9 – M4 L3a 08 Z Score V3

It’s common for researchers to normalize alpha factors by subtracting the mean and dividing by the standard deviation. We can also refer to this process as Z-scoring because the result is a Z-score. Z-scoring helps to standardize the data, so that it has a consistent range and distribution. This makes it easier to compare and combine more than one alpha factor. For instance, if we assume a somewhat Gaussian distribution, then about 95 percent of the values in a Z-scored distribution would be roughly between negative two and positive two. Notice that a ranking also has a similar benefit of setting different alpha vectors on the same scale. Whatever the original raw alpha values are for two different alpha factors when we convert to ranks, if we had a universe of 100 stocks, then the ranking for any alpha would be the integers 1-100. Note that Z-scoring has an additional benefit that you wouldn’t get from ranking. Z-scoring sets alpha vectors on a comparable scale even when we’re dealing with differently sized stock universes. For instance, certain alpha factors may be generated on different stock universes. So, if we had one alpha factor calculated on a universe of 100 stocks and another alpha factor calculated on 500 stocks, the rankings for the first would range from 1-100, while the rankings for the second would range from 1-500. Converting the ranks into a Z-score would rescale the two alpha vectors so that they could be comparable and more readily combined. Recall that ranking still makes our alpha vectors more robust against outliers and noisy data, and Z-scoring does not provide the same benefit. So, a valid approach would be to use ranking only when you know that all your alpha vectors are using the same stock universe. It’s also useful to apply ranking and then Z-scoring, if you think that some of your alpha vectors may be generated on different stock universes. One thing to remember is that when you work in a large asset management company, you may be one of many alpha researchers, and there may be other team members, portfolio managers, who use your alpha vectors. In this case, the portfolio managers want to get standardized outputs from all the quants. Z-scoring is one way to achieve this. Academic research often uses Z-scoring, as many papers are based on the work of Fama and French, who designed one of the first multi-factor models. Since this paper has influenced many subsequent papers in the study of factors, it’s likely you’ll see Z-scoring in academic papers.