Q. In this question, I would like you to test the CAPM. In class, we saw Elucidate how to get historical return data also Elucidate how to estimate betas. Now, I would like you to choose 10 firms that have return data from 2000-2010 (Ideally, we should test the CAPM with portfolios, because individual stock returns are nosy realizations of random variables, but for our purposes individual stocks should be ok).

Then, I would like you to estimate their betas using only monthly data from 2000-2005. Ideally, I would like you to pick stocks that have some dispersion in their betas (at least a couple with betas higher than 1, a couple with betas close to zero, also the rest in between). Try using at least a few utility firms (for the low betas) also a few technology firms (for the high betas). This should results in 10 numbers corresponding to the betas of each stock.

a. In three sentences or less explain Elucidate how you estimated the betas for the 2000-2005 periods.

Next, estimate the stocks' average monthly returns (from the data!) using the 2005-2010 period. This should result in 10 numbers corresponding to the average realized monthly returns.

b. In three sentences or less explain Elucidate how you estimated the realized returns from 2005-2010.

We have estimated the returns using the following formula:

In addition, estimate the average market monthly excess return also the average risk-free rate over the 2005-2010 periods (2 numbers). Use the average market monthly excess return, the average risk-free rate, the betas, also the CAPM equation to get the predicted returns on the 10 stocks. This should results in 10 numbers corresponding to the predicted monthly returns by the CAPM.

c. In three sentences or less explain Elucidate how you estimated the predicted returns for 2005-2010.

d. Illustrate is the average error between the predicted also actual returns? Do the CAPM predictions over or underestimate the actual returns?
Construct a scatter plot with the predicted returns on the x-axis also the realized returns on the y-axis.

e. Present the scatter plot. If CAPM worked perfectly Illustrate would the scatter plot look like?