The use of asset class correlation in portfolio management has become commonplace. When designing and implementing investment portfolios, many financial advisors use a mean variance optimization model that is based on historic correlation analysis. The practice has become widely accepted - as evidenced by the deluge of articles recommending various portfolios based on historic correlation data. However, investors and practitioners need to be careful not to base their investment decisions solely on these simple mathematical regressions. What is often left out of the model is that the correlation between asset classes is dynamic and can unexpectedly change by a large amount in either direction.
Correlation Overview
Before continuing with this discussion, a basic review of correlation principles is in order. Correlation is the tendency of one investment to move in the same direction as another. This tendency is measured on a scale that ranges from +1 to -1. Positive correlation over 0 means that two investments generally move in the same direction at the same time, and a negative correlation less than 0 means that two investments move in generally opposite directions at the same time. A correlation of 0 or close to 0 is no correlation, which means that the two investments move independent of each other.
Although correlation measures the tendency of two investments to move in the same or opposite direction, it does not measure the amplitude of the movements. To illustrate this fact, assume an asset class has the following returns:
Asset Class Returns
Year 1 |
Year 2 |
Year 3 |
+10% |
-5% |
+10% |
Portfolios with the following returns will exhibit positive correlation of +1 with the asset class:
Year 1 |
Year 2 |
Year 3 |
+2% |
-1% |
+2% |
+40% |
-20% |
+40% |
+100% |
-50% |
+100% |
Portfolios with the following returns will exhibit negative correlation of -1 with the asset class:
Year 1 |
Year 2 |
Year 3 |
-2% |
+1% |
-2% |
-20% |
+10% |
-20% |
-100% |
+50% |
-100% |
Correlation in Portfolio Design
The essence of modern portfolio management is to design portfolios that have a high probability of meeting an investor's financial goal, while at the same time taking the least amount of risk feasible. The practice of asset allocation is central to this strategy. New investors learn quickly that they should diversify portfolios asset classes to reduce the risk of a large loss.
The concept of correlation is central to asset class selection. The idea is to choose investments that have the lowest correlation with each other so that the greatest benefit is derived from the strategy. If successfully designed, a portfolio of low and non-correlated investments from various asset classes will lead to less overall risk and greater returns. Additionally, periodic rebalancing is needed to get the portfolio back to its original level of risk, as asset classes go in and out of favor.
Choosing investments that have low or no correlation presents investors with several problems. The most difficult is to find asset classes that have low correlation with one another. Some suitable asset classes are not investable, or their securities are illiquid, which results in transaction and market impact costs. Some suitable asset classes may simply prove prohibitively expensive, thereby negating the benefit of their use. For example, hedge fund strategies are expensive to implement. Finally, past asset class correlation is often a poor predictor of future asset class correlation. As a result, investment plans designed primarily on only historic correlations often don't perform as predicted.
Problems with Historic Correlation
Measurement of asset class correlation over different periods of time show that there are wide variations in the results. One of the biggest flaws in most asset allocation models is that they use correlation coefficients based on a simple average rather than looking at different time periods. For example, from January 1967 to October 2003, the correlation of monthly returns between the S&P 500 and long-term U.S. Government bonds was +0.31. A positive correlation infers there is a tendency for the returns of stocks and the returns of bonds to move in the same general direction. As a result, an asset allocation model based on a simple average correlation might limit the amount of one or the other of these asset classes in a portfolio because they are positively correlated, and favor other asset classes that are less correlated.
A closer analysis of the rolling three-year correlation between S&P 500 and long-term U.S. Government bonds over the period reveals a different picture.
The rolling correlation between stocks and bonds from the mid-1960s through the mid 1990s was positive. A portfolio designed in the mid-1990s based on an optimization model that used linear regression data would not have been the optimized for the bear market in stocks and bull market in bonds that occurred from 2000 to 2002. The resulting negative correlation that occurred between stocks and long-term bonds over the period indeed proved to be a good hedge against a severe stock market downturn. In other words, sometimes the future doesn't look like the past.
In addition, based on correlations in the 1960s through 1990s, many academics and portfolio managers had concluded that long-term bonds had little use in portfolios. However, brief periods of negative correlation occurred several times over the past seventy-five years, particularly during difficult periods in the stock market.
A second problem with asset allocation models based on historic correlations is that much in the data is discarded when it does not fit into the equation. In multi-asset class models, the matrix used to generate a recommended portfolio is based on the average correlation between asset classes, but it only goes back as far as the newest asset class. If one asset class has only fifteen years of historic data, then the entire correlation matrix is only valid for that period of time.
The rolling correlation of various asset classes and sub-asset classes show that correlations are constantly moving, and that newer asset classes have not fully revealed their tendencies. During the 1980s, the Wilshire All REIT index had a high correlation with the S&P 500, but in the 1990s had become less correlated, and even become slightly negatively correlated in 2001.
A casual observation of REIT correlations might lead one to conclude that the asset class had a high degree of interest rate sensitivity and was acting like long-term U.S. government bonds. However, an analysis of the correlation between a REIT index and long-term government bonds shows that this is not the case.
Forecasting Correlations
One solution to correcting the problem of static correlations in financial models is to use forecasts. If an accurate assumption about the relationship between asset classes can be made, than a better portfolio can be designed. Unfortunately, forecasting creates it own set of problems. Namely, how does one do it?
Trend following happens to be a favorite of portfolio managers and analysts. If the correlations of one asset class are becoming more positive, the tendency is to forecast that correlations will become more positive. Such has been the case with many investors' view of the international stock market. It is often proclaimed that the benefits of international investing are not as great as they used to be, and correlations will continue to increase. Figure 5 illustrates the rolling three-year correlations between the S&P 500 and two foreign indexes, the MSCI Japanese Large Company Index and the MSCI Europe (ex-UK).
A review of correlations between the U.S. stocks and the indexes reveal a few notable observations. First, there is a positive correlation of returns between the S&P 500 and large developed market indexes around the world. Second, those correlations became stronger in the late 1990s. Third, there has been a recent divergence between the direction of the correlation trend in Japan and Europe.
It is often proclaimed that the benefits of international investing are not as great as they used to be, and correlations will continue to increase. In this authors' opinion, a recent increase in the correlation of asset classes is not a good reason to ignore that asset class. It is a mistake to conclude that the benefits of diversification into international equity markets has somehow been permanently reduced. My belief is based in part on the sudden and unexpected reversal in the correlation of other asset classes after the same proclamation was made. Over the last three years the correlation between U.S. stocks and European stocks increased to its highest level on record, while the correlation between U.S. stocks and long-term U.S. Government bonds decreased to its lowest level. I do not believe either of those events could have been predicted in advance.
Conclusion
Correlation analysis is important to designing and implementing efficient portfolios. However, investors should be aware that correlations between asset classes are not static, and using models that employ static correlations may lead to a portfolio recommendation that is not suited to the investor's need.
Correlations between asset classes change, sometimes abruptly and by a large amount. A better method is to design portfolios that have a broad array of asset classes and sub-asset classes, with each asset class having a fixed target. Then rebalance the portfolio when the target allocations are out of line. It is clear that some asset classes will become more correlated in the future, and some will become less correlated. The problem is, we do not know which ones they will be. A multi-asset class portfolio solves this dilemma by always being invested in a large number of classes and averaging out the correlation changes.
****
Richard A. Ferri, CFA, is the president of Portfolio Solutions, LLC, an SEC registered investment advisor in Troy, Michigan. Ferri has written extensively on passive investing including the use of index funds. He has published three books, Serious Money, All About Index Funds, and Protecting Your Wealth, and is currently working on a fourth book titled All About Asset Allocation. Website -- http://www.psinvest.com/