4 – M4 L1A 04 Standardizing A Factor V5

Now, let’s see how to convert this raw calculation into a standardized factor. We want the resulting weights to satisfy two conditions. First, we want the sum of the weights to add up to zero. Second, we want the absolute values of the weights to sum to one. To satisfy the first condition, we want to find the mean or average of the list of raw factor values for all the stocks. Then, subtract that mean from each of the raw factor values. We say that we de-mean the factor, because we’re subtracting it’s mean. To satisfy the second condition, we want to re-scale the values. To re-scale, we divide each value by a number. This scalar, equals the sum of the absolute values. So, we re-scale the values by dividing each value by this scalar. To standardize a vector of factor values, we both de-mean and re-scale, so that the mean of this two list of numbers equals zero, and the sum of the absolute values equals one. We could do the de-mean or re-scale, one after the other in either order. Let’s walk through an example with three stocks, each with a factor value such as a one year return. First, we want to de-mean the values so that they sum to zero. So, we calculate the mean by adding up the values of A, B, and C, then divide by the number of stocks. Then, for each stock, we get the raw factor value minus the mean. Next, we want to re-scale so that the sum of absolute values equals one. We can get the scalar by adding up the absolute values of the numbers. To re-scale, we divide each value by the scalar. This gives us the standardized values for the factor. We can verify the conditions that the sum is equal to zero and the sum of the absolute values equals one. Feel free to pause the video, if you want to study these steps in detail. Great. So, now you know how de-meaning and re-scaling can convert raw calculations into candidates for alpha factors. This is actually how we standardize factors so that we can evaluate them and compare them with other factors. Next, we’ll look at how to interpret, why we take these steps to standardize a factor. But first, here’s a random question to ponder, why were the normal distribution and the raw factor both very unhappy when they were told that they would be standardized? One, I know the answer, because they thought it was de-meaning. Get it? De-meaning.

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