24 – M4 L3a 182 Quantile Analysis Part 2 V3

Here’s an example of an ideal Alpha factors quintile performance. The fifth group containing the highest Alpha values would ideally give the highest returns. There would also ideally be a smooth progression, down the fourth, third, second, and first groups. That is the fourth group would have lower returns than the fifth group, but higher than the other groups. The first group would ideally have the lowest returns, and the second group would have the second lowest returns. It’s common for the tails to show predictive power; that is group five may have higher returns, group one low returns, but groups two, three, and four have returns not that much distinguishable from zero. In these scenarios, the Alpha model’s performance is more reliant on a smaller subset of the Alpha vector. In other words, on any given day, the factor return is due to the model being right on a subset of the stocks. Similarly, it’s also possible for the tails to show less predictive power and for most of the factor return to be attributed to the middle groups; two, three, and four. Again, this means that a subset of the entire Alpha vector appears to get it right on any given day, and it’s usually less correct when the Alpha number is either very high or very low. You must diagnose these situations very carefully. In most cases you want to see a monotonic relationship. Each successive quantile produces a higher return than the previous one. In general, if you don’t see this it could indicate that your factor is not robust and invalid. However, there are exceptions and you should think about this before you run the quintile analysis. One example is the Sloan’s accrual anomaly which you can read about on the link below. Whenever the factor return relies on a smaller subset of the Alpha vector having predictive power, then there’s higher risk associated with using that Alpha.

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