16 – M4 L3A 142 Ranked Information Coefficient Part 2 V5

More formally, here are the steps we’ll take to calculate the Rank IC. For each time period, rank the raw Alpha factor. For instance, with a stock universe of three stocks, the lowest Alpha value has a rank of 1, and the highest Alpha value has a rank of 3. Also, calculate the forward asset returns and rank them. The stock with the lowest forward return has a rank of 1, and the stock with the highest forward return has a rank of 3. The correlation of ranked values is called the Spearman rank correlation to distinguish it from the Pearson correlation. Let’s clarify these two terms. The Pearson correlation is what you’re probably familiar with, is the covariance of two variables which is then re-scaled using the standard deviations of the two variables. The denominator makes the correlation range from negative 1 to 1. The Pearson Correlation is also the square root of the R-squared in a linear regression. Recall that the R-squared represents the proportion of variance in one variable that is explained by the second variable. The Spearman rank correlation is the same as the Pearson correlation, except the variables x and y are converted to ranks before calculating the covariance and standard deviations. To get the rank IC, calculate the correlation between the ranked Alpha vector and the ranked forward asset returns for a single time period. Repeat this over multiple time periods to get a time series. You may be wondering why we use the Spearman rank correlation as opposed to the Pearson correlation. That is why do we use ranking? The answer is because we don’t care about being wrong in the right direction. Let’s say stock ABC is our top Alpha value in a universe of 2,000 stocks. Our alpha value will likely be a small positive value, then imagine that ABC outperforms all the other stocks not by a small amount, but by a very large amount. The Pearson correlation would calculate a lower score effectively penalizing us because we didn’t get the relative magnitude correct. On the other hand, the Spearman rank correlation would not be affected by this. We prefer to use ranking to evaluate our performance because what matters is that our Alpha is still profitable as we had hoped.