem: (a) use of robust statistical methods, and (b) the use of Stable distributions to model the heavy-tailed nature of returns, coupled with either Value-at-Risk (VaR) or expected tail loss (ETL) as a natural asymmetric risk measure replacements for standard deviation. We point out the obvious weakness of VaR as a risk measure (in spite of its blessing by regulatory agencies) and the great appeal of ETL as a risk measure. The second approach requires fairly large sample sizes while the first is valuable, if only as a diagnostic, for smaller sample sizes. We illustrate use of these new approaches with several examples, including a "selection-of-fund-managers" application such as that used by the University of Washington's billion-dollar endowment fund. While much additional study is needed to determine the ultimate usefulness of the approaches discussed, we conjecture that they will eventually see mainstream use.