Information Coefficient: Pearson or Rank Correlation?
Summary
The document addresses an ambiguity in the definition of information coefficient (IC), a measure used to evaluate the relationship between an investment manager’s forecasts and subsequent returns. Some sources say simply “correlation,” which can reasonably be read as Pearson correlation when no alternative is specified. Other practitioners use rank correlation, especially Spearman correlation, and Kendall’s tau is also identified as an option.
The discussion explains that Spearman measures the association between ranked values and is often favored in practice for being less sensitive to outliers than Pearson while remaining easier to calculate than Kendall’s tau. It also notes that rank correlation can suit cross-sectional strategies that sort assets into long and short groups. The central lesson is that IC has no universally fixed calculation in the material presented: the appropriate choice depends on an author’s convention and the strategy’s purpose. Researchers should state which correlation measure they use; the discussion does not establish a single mandatory standard.
Key ideas
- Information coefficient describes the relationship between forecasts and later returns.
- An unspecified reference to correlation may mean Pearson correlation.
- Spearman rank correlation is often used in practice and is less affected by outliers than Pearson.
- Kendall’s tau is another possible measure, though the document describes it as less convenient to calculate.
- Rank correlation can be suitable for cross-sectional strategies that rank assets for long and short positions.
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Full text
# Is "Information Coefficient" correlation or rank correlation? # 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? ## Answer by nbbo2 (score 2) https://quant.stackexchange.com/a/79161 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. ## Answer by aras edeş (score 0) https://quant.stackexchange.com/a/77549 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.
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