1. This exercise fits the security characteristic line to data: Rj4 = Hf,t + B;(RM,t - H5.a) + j,t. (1) The S&P 500 index will be a proxy for the market portfolio and the 90-day Trea- sury rate will serve as the risk-free rate. The data set used is Stock Bond 2004-to 2006.csv which contains a subset of the data in the data set Stock Bond.csv. In order to fit model (1), first run the following commands to read the data, extract the prices, and find the number of observations: dat = read.csv("Stock Bond_2004 to_2006.csv", header = TRUE) prices = dat[ , c(5, 7, 9, 11, 13, 15, 17, 24)] dim(prices) [1] n = Next, run these commands to convert the risk-free rate to a daily rate, compute net returns, extract the Treasury rate, and compute excess returns for the market and for seven stocks. The risk-free rate is given as a percentage so the returns are also computed as percentages. dat2 = as.matrix(cbind (dat [(2:n), 3] / 365, 100 * (prices [2:n,] / prices [1: (n-1), ] - 1))) names (dat2) [1] = "treasury" risk_free = dat2[,1] ExRet = dat2[ ,2:9] - risk_free market = ExRet [ ,8] stockExRet = ExRet [ ,1:7] Now fit model (1) to each stock, compute the residuals, look at a scatter-plot matrix of the residuals, and extract the estimated betas. fit_reg = lm(stockExRet summary(fit_reg) res = residuals (fit_reg) pairs(res) options (digits betas = fit_reg$coeff[2, ] market) 3) %3D 1 (a) Would you reject the null hypothesis that alpha is zero for any of the seven stocks? Why or why not? (b) Use model (1) to estimate the expected excess return for all seven stocks. Compare these results to using the sample means of the excess returns to estimate these parameters. Assume for the remainder of this exercise that all alphas are zero. (Note: Because of this assumption, one might consider reestimating the betas and the residuals with a no-intercept model. However, since the estimated alphas were close to zero, forcing the alphas to be exactly zero will not change the estimates of the betas or the residuals by much. Therefore, for simplicity, do not reestimate.) (c) Compute the correlation matrix of the residuals. Do any of the residual correlations seem large? Could you suggest a reason why the large correla- tions might be large? (Information about the companies in this data set is available at Yahoo Finance and R quantmod package.) (d) Use model (1) to estimate the covariance matrix of the excess returns for the seven companies. (e) What percentage of the excess return variance for UTX is due to the market? (f) An analyst predicts that the expected excess return on the market next year will be 4%. Assume that the betas estimated here using data from 2004-2006 are suitable as estimates of next year's betas. Estimate the expected excess returns for the seven stocks for next year