Diversification and generalized tracking errors for correlated non‐normal returns
研究了当基准资产收益非正态时，从基准中选取子集构建的投资组合的相对收益分布，发现随着子集规模增大，广义跟踪误差会变小，且分布近似对称并集中于原点。
The probability distribution for the relative return of a portfolio constructed from a subset n of the assets from a benchmark, consisting of N assets whose returns are multivariate normal, is completely characterized by its tracking error. However, if the benchmark asset returns are not multivariate normal then higher moments of the probability distribution for the portfolio's relative return are not related to its tracking error. We discuss the convergence of generalized tracking error measures as the size of the subset of benchmark assets increases. Assuming that the joint probability distribution for the returns of the assets is symmetric under their permutations we show that increasing n makes these generalized tracking errors small (even though n « N). For n » 1 the probability distribution for the portfolio's relative return is approximately symmetric and strongly peaked about the origin. The results of this paper generalize the conclusions of Dynkin et al (Dynkin L, Hyman J and Konstantinovsky V 2002 Sufficient Diversification in Credit Portfolios (Lehman Brothers Fixed Income Research)) to more general underlying asset distributions.