Correlation, Return Gaps and the Benefits of Diversification

Abstract

Correlation is the common indicator for the benefits of diversification, but it is not a good indicator. This is for two reasons. First, the benefits of diversification depend not only on the correlations between returns but also on the standard deviations of returns. Second, correlation does not provide an intuitive measure of the benefits of diversification. Return gaps are better indicators. Return gaps are the difference between the returns of two assets or between two portfolios. For example, the estimated 12-month return gap between the S&P 500 Index and the Russell 2000 Index and during February 2002 - January 2007 was 8.90%, implying that investors who concentrated their portfolios in one index or the other should have expected to lead or lag investors who diversified between the two in equal proportions by 4.45%. The realized 12-month return gaps ranged from 0.1% to 28.7%. It is hard to deduce these figure intuitively from the relatively high 0.82 correlation between the two. Similarly, it is hard to deduce intuitively from the relatively high 0.86 correlation between the S&P 500 and EAFE Indexes that their estimated 12-month return gap was 6.86% and their realized 12-month return gaps ranged from 1.8% to 23.0%. Moreover, the figures belie any claim that these assets' risk-reduction benefits have largely vanished.