23 – M4 L3a 181 Quantile Analysis Part 1 V2

We saw earlier that the rank IC can tell us overall how well an Alpha vector’s predictions align with the subsequent stock returns for the next period. You may be wondering if it’s possible to drill down deeper to look at the Alpha values assigned each stock to see which subset of stocks actually contribute most or least to the factor return of the portfolio. Ideally, if our Alpha model and hypothesis were accurate, the stock with the highest Alpha value for that day would also have the highest positive return the next day. Similarly, the stock with the lowest Alpha value for that day would also have the lowest return in the next day, which would be good for our theoretical portfolio since we would be shorting that stock. Remember, that we are working with perhaps hundreds or even thousands of stocks in our universe. So, a good middle ground is to divide our Alpha vector into quantiles and analyze their returns and volatility within those quantiles. An ideal Alpha model would be one where the group of stocks containing the highest Alpha values for that day would also have the highest average return, and possibly, the highest risk adjusted to return. Similarly, the group of stocks containing the lowest Alpha values would ideally have the lowest returns. For example, if we have 25 stocks in our universe and wanted divide them up each into five groups of equal size, we would be using five quantiles also called quintiles. For each day, we’ll sort the stocks by their Alpha value. The five highest values go in the fifth group, which are above the fourth quintile. The stocks with the lowest five values go in the first group, which are below the first quintile. Similarly, we fill groups 2, 3, 4, with five stocks each based on their Alpha value. We can keep track of the individual returns within each of the five groups over a time window such as one, three, or five years. Then we can calculate the mean return within each group as well as the standard deviation. We can call what we just did quantile analysis or quantile performance. Since we chose five quantiles, we can also call this quintile performance.