# Is "Information Coefficient" correlation or rank correlation?

From the textbook, information coefficient (IC) is a measure of the depth of an active manager’s skill. On a more formal basis, IC measures the “correlation” between actual returns and those predicted by the portfolio manager (Grinold & Kahn, 2000; Fabozzi & Markowitz, 2011). Cross-checking Investopedia suggests the same thing. That is, it's the pearson correlation between returns and scores. However, my colleague is adamant that it's the rank correlation not the pearson correlation. Which one is correct?

In a scientific field there is no ultimate judge or authority than can tell you what the "right answer" is. You can look at various authors that you respect to see how they define and use a term like IC. (I don't particularly respect Investopedia btw).

Often (for example in the book by Grinold and Kahn that puts the Information Ratio and Information Coefficient at the center of its exposition) IC is defined as "correlation" without specifying what kind of correlation they are talking about. In this case it is understandable and probably correct to interpret correlation as Pearson correlation.

However you can also find articles that point in a different direction. For example Dan Bartolomeo's Implementation of Equity Return Forecasting Methods (December 20, 1998) (link) gives a formula for Alpha in terms of IC and then states:

IC is the correlation between the investor’s forecasts and subsequent returns often called the information coefficient. [...] There are three popular ways to estimate the correlation between two sets of data. The first is the traditional Pearson correlation coefficient (arises from a standard ordinary least squares regression) that gives the actual correlation between the two data sets. The second is the Spearman rank correlation coefficient that approximates the correlation as the correlation of the rank positions of the related elements of the two data sets. The third is another form of rank correlation called Kendall’s Tau coefficient (for discussion see Gibbons, 1971). Of these three methods, Spearman rank correlation is most often used in practice. It is considered more robust (less affected by data outliers) than the Pearson method but is much easier to calculate than the Kendall Tau.

Given that the author is an well-known investment consultant whose firm presumably calculates IC's and uses them in its work, I would conclude that he uses and recommends Spearman correlation for computing IC. But of course that is just one professional's opinion.

Depends on your purpose. Rank correlation as information coefficient makes sense for cross-sectional strategies.

Example: You are running a long-short fund. Start by ranking the returns of assets for the next time period then go long on high ranked assets and go short on low ranked assets.