Why do some investors care so much about the correlation between equities and Treasuries? Presumably, many believe the historically negative stock-bond correlation reflects the degree to which bonds will effectively hedge against a significant equity market sell-off, as happened in the 2008 global financial crisis. Yet, taken literally, the stock-bond correlation generally says little about the relative performance of stocks and bonds – arguably what investors actually care about.
Investors’ focus on the stock-bond correlation is understandable. Intuitively, a negative correlation between equities and bonds – which has been largely true of U.S. equities and Treasuries since the late 1990s – would suggest that bonds perform well when equities sell off, whereas a positive correlation would be evidence that bonds are not an effective hedge against equity risk.
In fact, however, this is not true.
To see why, one must first understand what a correlation is, and what it isn’t.
The meaning of correlation
Correlation measures the commonality in the deviation from trend for two series of returns. If both series tend to be above or below their respective trends at the same time, then they are positively correlated. Conversely, if the variables are generally on opposite sides of their means at the same time, they are negatively correlated. This can be shown mathematically in the correlation equation below. x and y represent two time-series (say, stock and bond returns) and the terms (xi- x) and (yi - y) represent each variable’s deviation from its own trend, or average return, over the measurement period.
What the correlation does not measure, however, is the relative performance of the two time-series. For example, it’s entirely possible for one time-series to have a positive trend and another to have a negative trend – and for the two series to be positively correlated. This is likely “counterintuitive” to how most people interpret the correlation measure. As such, the correlation tells us nothing about the actual returns of each series and hence the stock-bond correlation may say very little about the relative performance of stocks and bonds.
Figure 1 illustrates a real-world example. It shows cumulative returns over cash (represented by 90-day T-bills) of both Treasuries and U.S. equities during the recession that lasted from December 1969 to November 1970. During this period bonds returned 10.9% over cash while equities returned -7.0%. Hence, bonds provided diversification for equity investors during this turbulent period.
What is intriguing, however, is that the correlation between equities and bonds was positive, at 0.4, measured over the same period as the recession, using daily data. How is this possible? Simply put, bonds tended to be above their (positive) trend at the same time equities were above their (negative) trend, and vice versa. If investors had relied only on the correlation measure, they may have erroneously inferred that bonds and equities both performed poorly during the 1970 recession.
The upshot: Investors should care less about how the returns of assets deviate from their trends and more about the trends themselves – particularly when we are considering how bonds will perform in an equity market drawdown or in recessionary periods.
Might this simply be a one-off anomaly? It seems intuitive that if equities tend to fall in recessions and Treasuries rally, that they must be negatively correlated over the period. In fact, however, this is generally not the case.
Figure 2 shows the in-sample (daily) correlation between stocks and bonds and the performance of each asset class in the first half of every U.S. recession since 1970. We chose the first half of recessions because this is when equity drawdowns tend to be largest, as stocks generally recover in the second half of recessions. Rows in red correspond to periods when the relative return of each asset class is counterintuitive to the sign of the correlation, whereas blue denotes periods in which the returns are “intuitive” with the sign. For example, in the 1981–1982 recession, the in-sample correlation was 0.41, yet equities returned -11.2%, while bonds returned 12.9%. Hence, the sign of the correlation was counterintuitive to the relative returns.
In fact, in five of the seven past recessions, relative returns were counterintuitive to what the sign of the correlation implied. This result shows that the correlation provides little information about the relative performance of stocks and bonds.
What is key from an investment perspective, however, is that bonds provided needed diversification to equity risk in six of the past seven recessions. And this was true regardless of the sign of the stock-bond correlation. The sole exception was 1973, when Treasuries returned -3.5% during the recession’s first half (but ultimately produced positive nominal returns by the end of the recession).
Looking at correlations is too narrow. Average returns are what matter and the correlation is silent on returns. Bonds have historically hedged equity risk in recessions because returns have been positive, not necessarily because correlations have been negative. So, does the correlation matter? In our view, not really.
For more on the stock-bond correlation, please see our Viewpoint “Treasuries, Stocks and Shocks.” For a more technical treatment of the topic, please see “Stocks, Bonds and Causality.”
Jamil Baz is a managing director and head of PIMCO’s client solutions and analytics team. Steve Sapra is an executive vice president on the client solutions and analytics team. German Ramirez is a quantitative research analyst on the client solutions and analytics team. All are based in Newport Beach, Calif.