As of right now, we have this as our optimization objective function. But there’s one other term that it’s a good idea to add to it at this point. This is what’s called a regularization term. Here we use the L2 norm of the portfolio weights as the regularization term. In other types of problems, you might use a different term. What this do? Well, as you’ll recall, the L2 norm of a vector is its length. So, in this case, the term is basically the length of the vector of portfolio weights. This entire quantity will get very large if the weight on any single asset gets large. So, the effect is to penalize this behavior and enforce the spreading of weight amongst assets. The parameter here controls the balance between maximizing the portfolio alpha and enforcing the spreading of the weights across assets. To further clarify this, let’s imagine two possible extreme states of the world. In the first, you feel maximally confident in your alpha factors. You know for sure which stocks are going to go up and down in the future and by how much. In this situation you’d put all your long money in the stocks that will go up the most and all your short money in the stocks that will go down the most. In the second extreme state, you are absolutely sure that you know which stocks are going to go up and which are going to go down, but you don’t know by how much. You only know the sign of the change. So, in this case, the optimal portfolio is equal weight on all the stocks you take long positions on, and equal weight on all the stocks you take short positions on. You can think of the regularization parameter as a dial that you can use to tune between these two extreme versions of your prior knowledge of the world. This is the Bayesian interpretation of this technique. If you set the parameter equal to zero, that’s the state where you have full confidence in the alpha vector. As the parameter approaches infinity, the output weights approach equal weighting. So, you can think of the regularization parameter as your conviction dial.