(Data) Monthly rate of return data (in percentage points) are presented below for three stocks and the S&P index for a 12-momth period. Month 1 2 3 4 5 6 7 8 9 10 11 12 Stock 1 12.05 15.27 -4.12 1.57 3.16 -2.79 -8.97 -1.18 1.07 12.75 7.48 -0.94 Stock 2 25.20 2.86 5.45 4.56 3.72 10.79 5.38 -2.97 1.52 10.75 3.79 1.32 Stock 3 31.67 15.82 10.58 -14.43 31.98 -0.72 -19.64 -10.00 -11.51 5.63 -4.67 7.94 S&P 12.28 5.99 2.41 4.48 4.41 4.43 -6.77 -2.11 3.46 6.16 2.47 -1.15 om We wish to estimate the necessary mean-variance analysis paran parameters based on the single-factor model r = a + Bir + e,i = 1,2,3, where r, is the rate return of asset i, M is the rate of return of the S&P index, e, are random variables which are uncorrelated with each other and , and a; and are constants. (a) Estimate the mean and variance of the S&P index. (b) Estimate the mean and variance of each stock's return. (c) Estimate a, B; and the variance of the error term (o) for each stock. (d) Comment on the goodness of fit of the single-factor model. (e) Use the factor model to estimate the covariance matrix of the three stocks.