Role Of Correlation In Portfolio Construction
Correlation is one of the primary building blocks of portfolio construction, along with expected returns and expected volatility. Because correlation summarizes the historical relationship between two assets, investors often focus on correlation to frame expectations for how a portfolio may perform over time. Specifically, by combining imperfectly correlated assets, a portfolio's expected volatility may be reduced, often without a significant effect on returns.2 As Figure 1 illustrates, from Jan. 1, 1926, through Dec. 31, 2011, adding a 10 percent bond allocation3 to a U.S. stock portfolio4 would have reduced volatility from 22.96 percent to 20.81 percent, but would have only reduced annualized returns from 10.17 percent to 9.95 percent. It's clear that the low average correlation between the U.S. stock market and the U.S. bond market (historically, 0.25), combined with significantly lower overall volatility for U.S. bonds, has produced a significant diversification benefit. This is particularly true in equity-heavy portfolios, where an addition of bonds has led to a reduction in portfolio volatility that has been disproportionately large relative to the reduction in average returns. And so long as the observed correlation remains constant over time, this relationship will tend to hold. However, challenges to portfolio construction arise when the correlations among assets do not remain constant, and instead shift, sometimes significantly.
Correlation And Portfolio Variance
Correlation differences may actually have a more modest diversification benefit than many investors perceive. In fact, in the case of combining stocks and bonds, the single largest factor contributing to the decline in portfolio volatility arises from the lower total volatility of bonds, not the fact that stocks and bonds have low correlation. From the mathematical definition of portfolio variance, the following relationship must hold for all two-asset portfolios:
Portfolio Variance = Variance1 + Weight1 2
+ Variance2 × Weight2 2 + Correlation effect
where "Correlation effect" is a function of the weights of the assets in the portfolio and their correlation with each other. A direct implication of this equation is that correlation is most relevant to diversification arguments, and most powerful in reducing portfolio volatility, when asset volatilities are more similar.
Volatility is typically associated with returns; however, measured correlations can also be volatile, often to the detriment of portfolios believed to be adequately diversified. And the shorter the window of observation, the greater the likelihood that realized correlation will differ from the long-term average. Figure 2 illustrates five-year correlations between monthly U.S. stock and U.S. bond total returns over five-year intervals since 1926 (17 distinct, nonoverlapping periods). While the long-term average correlation between these two asset classes has been 0.25, the figure shows that correlations over shorter windows vary widely from this average, with a range of 0.72 for the five years ended 1975 to -0.54 for the five years ended 2005.5
Volatility in realized correlations can have serious implications for investors, as the diversification and portfolio efficiency that is realized may differ from expectations. For example, over the 20-year period ended Dec. 31, 1985, the correlation between U.S. stocks and U.S. bonds was 0.57. This meant that the ex-post realized reduction in portfolio volatility achieved by adding bonds to a stock portfolio was reduced; that is, adding a 10 percent allocation to bonds to a 100 percent stock portfolio reduced volatility 6.8 percent (versus the long-term average of 9.3 percent). In contrast, from 1986 through December 2011, the realized correlation between U.S. stocks and U.S. bonds was -0.10, which translated into a volatility reduction of 10.2 percent when a 10 percent bond allocation was added to a 100 percent stock portfolio.