Residual risk under CAPM

Residual Risk under CAPM Under CAPM excess return are given by Ri - R; = Bi(Rmn Rp) + Ei, where B; = Oimom, and the random variable e; is uncorrelated with the market port- folio. (a) Show that you can write the covariance matrix as V = 0%B8T +T where T is the covariance matrix of residual risk, i.e., Tij = Cov(Ei, ej). (b) Show that Tem = 0. (c) Show that for any portfolio Ip, the residual variance can be written as w. = 2[Ttp = 0% - 07B, where o = z[VIp, and Bp = B7 Ep. (d) Argue that the market portfolio is the minimum variance portfolio with beta equal to one. Residual Risk under CAPM Under CAPM excess return are given by Ri - R; = Bi(Rmn Rp) + Ei, where B; = Oimom, and the random variable e; is uncorrelated with the market port- folio. (a) Show that you can write the covariance matrix as V = 0%B8T +T where T is the covariance matrix of residual risk, i.e., Tij = Cov(Ei, ej). (b) Show that Tem = 0. (c) Show that for any portfolio Ip, the residual variance can be written as w. = 2[Ttp = 0% - 07B, where o = z[VIp, and Bp = B7 Ep. (d) Argue that the market portfolio is the minimum variance portfolio with beta equal to one