## Download A Solution Manual To The Econometrics Of Financial Markets by Petr Adamek, John Y. Campbell, Andrew W. Lo, A. Craig PDF

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

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9) ! e( + 2 )T which is the moment-generating function for a normal random variable with mean T and variance 2 T . 3 Consider n observations in the interval 0 T ] equally spaced at intervals h T=n, and let p(0) = 0 to simplify the algebra. Let pk p(kh). 1) kh;h e; (kh;s) dB (s) : Now let = e; h . 4) by the Principle of Invariance (see Zehna 1966]). 3 47 From here we will assume that the trend is known exactly. 12) n(^ 2 ; 2 ) a N 0 2 4 1 + 2e 2 h2 1 ; e;2 h (1 + 2 h)]2 : To derive the continuous-record asymptotics of ^ and ^ 2 , we let n !

2 except that 2 = 0:006 instead of 0:003. Using this value for 2 , we have 1 = 1:162 and 2 = 1:225 giving P1 = 21:3% and P2 = 23:3%. 4) 0 = a ; ( aop op + ap p ) since Cov Rp Rop ] = 0. The result 2 = ap is immediate, thus we need to show that 1 = 1 ; ap and 0 = 0 to complete the solution. Let r be the minimum variance portfolio with expected return equal to that of portfolio a, a = r . 5) Rr = (1 ; )Rop + Rp where = ( r ; op )=( p ; op ). 8) r = rop op + rp p : Portfolio a can be expressed as portfolio r plus an arbitrage (zero-investment) portfolio a composed of portfolio a minus portfolio r (long a and short r).

The calculations for three selected stocks are left to the reader. 4 Let Zt be a (N +1 1) vector of excess asset returns with mean and covariance matrix . Designate asset N + 1 as the market portfolio m. Assume that is full rank. 1) Using straight forward algebra we have 2 (! 5) 2 m 0 m 2 2 m 3 5 0 m 2 + 2 m 0 m 2 2 m 3 5 where = 0 m2 + is substituted. 3). 1 Let the number of portfolios in the set be K and let RKt be the (K 1) vector of time period t returns for the portfolios. Since the entire minimum variance boundary can be generated from the K portfolios, for any value of the constant y, there exists a combination of the portfolios with expected return y which is minimum variance with respect to the K portfolios plus the N assets.