# 6 – M4 L2A 06 Variance Of One Stock V3

Let’s begin with our matrix notation, and consider a portfolio with two stocks, in a model that uses two factors. The variance of the portfolio is the weighted sum of the variances and pairwise covariances of its stocks. We can think of each stock as a different flavor of ice cream, such as butter pecan or mint chocolate chip. We’ll start with the first stock. Its return is modeled as a linear combination of the factors plus the specific return. These factors are used in the model to describe all the stocks. So, in the context of risk modeling we call these common factors. Risk factors, or common risk factors. Let’s take the variance of both sides of the equation. This becomes the variance of each factor plus twice the covariance of the factors. Plus the variance of the specific return. The model assumption is that the specific return is not correlated with the factors. So, this specific return doesn’t show up in any covariance operator. You can pause the video to study these formulas as needed. For constant like the factor exposure, we can move it to the outside of the variance operator if we square it. Similarly, we can move the factor exposures to the outside of the covariance operators. The sum of the first three terms containing the factors is the systematic variance. The last term is the specific variance also called the idiosyncratic variance. If we think of this first stock as butter pecan ice cream, then the systematic variance describes the main ingredients such as sugar and milk. While the specific variance describes the pecans. Okay. That was the variance of one stock. Let’s look at the second stock, and see how these two mixed together to create a bowl of ice cream. I mean, a portfolio of stocks.