# 1 – M4 L2A 01 Intro V1

Hi there. So far, you’ve been introduced to the concept of a factor and the framework of the multifactor model. We’ve also touched upon how in practice we defined some factors as risk factors and other factors as alpha factors. In this lesson, we will focus on risk factors and the fundamentals of the risk factor model. Risk factor models are used to describe the volatility or risk of assets such as stocks based on the movements of the risk factors. The goal of a risk factor model is to measure, control and possibly neutralize a portfolio’s exposure to major sources of risk. In order to achieve this goal, we need a way to model the portfolio’s risk in terms of the common risk factors. To model a portfolio’s risk, we want to model individual asset variances and pairwise asset covariances in terms of these risk factors. To model asset variance and covariance in terms of risk factors, we need a couple pieces of information; the variances and covariances of risk factors, the factor exposures which measure how exposed each asset is to each risk factor, and the specific variance of each asset that is not explained by the risk factors. To calculate the variances and covariances of the risk factors, we also need to calculate the returns of the factors which are called the factor returns. We’ll also make use of the asset returns which will help us either estimate the factor exposures or the factor returns depending on the type of risk model. We can then use these pieces of information to estimate the specific variants of each asset. To start off, we also should decide what factors we’ll use in our model. By the way, don’t worry if these terms don’t look familiar yet, you’ll see a couple of ways of getting all the pieces that go into a risk model. So along the way, you’ll see what these words mean. We’ll begin with the motivation for using risk factor models. Factor models have some benefits over modelling portfolio risk directly from the covariances of its individual assets. Next, we will cover the framework for the risk factor model. The risk factor model attempts to explain the variance of a portfolio as the sum of two parts; the variance that can be attributed to the common risk factors plus variance that is not explained by those risk factors. I just want to point out that risk factor modeling combined with alpha factor modeling are both crucial to successful portfolio optimization. Just as a car needs both a brake pedal and an accelerator or a good basketball team needs both a good defense and also a good offense. An effectively optimized portfolio needs to both control risk using risk factors, while seeking higher than expected returns using alpha factors.