Once we’ve calculated an Alpha factor, we can calculate some evaluation metrics, that let us compare it to other Alpha factors and get a sense for how it might perform when used to design a real-world portfolio. These metrics include factor returns, sharpe ratio, information coefficient, information ratio, quantile analysis, and turnover analysis. We evaluate Alpha factors to help us decide whether we’ll use them in creating a combined Alpha factor, which we’ll then use within portfolio optimization. One useful construct, is the return of the factor, which is called the factor return. The idea is that this is the return that a theoretical portfolio designed to capitalize on the arbitrage idea presented by the factor would produce. You can think of this as a way to directly measure the returns your portfolio would have if their weights were determined purely by the Alpha factor. To calculate the factor return we create a theoretical portfolio in which the weights for each stock on each day are set equal to the Alpha value for each stock on that day. So, every day we use the prior day’s known data to calculate an Alpha vector, which we would standardize to have mean zero, and the sum of absolute values equal to one. We use the Alpha value of each stock i, as the weight for that stock on the current day T. At the end of that day we check the returns of each stock i, for that day T, which we’ll call the single day return. Then, we can calculate the weighted average of the returns, using the Alpha values as weights. This gives us the factor return for a single day. We can repeat this for multiple days for a window of a year or more. This time series of daily portfolio returns is the factor return. Note that we’ll use historical data to calculate the factor return. So, the example of calculating this one day at a time, is to help you see that we’re simulating daily portfolio decisions that are only based on information that existed at the time of the theoretical trade, and these portfolio decisions are refreshed every day. Notice that the factor return depends upon the stock universe and time window of our theoretical portfolio, but it’s a useful way to compare various Alpha factors to each other if we choose the same universe and time window.