Correlation is a critical metric that can provide useful information in the portfolio construction process. Nevertheless, it is important for investors to understand that correlation is a property of random variables, and so does not describe a fixed relationship between variables: Assets with low and unchanging correlation can and do move in the same direction from time to time. In addition, correlations between asset class returns can and do change over time or in particular circumstances. Future correlations may also differ from those in the past because of changing economic and market regimes. Investors should take these factors into consideration when using correlation as a key input for constructing investment portfolios, not relying solely on statistical measures, but mixing in common sense and qualitative judgment as well. In addition, investors should recognize that low historical or estimated correlation does not ensure against loss, particularly in times of stress, and that bonds and other low-risk assets can provide valuable protection during such periods. The goal of portfolio construction should be to minimize risk while maximizing returns, but with a core understanding of how different assets react to different market environments and with the knowledge that low average portfolio variance is only one dimension of risk.
Investing over the long term will almost inevitably include short-term periods of (sometimes severe) market stress, during which the value of diversification for risky assets is less evident. Because investors tend to pay significant attention to large losses, it can be especially troubling when correlations "go to 1." It is in these periods that downside protection is needed the most, and the value of bonds—particularly high-quality bonds—shines. Of course, while correlations "go to 1" during market dislocations, investors can take some solace that a modicum of diversification can be achieved when assets do not move by the same amount, even when they move in the same direction. Investors can also feel some reassurance that systematic factors will occasionally drive "uncorrelated" assets higher in tandem during periods of relief from systemic crisis.
History supports the notion that over longer-term periods, diversification within and across asset classes offers substantial benefit. As a result, investors should continue to focus on their strategic asset allocation with regard to overall risk and return objectives/constraints, and the long-term expected returns, risks and correlations of the assets in which they invest. For those investors with greater sensitivity to significant near-term loss, lower-risk, lower-returning asset classes such as investment-grade bonds or even cash—whose diversifying properties tend to hold up during periods of market stress—may make more sense. On the other hand, investors who are less sensitive to significant near-term losses, or who are willing to endure significant near-term loss in the pursuit of long-term higher returns, may find it reasonable to allow higher-risk-premium asset classes to play a more substantial role in their portfolios. Each of these approaches can be considered prudent, and the decision of which path to take ultimately depends on the broad objectives of the investor.
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1 During periods of severe equity market stress, cash has historically been the most consistent diversifier for risky assets such as stocks. However, cash is more generally associated with short-term needs than investing with the goal of increasing the real value of a long-term investment portfolio. For this reason, we have chosen not to focus on cash in this paper.
2 Correlation has been widely used when constructing investment portfolios ever since Harry M. Markowitz first developed the theory of mean-variance analysis in the 1950s. The basic premise of mean-variance analysis is that investors face a trade-off between risk and expected return. In mean-variance analysis, risky assets can be combined in a portfolio in an attempt to minimize the total portfolio risk at any desired level of expected return. Markowitz discovered that portfolio standard deviation is a function not only of the standard deviations of all the individual assets in a portfolio but also of the covariance between the rates of return for all the assets in the portfolio. Optimal mean-variance combinations lie along the efficient frontier—a set of portfolios that has the maximum expected return for a given level of risk and the minimum risk for a given level of expected return. According to the theory, any risk/return combination that does not lie along the efficient frontier would be suboptimal. All rational investors would therefore wish to be positioned at some point along the efficient frontier commensurate with their return expectations and risk tolerance.
3 Throughout this analysis, references to "bonds" or "U.S. bonds" or "investment-grade bonds" are synonymous with the broad U.S. bond market. We represent the U.S. bond market by combining the following historical benchmarks: the S&P High Grade Corporate Bond Index from 1926 through 1968; the Citigroup High Grade Index from 1969 through 1972; the Barclays U.S. Long Credit Aa Bond Index from 1973 through 1975; the Barclays U.S. Aggregate Bond Index thereafter.
4 Throughout this analysis, references to "stocks" or "U.S. stocks" are synonymous with the broad U.S. stock market. We represent the U.S. stock market by combining the following historical benchmarks: the S&P 500 Index from 1926 through 1970; the Dow Jones U.S. Total Stock Market Index from 1971 through April 22, 2005; the MSCI U.S. Broad Market Index thereafter.
5 The correlation between monthly U.S. stock and U.S. bond returns from Jan. 1, 2011 through Dec. 31, 2011 was -0.91.
6 For a discussion of the correlation between U.S. and international equities, see Philips .
7 Other factors may also contribute to changing correlations. For example, increasing global interdependence among countries may cause correlations between U.S. and international stocks to increase over time. Solnik  has argued that increasing correlations are a natural progression as markets mature, develop and become more integrated.
8 We also looked at the correlation of hedge funds to U.S. stocks and bonds. The Dow Jones Credit Suisse Hedge Fund Index, however, started in 1994, so we excluded the index's results from this paper. That said, since 1994, hedge funds and U.S. equities have realized a 0.61 correlation, similar to that of U.S. stocks to REITs.
9 These findings cover the period April 2000 through February 2003.
10 Another potential strategy is to maintain the equity allocation and diversify the bond allocation across these assets. Over this period, such a portfolio would have averaged an 11.4 percent annual return but with higher volatility (9.6 percent) than that of the starting portfolio.
11 For a broader, more detailed discussion of the implications of combining nontraditional assets in a portfolio, see Kinniry and Philips .
12 As with average correlations, we also evaluated hedge funds over the course of the global financial crisis, and found that correlations to equities increased: Specifically, the correlation of hedge funds to equities increased to 0.72.
13 During the global financial crisis, the Barclays U.S. Treasury Bond Index returned 14.2 percent.
14 Other assets or tools that may be just as effective, if not more effective than bonds at hedging downside equity risk, include Treasury bills, derivatives or ETFs linked to the VIX (ticker symbol for the Chicago Board Options Exchange Market Volatility Index), inverse funds and ETFs, put options and other forms of portfolio insurance.