Jan 08

Limits of correlation - 12 min. tutorial

by David Harper, CFA, FRM, CIPM

In a previous tutorial, I explained that correlation is covariance standardized (i.e., translated into an intuitive, unit-less metric) by the product of volatilities:

In this tutorial, I drew a (very) small sample of monthly periodic returns for three series...

Russell 3000 as proxy for stock market (unlike S&P 500, spans mid- and small-cap)
HFRI equity hedge index (long/short strategies)
HFRI fixed income high-yield (speculative debt)

...in order to calculate the correlations between

the Russell 3000 and the equity hedge fund index, and
the Russell 3000 and the fixed income high-yield index

But please note: my samples are very small. I am just trying to illustrate the calculation of correlation. Mainly, to show two "weaknesses" or limits of the metric:

The FI high-yield shows a higher correlation despite a lower covariance (relationship)! How can this be? Its volatility is lower
The correlations were pretty near to each other (73% versus 71%) but their respective out-performances vis-a-vis the Russell were very different. Equity hedge outperformed, fixed income high-yield under-performed. (Again, this is an illustrative sample of monthly returns over a single year, so no generalizations can be made; e.g., I did not run significance tests). On a scatterplot, this is shown by the y-intercepts: one is above the origin while the other is below the origin. The scatterplots reveal much that the correlation does not tell us.