Okay. Let’s say we’ve read a paper, extracted some ideas, and have come up with an Alpha factor. Now, let’s talk about some of the common early transformations we might do to that factor in order to move it closer towards our goal. A vector of numbers that represents the weights we’d use to create a portfolio. These transformations help to enhance, improve, and prepare our Alpha factors so that they may be used during portfolio optimization to choose actual portfolio weights. When we actually implement traits for our portfolio, we want that portfolio to be neutral to common risk factors. We should not wait however for the optimization step to think about common risk as we do not want to rely exclusively on optimization to make this happen. Rather, it’s best to consider obvious common risks even at the Alpha research stage. The most significant common factor risks are market risk and sector risk. We control market risks explicitly by the definition of an Alpha factor. The sum of the values is zero implying zero exposure to the market. Note that an important assumption that we’ll make is that on average the Betas or exposure of the stocks to the market are all one. So even though in reality the regression Beta of stock ABC to the market may be 1.2 or the Beta of stock XYZ maybe 0.8. When dealing with stock universes of hundreds or thousands of stocks, we often can take the simplifying assumption that they all have the same Beta of one. To get the values to sum to zero, we subtract the mean from each Alpha value in the vector. When the value sums to zero, the theoretical portfolio is said to be dollar neutral, and so general market movements that affect all stocks are cancelled out. This may not precisely eliminate all market risk as market Betas may not all be equal to one, but this is often a fine assumption at this stage.