JEREMY C. STAUM is a Ph.D. candidate at Columbia Business School and Director of Research PARADIGM Capital Management in New York. A lthough considerable research in the alternative investment area concentrates on the performance characteristics of individual hedge funds or commodity tradŽ . Ž ing advisors CTAs e.g. Fung and Hsieh . 1997a, 1997b , many investors hold a portfolio of alternative investment managers. For traditional investments, the rule of thumb that nearly all of the diversifiable risk is eliminated in a portfolio of ten stocks dates back to Evans and Archer 1968 . Evans and Archer discussed the mathematical relationship between the size and variance of a portfolio and showed that for an equally weighted portfolio each randomly selected security added to the portfolio produces an ever smaller decrease in portfolio variance. The actual impact of random security diversification for stock and bond portfolios has been analyzed by various authors. Both Elton and Gruber 1977 and Hill and Schneeweis 1980 illustrated the impact of random security selection on portfolio variance for stocks and bonds, respectively. In both cases, the final impact is determined by the intrasample correlations. For instance, Hill and Schneeweis show that for portfolios of AAA bonds, the high intracorrelation of AAA rated bonds, in contrast to BAA rated bonds, lessens the impact of diversification on portfolio variance. Hill and Schneeweis also showed that as secuŽ rities are added, the tracking error the difference of the randomly selected portfolio’s variance from its expected vari. 1 ance decreases. As such, investors must realize that not only does diversification reduce portfolio variance, it also increases accuracy in achieving the expected level of risk.