Two ways to measure beta
Use the formula
Cov(Ri,RMkt Var(RMkt)
Run a regression of the asset's returns on the market return. The slope is the beta of that asset : Both methods should give the same answer.
Regressions and beta
Why does regressing Ri on Rm give you an estimate of beta? Suppose Iregress y on x . Estimate y=a+bx+e a is ,b is Two facts: Fact 1: The best estimate of the slope is just Cov(y,x)/Var(x) Fact 2: Can break up the variance of y into two parts: one part correlated with x, and one part not. Var(y)=Var(b*x)+Var(e)=b2Var(x)+Var(e) Because of fact 1 we can: : Measure beta by running regressions : Assert that "beta says how much the asset moves when the market moves"
Estimating betas
Use historical data How do you calculate the market return? . Ideally : In practice Use the data in the excel sheet to estimate betas for the four assets with the formula and with regressions Regression is just fitting a line The two methods give the same answer (nearly)
You can see how the beta measures how much an asset's return responds to the market retu