By Petr Adamek, John Y. Campbell, Andrew W. Lo, A. Craig Mackinlay, Luis M. Viceira
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Additional info for A Solution Manual To The Econometrics Of Financial Markets
1 We see that, under this non-stochastic term structure given by P8 and P9 , all interest rates are nonnegative and P8 P9 , so that no arbitrage opportunity exists. 2. Assume that all one- to sevenyear zero-coupon bonds have price P70 per one dollar of their face value and that eight-year zero-coupon bond has price P80 . 4) 0:3125: P80 = PB ;1 + 0:08 P70 P80 , so again there is no arbitrage opportunity. Note however that the assumptions required to rationalize these bond prices are rather extreme, since they require zero nominal interest rates between one and eight years.
I in probability as L1 ! 3). 7) we have ^i = Ri ; Xi ^i ! Ri ; Xi i = i in probability, as L1 ! 1. Because abnormal returns i are independent (across time), the sample abnormal returns ^i are asymptotically independent as L1 ! 1. 2 We assume that the cumulative abnormal return test statistics are calculated using the known standard deviation of the abnormal returns, that the abnormal returns are independent through time and across observations and normally distributed, and that the abnormal returns are measured without parameter sampling error (L1 is large).
For a real consol paying a xed real dividend we have that di t+1+j = 0, so the unexpected return is in uenced only by changes in expected future interest rates. 3 Part (i). 19) = Cov ut+1 11;; ut+1 2 = 11;; u and we may write Cov( ) instead of Covt( ) because the process for ct+1 is homoskedastic. 20) Vcb = 1;; u2 : Part (ii). The bond premium has the opposite sign to because a positive implies that a positive endowment shock increases future consumption more than current consumption, so real interest rates rise and bond prices fall when consumption rises.