By Petr Adamek, John Y. Campbell, Andrew W. Lo, A. Craig Mackinlay, Luis M. Viceira
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Extra resources for A Solution Manual To The Econometrics Of Financial Markets
The reason is that the duration of coupon bonds does not increase linearly with their maturity, but increases at a decreasing rate. That is, Dc n+1 t ; Dc n t < 1. This in turn makes it easier to get negative forward rates for given yields. 2 Assume the postulated process and simplify notation, introducing at yt1 ; y1 t;1 and bt y2t ; y1t . 2) : It is straightforward to verify that with this value for , the y1t process satis es all the equations of the model, provided that < 2. 3) at+1=2 = + bt + ut+1 : As Et at+1 ] = xt and bt = ;1 xt, we see that the population parameters are = 0 and = =2.
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 ]. 2) E EJt (Et pt ] ; EJt pt ])(EJt pt ] ; E pt ])]] = 0 as EJt pt ] ; EJt pt ] conditional on Jt is a constant and EJt Et pt ] ; EJt pt ]] = 0. Calculations in other parts of the problem are similar. Intuitively, a price forecast based on less information is less volatile. 5) Var pt ; p^t ] Var pt ; p^t ] as was to be shown. Intuitively, a forecast based on inferior information has a larger error variance.
Quadratic utility has U 000 = 0 (\certainty equivalence") and uninsurable individual risk has no e ect. 3 43 The result also depends on the fact that there is more dispersion of individual endowments in bad times than in good times. 1 Without loss of generality, let us consider the random variable pn (T ) (the derivation for pn (t) is analogous). 7) that = 21 (1 + h ) and = h. 7) = cosh( h) + where cosh(x) and sinh(x) are the hyperbolic sine and cosine functions x ;x 2 4 cosh(x) = e +2 e = 1 + x2!
A Solution Manual To The Econometrics Of Financial Markets by Petr Adamek, John Y. Campbell, Andrew W. Lo, A. Craig Mackinlay, Luis M. Viceira