Correlation Doesn’t Measure What You Think!

This article originally appears in my risk.net column in February, 2015, which you can find here.

Take a quick look at the two panels of Figure 1 and estimate the correlation for the two funds in both panels. Really, please do it now. What’s your gut feel of the correlation of each set? If you are like virtually everyone I asked, it is quite obvious that the two funds in the left panel are uncorrelated or possibly negatively correlated while those in the right panel are highly correlated with each other. Estimates for the left range from zero to -0.7, and estimates for the right panel are often above 0.7. In reality, though, the funds in the left pane have a return correlation of +0.95 and the correlation for the set on the right is -0.92. That’s right: the funds on the left are positively correlation, and quite highly, while the funds on the right are negatively correlated.

In the left panel, over this simulated three-year time period, Fund 1 shows a 49% total return corresponding to a 14% annualized return. Fund 2 suffers a 29.6% total loss, or an annualized loss of 11%. Now take another look at that left panel and estimate which of these two funds is more volatile. Some people interpret Fund 2 as more volatile because it suffers a loss while Fund 1 has stellar returns, equating “risk” or “loss” with volatility, but most people recognize that Fund 1’s volatility is at least somewhat greater than the volatility of Fund 2. In fact, the volatility of Fund 1 is 2.5 times greater than the volatility of Fund 2.

Left Pane: who funds diverging in value. The blue fund's total return is 86% while the red fund's total loss is 22%. Right pane: Two funds both increasing in value.

Figure 1. Left Pane: two funds diverging in value. The blue fund’s total return is 86% while the red fund’s total loss is 22%. Right pane: Two funds both increasing in value.

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