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Extra info for A Solution Manual To The Econometrics Of Financial Markets
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 ].
1 "Y n pn t = log Et "X n i=1 Mt+i # ! 11) n X i=1 n X i=1 gt+i: gt+i = ; (1 ; n ) (xt ; ) the assumed model will be able to reproduce the expected short rates. 11) we can see that it is not possible to choose drift terms so they match simultaneously both current forward rates and expected future log short rates, since n 2 6= ( + n)2 + 11;; unless ! , unless the state variable in the true model follows a random walk. 11)|converges to ;(xt ; ) as n ! 7)| tends to ;1 as n ! 1. Therefore, if we choose the drift terms so they reproduce the forward rate structure of the true model, this will result in expected future log short rates declining without bound as we increase the horizon, while the true model implies that the expected future log short rates converge to a nite constant.
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. This solves part (i). 11) Et ri t+1 ; rf t+1 ] + 12 Vii = Vic so that the \premium" of the asset is proportional to the conditional covariance of the log asset return with consumption growth, with coe cient of proportionality . This solves part (ii). 40 PROBLEMS IN CHAPTER 8 Part (i).