Doubts about CAPM model


I have doubts concerning expected rate of return of an asset when using CAPM model. It concerns the Beta coefficient which as we know is a covariance between a realized return from the stock and a market, divided by a variance of the market. However, this covariance is in turn a function of the expected return from an asset we want to find!

So, isn’t it a situation where we try to explain the dependent variable by itself? Isn’t it a wrong econometric procedure?

The inputs to calculate beta are all from historic actual returns as you noted. Therefore, you are calcing expected behavior based on prior actual behavior, maybe I am missing what is so odd about that.

If I want to get an idea of how Wells Fargo might act, I would rather know how Wells Fargo has acted in the past rather than how JPM has…


Not exactly. The covariance is a function of the historical returns, not a function of the expected return.

I see nothing wrong with it. We’re trying to predict where something will be based, in part, on where it’s been. Gauss predicted where Ceres would be (about one year later) based on where it had been; if it’s good enough for Gauss, it’s good enough for us.

when we are using CAPM, we will first need to define the variable inputs such as RF, E(RM) and beta.

Typically, we can calculate the beta use the market variance, asset variance and the correlation between them.’

Or simply use Ri=a+bRm+e to do some regression test.

This procedure is known as the empirical analysis. We use historical results because we believe that historical output is a good representitive of future performence to show the sensitivity of the asset with regard to market performance.

Thanks to all for your responses. I’ve had a little brainstorm, because you are right- it’s just a simple linear regression on a sample (historical data). However, I am not sure that this is really a proper (however, probably it works…) method of estimation because:

  1. it may be a spurious regression i.e. does the return from the market (strictly speaking - its surplus over rf) influence the return from a particular share? There are probably some exogenuous factors that influence both of them

  2. Return from an index is just a weighted return from all shares so I’m not sure this should be regarder as a exogenuos variable…

Well, i’m not fully econometrician (yet) but such questions arise in my mind.

I would just like to say a couple things:

  1. CAPM is not used widely in reality (at least in my experience) nor relied on exclusively, and should not be seen as a perfect tool to derive expected returns (after all, beta changes with time period/decay factors, rfr, etc).

  2. CAPM has been around for a very long time and is accepted as somewhat rational. Not to be a dick but you are likely not the person to point out the first or novel flaw and debunk its usefulness.

  3. If you are focusing on this right now, you have either mastered all the other material or you are going to fail your level I exam. Seriously. My advice (thru experience) is to get the concept, realize that you will not agree with everything as presented, and move the F on…

Covariance is not derived from expected return. The volatility represents possible realized returns, not the mean expected return. Think of the expected return as some mean future value. Then, plot some volatility around that. Both the mean return and volatility can be specified independently.