Ranking is a broadly useful method in statistics to make calculations more robust and less sensitive to noise. So, how do we use ranking here? If we have just two stocks in our portfolio, we would sort them by the office signal in descending order. So, for instance, let’s say we had a Raw Alpha values for Apple, Alphabet, and IBM. If we sorted their values and gave a rank of one to the lowest value, two for the next highest value, and three for the highest value; we’ve converted an Alpha Vector of decimals into an Alpha Vector of ranks. Note that we use descending order to preserve the property that the highest numerical Alpha value is proportional to the stock we think will rise the most. Now, let’s see how ranking helps us deal with outliers. If Apple’s Alpha value surged from 0.33 to 0.50 from day one to day two, and the Alpha Values of the other two also increased by 0.01 to 0.02, then the relative order or ranks of the three stocks wouldn’t change. When this gets translated into portfolio weights, it means that we wouldn’t be expected to make a trade based on these ranks. We can also see how ranking helps us deal with noise. If Apple’s signal increases by one percent from day one to day two, and Alphabet signal also increases by one percent, their relative values don’t change. So, the rank of Apple stays at two on both days and the rank of Alphabet stays at one for both days. Again, ranking is a broadly useful method for making data analysis more robust. We’ll see ranking used again later in this lesson.