(5+5+5+5). Let Y be the excess return of risky assets. Let X=aTY be a portfolio with allocation vector a. Denote by =Var(Y) and 0=EY. Consider the following decomposition (regression) Y=+X+,E[]=0,Cov(,X)=0. - (a) Show that =(aa)1(a). - (b) Show that =E[Y]E[X]=0(aTa)1(aT0)a. - (c) Show that if a=c10 (optimal portfolio in the mean-variance efficiency), then =0. - (d) Conversely, if =0, there exists a constant c such that a=c10