Let’s take a moment to have a final discussion about what is going on here. We started with our alpha vector, which is a vector of numbers that we think will be proportional to future returns. We want to maximize our alpha times our weights and minimize risk as modeled by our risk model, and we use optimization to achieve this. We also apply several other constraints during optimization, such as a constraint that we are market neutral, for example. But if we apply the market neutral constraint now, why did we subtract the mean from each individual alpha to make them market neutral back when we were calculating our alphas? Isn’t this just duplicating alpha? Why not just wait for the optimizer to make the portfolio market neutral? We are using optimization so that we can control risk, but it creates a challenge when the optimization has a significant effect on the alpha vector. If your resulting portfolio is massively different than your alpha vector, then all your research and evaluation of your alpha factors up to that point might be invalidated if the final portfolio weights given by the optimizer don’t look anything like the original alpha factor. So, you don’t want the optimization to change your alpha vector too much. If you find some alphas and the optimization yields a very different portfolio than what you had when you started, then it’s hard to figure out how to adjust the parameters. It can be hard to know whether to adjust the risk model or the constraints and by how much. Your alpha research is your pure expression of expected return. Any deviation from that is a sub-optimal deviation. But you’re willing to accept that to trade off against risk, and you’re willing to change the alpha vector to optimize on risk. But that only goes so far. If you end up with a portfolio that is completely far away from the alpha vector, then this isn’t helpful either. You’ve evaluated the alpha factors and have some sense of how good they are, but the portfolio may no longer be following the signals of those alpha factors. So, what that means from a practical perspective is you want to introduce risk control as early in the process as possible. If you know that you’ll use your alpha in a portfolio that is sector neutral, then you should make the alpha factor sector neutral. That way, if the alpha factor already looks good given the sector neutral weights, it has a better chance of translating well from theoretical alpha to resulting portfolio.