By Petr Adamek, John Y. Campbell, Andrew W. Lo, A. Craig Mackinlay, Luis M. Viceira

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**Example text**

8) Cov Mt (M ) Rit ] = 1 ; E Mt (M )]E 1 + Rit ] and similarly for Rbt . 9) Cov Mt (M ) Rbt ] 1 ; E Mt (M )]E 1 + Rbt ] Note that E Mt (M )] = M and Mt (M ) = c(1 + Rbt ), where c = E Mt (M )2 ];1 > 0 is a constant. 17). 1 subject to Wt+1 + Ct+1 = wt0 ( + Rt+1 )Wt and Wt 0. 3) follows. 3) is not only necessary but also su cient for the optimum once it holds for all i's and t's. 5). 10) which is a linear function of Et ct+1 ] with slope coe cient |the coe cient of risk aversion for the power utility function.

6) xt+1 ; Et xt+1 ] = t+1 ; t+1 so that the covariance of the innovations is always negative. 5 Let us denote the expectation conditional on the full information set at time t as Et ] and the expectation conditional on information Jt as EJt ]. Thus, we have E Et ]] = E ], EJt Et ]] = EJt ], and so forth, by the law of iterated expectations. In particular, E pt ] = E Et pt ]] = E pt ]. Note that the following \prices" are expectations listed in order of decreasing conditioning information: pt , pt = Et pt ], p^t = EJt pt ], and E pt ].

9) Ra = Ra ; Rr : Since a = r , the expected return of a is zero. 10) c 25 26 PROBLEMS IN CHAPTER 5 is c = 0. Any other solution would contradict q being minimum variance. 12) Cov Rq Ra ] = 0: Thus the return of a is uncorrelated with the return of all minimum variance portfolios. 16) we have 1 = aop = 1 ; ap . 16) gives 0 = 0 which completes the solution. 1) for N assets. m we can calculate the (N 1) vector of covariances of the N asset returns with the market portfolio return, the expected excess return of the market, and the variance of the market return, Cov Z Zm ] = !

### A Solution Manual To The Econometrics Of Financial Markets by Petr Adamek, John Y. Campbell, Andrew W. Lo, A. Craig Mackinlay, Luis M. Viceira

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