# What is Multifactor Models?

The most widely known model for estimating the expected return of a security is the capital asset pricing model where it's modeling the expected return as a function of a single factor which is capturing systemic risk. This systemic risk is beta so we talked about the beta of security we're saying how many units of risk are in this security with respect to changes in the overall market. So the systemic risk that cannot be diversified away, it's saying how much does this securities return of changes in the overall market. So the market goes up to let's say we've got a beta of 1.5 that means if the market goes up by 1% then this security goes up by 1.5%.

The single-factor model is nice for its simplicity. However, we might think about this system's accuracy includes so many different things, including expectations about the overall economy and what the GDP is going to be? it includes expectations about what the inflation rate is going to be, what interest rates are going to be. All these different macroeconomic factors are part of this systemic risk. So you might consider them and say maybe different types of securities react in different ways to changes in interest rates or to changes in inflation, for example, might a bank respond differently to changes in interest rates than a grocery store. Sure that's reasonable to think that and so we just use a single factor that measures the systemic risk. That's a great start but some people have said "We can actually think about breaking this systemic risk into its component parts so that we might more accurately predict the expected return of this security." and when we do that when we have multiple factors here we call that a multi-factor model.

So I'm going to give you just an easy example so let's say that we are going to estimate a two-factor model for a fictional company called happy and our two factors, we're going to make this really simple we're just gonna have inflation and interest rate. Those will be the only two factors in the model and so we go and we estimate the model with regression analysis and we get the following result.

So we've got this (0.11) here that's going to be the expected excess return for happy Bank. That's 11% that's expected excess return but now we've got to think about our two factors. We've got two factors here 1st one there's 0.2 is telling us that if we have a 1% increase in inflation then that would lead to a 0.2 point increase in the expected return. Now conversely if we were to have an unexpected 1% increase in interest rates, then that would predict that we would have a decrease of 0.4 points in the expected return. So we don't have to have just two factors here we could have a third factor that measures GDP, we could have a fourth factor or we could have a fifth factor. Probably the most famous of the multi-factor models is the Fama French model and then also we've got Fama French Carhart Model and so forth.