Assume the CAPM holds. A portfolio P that combines the risk-free asset and the market portfolio has an expected return of E(RP)=10 percent and a standard deviation of P=20 percent. The risk-free rate is Rf=5 percent, and the expected return on the market portfolio is RM=8 percent. Find the standard deviation of the market portfolio M. II. Assume that the following market model adequately describes the return-generating behaviour of risky assets: Rit-RF=i+i(RMt-RF)+it, i=1,...,N. Here: RF= The return on the risk-free asset at time t. Rit= The return on the ith asset at time t. RMt= The return on the market portfolio at time t. The unsystematic components 1t, 2t,...,Nt are statistically independent. RMt and it are statistically independent such that Cov(RMt,it) =0. a. Suppose the return RMt on the market portfolio is the weighted sum of returns Rit on individual securities i=1,..., N, with weights wi, i=1,..., N, respectively, with N, the total number of securities. Show that w11+w22+...+wNN=1. b. Suppose that CAPM holds. Explain why i should be zero. Assume i=0. If you construct an equally weighted portfolio P with assets i=1,..., N, what is the portfolio beta? If in addition, the portfolio beta is one and the unsystematic component of the portfolio return is 0, show that the portfolio return equals the market portfolio return RMt.