# 3 – M4 L2A 03 Factor Model Of Asset Return V2

To get us ready to look at the risk factor model, let’s review the factor model of returns. Note that some of this may look familiar from an earlier lesson, which is great. Our team is really excited about what you’ll be able to do by the time you get to this next project. But we also recognize that it’s a pretty steep climb to reach the top of the mountain of knowledge. So, we’re trying to guide you up the mountain as gently as possible. Let’s begin by looking at a factor model of return. For a single stock and a single factor, the return of a stock can be modeled as the sum of two parts: the factor contribution to return plus the specific return. The contribution of the factors is also called the common return. The common return is defined as the stock’s exposure to that factor times the rate of return of the factor is the part of the stock’s return that can be explained by the factor. The stock’s exposure to the factor has a couple commonly used names: factor exposure, factor loading, factor sensitivity, or factor beta. We’ll refer to this as the factor exposure. The rate of return of the factor is the percent change of a particular factor. We’ll call this the factor return. An example of a factor that we’ve seen before is the market return, as approximated by an index such as the S&P 500. The other contributor to the stock return is the specific return which is the return of the stock that is not explained by the factors in the model. This may also be referred to as the idiosyncratic return or idiosyncratic shock. We’ll call this the specific return. So, to summarize, the stock return equals the factor exposure times the factor return plus the specific return. A model can have multiple factors contributing to the return of the stock. So, for instance, the return can be modeled as the contribution of one factor plus the contribution of a second factor. As before, the specific return represents the part of the stock return that isn’t explained by the chosen factors. In general, we can choose any number of factors in order to model stock’s return. We can refer to this as a multi-factor model of returns. Cool. So, that was how we model the return of a single stock, but as you may guess, we’re going to be more interested in a portfolio of stocks. Let’s see how factor models describe a portfolio of stocks next.