PROBLEM SET 5 In writing equation (1), I have followed the finance convention of denoting the intercept as or and the slope as B. In this equation, e is the diversifiable component - a random variable that cannot be predicted with information prior to date t. The CAPM presumes that the e for a stock is not correlated with the c for any other stock and hence is not correlated with fm. The variation in the return on the market, fm, is driven by changes in the economic environment. The systematic component of the return to the asset is the component associated with the market return. Coefficient B in equation (1) is the asset's "beta" in finance parlance. It is a measure of the systematic risk of the asset. For a given total expected return, an asset with a high beta is considered riskier than an asset with a low beta. Why? Suppose you buy equal amounts of shares in a large number of assets. Since the idiosyncratic return (e's) on these assets are uncorrelated, the variance of the idiosyncratic component of your portfolio will go to zero as the number of assets held gets large - thanks to the law of large numbers. In short, the risk on the e component of the asset return i can be diversified away. This implies that the variance of the non-diversifiable component of f is just 8 times the variance of fm (Recall that Var(o + Arm) = ' Var(7m) always holds when o and S are constants and fm is a random variable). As a consequence, assets with a larger beta have a larger non-diversifiable risk and should therefore have a larger expected return. We will compute alpha and beta for Amazon, using the data in the Excel spreadsheet Amazon in HW5data2020. (3.1) Challenging. Using the data provided, compute the monthly rates of return on Amazon's stock. Note that Amazon does not pay dividends, so the monthly rates of return can be computed directly from the stock prices in consecutive months (column B in the spreadsheet). For example, the monthly rate of return on 1-Aug-20 is =(B2-B3)/B3. Enter this formula in cell F2. Complete the computations by copying this formula down column F. You should now have 119 monthly rates of return (from 1-Oct-10 to 1-Aug-20). In the next column, compute the monthly excess rates of return on Amazon's stock. Use the 10-year Treasury Bill given in column D as the yearly risk-free rate. Divide by 12 to get the monthly risk-free rate. Thus Amazon's excess rate of return on 1-Aug-20 is =F2-D2/12. Enter this in cell G2. Complete the computations by copying this formula down column G. Repeat the same steps for the market's rates of return. Use the SP500 as the market; the monthly values of this index are given in column C. In cell 12, write the formula =(C2-C3)/C3 and copy the formula down column I; in cell J2, write the formula =12-D2/12 and copy it down column J. Run a linear regression where the independent variable is the market's excess rate of return and the dependent variable is Amazon's excess rate of return. What is the beta of Amazon