Note that the word alpha is used to mean different things within the world of finance. In the context of factor models, we’ll refer to an alpha model as an algorithm that transforms input data into a list of numbers, one number for each stock under consideration per time step. A higher positive number means we want to put more money on that stock law. A negative number means we want to short the stock. An alpha vector refers to this list of numbers for a single time period, such as a day. Each number in the alpha vector is proportional to the amount of money we want to allocate towards each stock, according to the alpha model. The alpha vector at each time step is standardized, so that it has mean zero and the sum of the absolute values adds up to one. We’ll use the term alpha value to refer to a single number in the alpha vector. So, it’s a number assigned to a single stock for a single time period, such as a day. We’ll refer to an alpha factor as a time series of alpha vectors. So, it’s the set of alpha vectors over multiple time periods, such as multiple days. A raw alpha factor is the initial output of the alpha model, excluding additional processing that is done to improve the alpha. We’ll use the term raw alpha factor to distinguish from an alpha factor that has been processed to improve its signal, and make it easier to work with. Note that within the finance industry, there is no single consistent way that practitioners use the term alpha or alpha factor. Though, our use is the most common. We’ll use these definitions to help us identify which step in our alpha generation we’re referring to. We’ll also be talking about our stock universe, or simply our universe. This refers to the set of stocks which we are considering in our portfolio at each time step. These are stocks that we may or may not hold positions in for our portfolio.