A recent article from Morningstar states that

“Correlation is bound between negative 1.0 and 1.0. A correlation of 1.0 indicates perfect positive correlation, meaning that as one investment rises (falls), the other rises (falls) at the same rate.”

And, in email correspondence with Alpholio™, a prominent blogger for one of the well-known financial publications (who shall remain anonymous) stated that

“If you’re then going to hang your hat on the distinction between equity and high-yield bonds, I’d point you to the correlation of JNK and HYG to the stock market – about 85% with the financial sector the last three years. Your bond-equity distinction here just doesn’t hold.”

Well, these statements create a good opportunity to explain what correlation really means. First, the correlation in question is a Pearson correlation coefficient between two time series of periodic returns within an analysis interval. In most of practical calculations, the return period is chosen to be one month (daily or weekly returns are considered too “noisy”) and the analysis interval to be three years. In addition, either linear or logarithmic returns are used (the latter to account for continuous compounding).

Second, a high correlation does not imply causation. The fact that two entities are strongly correlated does not imply that one makes the other happen.

Third, and most importantly in the context of this discussion, a high correlation does not imply identity. The fact that two entities are generally moving in the same direction in each period does not mean that they are identical. That is because the magnitude of each respective move can be very different.

To illustrate this, let’s take a look at correlations and returns of the following indexes and securities in the most recent three-year and five-year intervals:

It turns out that the differences between linear and logarithmic return correlations are very small in this case (0.001). The following table shows the latter ones:

Interval S&P 500 SPY SSO
3 Years 1.000 0.998 0.998
5 Years 1.000 0.998 0.996

In both analysis intervals, correlations of both SPY and SOO to the S&P 500® were virtually equal to one (correlation of the S&P 500® with itself equals one by definition).

The following table shows correlations between HYG and VFH:

Interval VFH HYG
3 Years 1.000 0.769
5 Years 1.000 0.669

In neither analysis interval was the correlation close to 0.85 mentioned above.

Now, let’s look at cumulative returns. In the simplest approach, price returns can be used:

Interval S&P 500® SPY SSO VFH HYG
3 Years 59.9% 60.1% 151.6% 45.1% 10.7%
5 Years 28.8% 29.1% 31.5% 7.7% 0.0%

The SPY did a pretty good job tracking its underlying S&P 500® index — its price returns were actually slightly higher than those of the index in both analysis intervals.

However, to make things equal (with the exception of the index), total returns, which factor in the reinvestment of respective dividends, should be used. The following table shows the results:

Interval S&P 500® SPY SSO VFH HYG
3 Years N/A 69.6% 155.1% 52.8% 35.9%
5 Years N/A 43.1% 36.3% 19.0% 50.0%

The above data clearly demonstrate that even when correlations are close to one, as is the case with SPY and SSO to the S&P 500, returns of securities can be very different. Moreover, there the returns of HYG and VFH were quite different in both intervals. Hence, high correlations do not imply that “investments rise and fall at the same rate” or that they are “indistinguishable.”

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