# 4 – M4 L2A 04 Factor Model Of Portfolio Return V3

Already know, let’s add one more layer of complexity, by using a factor model to describe a portfolio of stocks. A portfolio’s return can also be modeled as a sum of two parts, the returns that can be explained by a set of factors, and the returns that are specific to each stock within the portfolio. Let’s look at a single factors contribution to the portfolio. Assuming we had the factor exposures of each stock within the portfolio, and we also had the weight of each stock in the portfolio, how do we get the portfolios factor exposure? Well, a portfolio’s exposure to a factor is a weighted average of the exposures from his individual stocks. For each stock in the portfolio, we multiply the stocks portfolio weight, by that stocks exposure to that factor, and we sum up all these weighted Betas. This process may look familiar to you. We do the same with portfolio returns, by calculating a weighted average of the individual stock returns. The difference here is that we’re calculating the portfolio’s factor exposure, instead of the portfolio’s returns. So, now we can get the portfolio’s exposure to one factor, exposure to a second factor, and exposures to each factor in the model. If we have each factors contribution to the portfolio return, we can sum up the contributions of all the factors. The remaining part of the portfolio’s return is the specific return. Can you think of how to get the portfolios specific return, if we have the specific return of each stock? The portfolio’s specific return is the weighted sum of the specific return of each stock. So, we take each stock’s weight in the portfolio, multiplied by the stock’s specific return, and add this up for all stocks in the portfolio. This weighted sum is the portfolio’s specific return. This is the portfolio’s return, modeled in terms of factors. The point is to explain most of the portfolio return, using a set of common factors. Ideally, the chosen factors would explain more of the portfolio return, and the specific return would explain less. From here, we’ll get the portfolio’s variance, modelled in terms of these common factors. We’ll look at how to model portfolio variance for the rest of this lesson.