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 for two reasons. First, the benefits of diversification depend not only on the correlation between returns, but also on the standard deviation of returns. Second, correlation does not provide an intuitive measure of the benefits of diversification. Return gaps are better indicators. A return gap is the difference in return between two assets or two portfolios. For example, as the authors show, the estimated 12-month return gap between the S&amp;P 500 Index and the Russell 2000 Index from February 2002 to January 2007 was 8.90%. This return gap implied 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 difficult to intuitively deduce these figures from the relatively high 0.82 correlation between the two indices. Likewise, it is difficult to intuitively deduce from the relatively high 0.86 correlation between the S&amp;P 500 and EAFE indices that, over this same period, their estimated 12-month return gap was 6.86% and realized 12-month return gaps ranged from 1.8% to 23.0%. Moreover, the figures belie any claim that these assets9 risk-reduction benefits have largely vanished. <b>TOPICS:</b>Accounting and ratio analysis, in markets, global