Rank correlation, usually the Spearman coefficient, replaces each observation with its position in the ordering and then computes an ordinary correlation on those positions.
rho = Pearson correlation of rank(x) and rank(y)
The result runs from -1 to +1 and answers a narrower question than Pearson does. It asks whether higher values of one variable go with higher values of the other, without any claim about how much higher.
Why the ranks help
Take a cross-section of the Nifty 500 scored on earnings yield against forward return. One company posts a near-zero profit, so its price-to-earnings ratio reads 900 and its earnings yield sits far outside the rest of the distribution. Pearson correlation is a function of the products of deviations from the mean, so that one company can move the coefficient by a large fraction on its own. Spearman sees it as rank 500 out of 500 and nothing more.
| Property | Pearson | Spearman |
|---|---|---|
| Measures | Linear association in raw units | Monotone association in ranks |
| Sensitivity to one extreme value | High | Low |
| Handles a curved but consistent relationship | Poorly | Well |
| Uses magnitude information | Yes | No |
| Requires comparable units | Yes | No |
The last row is why factor research defaults to rank correlation. Return on equity in percent, debt to equity as a ratio and 12-month momentum as a fraction cannot be compared on their raw scales, but their orderings can.
Where it is used
The Information Coefficient is a rank correlation. So is any check of whether two signals are measuring the same thing before you combine them into a composite. Two signals with a rank correlation above about 0.8 are close to one signal, and averaging them adds cost rather than diversification.
Caveats
Discarding magnitude discards information you may want. If the top three stocks on a signal are far ahead of the fourth, rank correlation treats the gap as one step, and a portfolio that concentrates on the leaders will behave differently from what the coefficient suggests.
Ties compress the ranking. Signals with many identical values, such as a count that is zero for most of the universe, produce large tied blocks and an unstable coefficient.
Non-monotone relationships defeat both measures. If moderate values of a signal predict well and both extremes predict badly, Spearman reports close to zero and a quantile sort will show you the shape that the single number hid.
Robustness to outliers is not robustness to spurious correlation. Shared trends, overlapping windows and small samples inflate a rank correlation exactly as they inflate a Pearson one.