VI. Single Index Model (24 points, 4 points each except question 5) Consider the single index model regression Rit = di + BiRMt + Eitit = 1, ..., T,i = 1, ... , N RMt ~ iid N(0, OM) Eit ~ iid N(0, oz;) cov(Eis, Ejt) = 0 for all i # j, t and s RMt is independent of fit for all i and t where Rit denotes the return on asset i and RMt denotes the return on the market portfolio proxy. Let u; and UM denote the expected returns on the asset and the market, respectively, and let oci and om denote the variances of the asset and the market, respectively. Finally, let im denote the covariance between the asset and the market. 1. Use the model above to explain "market-wide" news and "firm-specific" news. 2. Using the single index regression, compute E [Rit], var(Rit), cov(Rit, Rit) and cov(Rit, Ris). 3. Consider the special case of three assets (i = 1,2,3). Give an expression for the covariance matrix, ), based on the single index model.4. Using the expression for var (RH), what is the proportion of the variance of the asset due to the variability in the market return and what is the proportion unexplained by variability in the market? 5. (8 points) Briey prove the following estimator is consistent: 1 3222?" M T _ 1 t=1(RMf M)2