Back-to-Basics: The Importance of Correlation

Teri Geske
Senior Vice President, Product Development

Correlation is a notion from probability. It is a measure of the extent to which movements in two random variables track one another. The correlation between two variables can range from –1 to +1; a correlation of –1 means that every time one variable goes up, the other variable goes down, and vice versa. Similarly, a correlation of +1 ("perfect positive correlation") means that two variables always rise and fall in tandem. In these Back-to-Basics columns we shy away from mathematical formulas, but it is useful to remember that correlation is the "covariance" of two variables divided by the product of the standard deviations of those two variables. Even if we don’t recall the math behind a covariance calculation, intuitively we know that if two variables tend to go up or down at the same time, their covariance will be positive; conversely, if two variables tend to go up and down at opposite times, their covariance will be negative – dividing the covariance by the product of the standard deviations of the variables "normalizes" the number to a correlation value be between –1 and +1. A correlation of zero means the two variables are basically not linearly related – for example, you might expect that changes in the price of orange juice and changes in the US$/Yen exchange rate would have a correlation of zero – when orange juice prices rise, the $/Yen exchange rate might rise sometimes, fall at other times, or not change at all.

We are accustomed to thinking that the prices of almost all fixed income securities (except CMO Interest-Only tranches, inverse floating rate notes and certain others) are predictably, negatively correlated with changes in interest rates; a given change in rates causes a certain change in price (described by duration and convexity) and bond prices all move in the same direction as rates change. However, high yield bond prices are not as highly correlated to changes in interest rates as the prices of other bonds with similar features; the price of a high yield bond can be substantially affected by changes in the equity markets, regardless of what interest rates are doing, as a change in an issuer’s stock price may indicate a change in the perceived ability of the issuer to repay its debts and avoid bankruptcy. So, it is useful to know the correlation between changes in investment grade and non-investment grade bond yields. For non-US$ bonds, the expected change in price is a function of a shift in the yield curve corresponding to that bond’s currency. Since it is unlikely that the yield curves of the different countries represented in a global portfolio all move in the same direction at the same time, by the same amount, it is useful to know the correlation across the term structures. Imagine that changes in the yield curve in Australia were negatively correlated with changes in the yield curve in the U.S. – we could diversify our interest rate risk by holding bonds in both currencies. Even if we confine ourselves to US$-denominated investment grade securities, we need to consider the correlation between changes in interest rates and other risk factors such as sector spreads for both corporate bonds and mortgage-backed securities. We can use these correlations to estimate the expected return of a portfolio, or a portfolio vs. a benchmark given the volatility and correlations across key risk variables, and the portfolio’s (and benchmark’s) exposure to each risk factor.

Of course, as important as the concept of correlation is, we must remember that correlations are not necessarily stable over time. In fact, correlations can even change signs, depending upon what period of time is used to compute the statistic. So, although we might find that over one period of time, corporate spreads widened as interest rates rose, we could also find periods where the opposite was true. Or, we could find periods when corporate and mortgage spreads widened and tightened together, and other times when spreads moved differently between these asset classes. Similarly with correlations of yield curve shifts between two countries – in some periods we might find the yield curves of the U.K. and Germany displayed a weak positive correlation, and other times a somewhat negative correlation. For hedging and risk management this is a critical issue. Imagine a portfolio manager constructs a portfolio that contains bonds of two countries with negatively correlated interest rate risk, based on historical data. So, if rates in one country rise, rates in the other country tend to fall, and losses on some of the bonds would be at least partially offset by gains in the others. Now, imagine a situation such as the Russian default/Long Term Capital Management crisis of the Fall 1998. One of the most important and painful lessons learned from that experience is that in a crisis, all correlations may tend to move quickly to +1.0 – in other words, all markets may move together, in the same direction. In that environment, what was intended to be a hedge will actually magnify risk. This is, of course, a rare and extreme event, but is not unheard of. The experience highlights the importance of stress-tests as a complement to other risk measures that are based on model inputs such as correlation that may be unstable over time.

We hope this discussion of correlation has been a useful review – as always, we welcome your comments and suggestions for future Back-to-Basics articles. Please contact Marketing at fia.marketing@interactivedata.com with your ideas!

¹ These topics have been covered in previous Back-to-Basics articles, available on the previous page.