Correlation is the statistical measure of diversification; when calculated between the S&P 500 and MSCI EAFE indices over the last 30 years, a noticeable trend occurs. Correlation increased from 0.47 (from 1980 to 1990) to 0.54 (from 1990 to 2000) to 0.83 (from 2000 to 2009).
Clearly, understanding how diversification of investments changes over time is very relevant. For example, when liquidity became an issue in the fourth quarter of 2008, asset correlations began to approach 1.0, the point at which diversification can fail. Such failure is largely due to the variation of asset correlations over time. The market stresses of 2008 and their effect on asset correlation were reported by others who saw greater positive correlation. The effect of buy-and-hold strategies, along with the need for more active management techniques, was further reinforced by market observations.
Hypothesis and Simple Illustration
Is there a simple, repeatable approach that can continue to provide the practical benefits of diversification? To develop assumptions and test such an approach, the following questions were addressed:
- What publicly available asset classes should be considered in building a diversified portfolio?
- How much history should be examined before making decisions?
- How frequently should portfolio changes be made and how do switching costs influence such decisions?
- What is an appropriate correlation coefficient threshold?
- What allocation strategy should be employed?
To explore these questions and to develop a rationale on an analytical framework, Figure 1 was constructed and tracked by representative exchange-traded funds (ETFs).
Figure 1 shows a time series of gains and losses for each of the asset classes listed in Table 1 below. All of the asset classes, except bonds, suffered a significant loss in 2008. A broader look at 2008’s gains and losses shows that real estate and commodities fell by 39 percent and 47 percent, respectively, in addition to the domestic and international equity assets shown in Figure 1. Domestic bonds gained 5 percent, non-U.S. bonds gained 10 percent, and short-term Treasury bills returned 1.5 percent.
Table 2 illustrates the result of a naïve approach, which spreads assets equally across asset classes. In 2008, applying this approach to these four funds would have led to a 27-percent loss.
The concept of diversification suggests that only uncorrelated assets should be held in a portfolio. To measure the correlation, or lack thereof, among assets, we calculated correlation coefficients based on returns of risky assets over a fixed period of time. A positive correlation coefficient indicates asset returns are directly related to one another, while a negative correlation coefficient suggests an inverse relationship. A correlation coefficient near zero implies the change in one risky asset has little to no effect on the change of the other.
Applying this active approach, Table 3 shows the correlation coefficient based on daily returns from 2007. The value of 1.0 along the diagonal is expected, as it is a measure of an asset’s price movement relative to itself. A correlation threshold of 80 percent implies a diversified portfolio should only hold two of these assets because the correlation coefficients associated with SPY, EFA, and IWM are all greater than 0.80. Thus, bond (AGG) and domestic large cap equities (SPY) should be selected for future allocations and SPY could be replaced with either IWM or EFA in order to satisfy the 0.80 correlation threshold.
After selecting AGG and SPY, a naïve allocation strategy was applied to construct a portfolio and to test its performance in 2008 (Table 4). Both classes demonstrate the first part of our hypothesis—that a simple approach to diversification (e.g., applying an 80-percent threshold on correlations from the previous year) could lead to significant protection against loss of principle the following year. The results also showed that in a downward-trending equity market such as 2008, one should move to less risky, lower beta assets, thus adhering to the precepts of modern portfolio theory (MPT). The challenge is that the three equity classes had small gains and losses in 2007, providing inconclusive evidence about the broad equity market downturn to come.
Analysis Assumptions and Methodology
The assumptions and methodology were based on the previous simple illustration. To address the first question—what publicly available asset classes should be considered when building a diversified portfolio?—a broad set of asset classes that have been publicly available as ETFs since January 2004 were identified. These comprised of 136 unique funds in the following asset categories: large, mid, and small cap domestic equity; international developed markets; emerging markets; commodities; bonds; domestic sectors; and real estate.
Exchange-traded funds were chosen because they are passive investments designed to track a wide variety of asset classes, and the funds are readily available to the investment community. They also carry many other advantages, including:
- Reduction of firm-specific risk by spreading a single investment across an assortment of individual firms,
- Transparency of holdings,
- Low cost inherent in passive investment approach, and
The author chose to carry forward the 12-month assumption applied in the previous simple illustration, similar to the certified financial advisor community’s employment of a 200-day average to assess rapidly changing market conditions. In addition, Louis G. Navellier, a well-known investment advisor, calculated his MPT review and the critical alpha/standard deviation statistic based on a year.
Portfolio rebalancing and the associated switching costs are important practical considerations. The author examined them over a range of possibilities, including yearly, biannually, and quarterly. By including trading commissions at $10 per trade against an initial portfolio size of $100,000 in a tax-free account, an optimal reallocation period became apparent. (Taxes are an important cost to consider, particularly for non-pension investors; however, the effect of taxes on performance was not explored in this article.)
Based on the results from the previous illustration, a threshold of 80 percent appears to provide diversification. Other studies have used 0.95 based on mutual funds with no trading costs. However, because trading costs were included in this study, the 80-percent threshold was applied to reduce the number of potential positions in the portfolio and to address the longer-term correlation growth trend observed between the S&P 500 and MSCI EAFE indices. Lastly, in an effort to maintain a simple overall approach, the aforementioned naïve strategy was employed.
Figure 2 shows the resulting time series associated with the number of ETFs that were less than 80 percent correlated over the three-year study—from January 1, 2006 to December 31, 2008. The increasing correlation among asset classes is clearly illustrated by the reduction in uncorrelated funds available. The reduction of uncorrelated assets from 2006 to 2008 is consistent with the longer-term hypothesis confirmed in a similar 10-year study, which examined 30 stocks in the Dow Jones Index and 500 stocks in the S&P 500 index.
With knowledge of uncorrelated funds, the naïve allocation strategy was applied annually, biannually, and quarterly. The resulting portfolios are shown in Tables 5, 6, and 7. It is important to observe the long-term relationship of bonds to stocks in these figures; as one would expect—and was shown in the previous simplified illustration—the correlation coefficient between stocks and bonds was consistently below the 80-percent threshold selected for this study. Bonds continually appeared in the portfolios over time with allocations varying between 2.4 percent and 16.7 percent.
Table 8 shows the annual net returns based on the three reallocation periods. Due to the large allocations to domestic sectors, the S&P 500 benchmark was included for comparison. In all cases, net returns exceeded the S&P 500 benchmark on an absolute basis in each of the three years, and the best return came from annual reallocations. In addition, the author minimized 2008 losses using biannual allocations, which beat the quarterly reallocation results because of the fewer trades required (28 versus 61).
To provide an alternate perspective, the author computed the Sharpe ratio based on monthly returns, monthly standard deviations, and a negligible risk-free rate. The results in Table 9 illustrate that, on a risk-adjusted basis over the three-year period, annual reallocations provided the optimal risk-adjusted performance. In addition, trading costs associated with increased frequency of reallocations consistently decreased the Sharpe ratio. For quarterly reallocation intervals, the naïve allocation strategy no longer beat the performance of the S&P 500 on a risk-adjusted basis.
Periodically reallocating a portfolio using uncorrelated assets appears to be a practical approach to diversification. The events of 2008 clearly necessitate the need for such strategies to manage investment risk.
Utilizing the latest investment vehicles available from ETFs, this article provides a simple methodology, based on a naïve reallocation strategy, which accounts for the practical impact of trading costs. While diversification still appears to reduce the likelihood and severity of loss, it should not be considered foolproof and should be considered in conjunction with other forms of risk mitigation. It should be noted that this study’s results are based on a limited testing period representing a global market with some stressing conditions, including moderate upward and significant downward trends.
For individuals interested in examining their ETF portfolios and correlation coefficients, a few options are available. First, there are online tools, such as Correlation Tracker, which provides correlation coefficients for six-month, one-year, and three-year spans. For certain sector ETFs, fund providers publish information about correlation among their offerings. Lastly, free internet sites, such as Google Finance and Yahoo! Finance, offer downloadable closing price information, which can be analyzed using Excel’s “covar” function.
DISCLAIMER: The exchange trade products analyzed in this article were chosen from those publicly available. They do not represent the author’s recommendations and were only used to support observations. Investment advice is neither implied, nor suggested.
 “Modern Portfolio Theory is History,” Money Management Executive, February 2009.
 U.S. Securities and Exchange Commission, Beginners’ Guide to Asset Allocation, Diversification, and Rebalancing, http://www.sec.gov/investor/pubs/assetallocation.htm.
 Lawrence C. Strauss, “Backing Up Equity Bets With Hard Assets,” Barron’s, April 27, 2009.
 Jane Bryant Quinn, “The Right Way To Diversify Your Portfolio,” The Washington Post, April 26, 2009; Steve Hanke, “Unconventional Wisdom,” Forbes, March 16, 2009; and William J. Bernstein, “Yes, Diversification Works – Eventually,” Money Magazine, April 1, 2009.
 Anton Troianovski, “REITs Rise Sets Back Day Traders,” The Wall Street Journal, May 2, 2009; David Pett, “Don’t Drop Portfolio Theory, Report Says,” Financial Post, April 28, 2009.
 Craig L. Israelsen, “Gauging the Mess,” Financial Planning, March 1, 2009.
 Brian Healy and Niall Gibney, “Exchange Traded Funds: Opportunities for Portfolio Diversification,” Accountancy Ireland, February 1, 2009.
 Don Ogden, “Market Notes,” Raymond James, May 2009.
 John O’Brien, “Rebalancing: A Tool for Managing Portfolio Risk,” Journal of Financial Service Professionals, 60, no. 3, (2006).
 J. Angus, W.O. Brown, J.K. Smith, R. Smith, “What’s in Your 403(b)? Academic Retirement Plans and the Costs of Underdiversification,” Financial Management, 36, no. 2, (2007): 1–38.
 M. Medo, C.H. Yeung, Y.C. Zhang, “How to Quantify the Influence of Correlations on Investment Diversification,” International Review of Financial Analysis, 18 (1–2): 34–39, 2009.
 Jeff Tjornehoj, Don Cassidy, and Michael Porter, “The Growing Attraction of Sector ETFs,” Lipper FundIndustry Insight Reports, October 20, 2005.