Problem 1 Assume the following market model: T = ; + BjMTM + E with I = the rate of return on asset j ; = a constant BjM = the sensitivity of asset j to fluctuations in the market return IM the market rate of return &; = a stochastic component with E(;)=0, Var(;)=o and cov(;,&;) = 0, Vi, j. = 2 a. Prove that o=B0 +0. 2 b. Prove that = ;0 M

Problem 1 Assume the following market model: rj=j+jMrM+j with rj=therateofreturnonassetjj=aconstantjM=thesensitivityofassetjtofluctuationsinthemarketreturnrM=themarketrateofreturnj=astochasticcomponentwithE(~j)=0,Var(~j)=j2andcov(~i,~j)=0,i,j. a. Prove that j2=j2M2+kj2. b. Prove that ij=ijM2