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Extra info for A Solution Manual To The Econometrics Of Financial Markets
Consider a two-sided test of size based on J1 and J2 , respectively, of the null hypothesis H0 : 1 2 ] = 0 0] against the alternative hypothesis HA : 1 2 ] = 0:003 0:003]. 6) = (; 1 + ;1 ( =2))] + 1 ; ( 1 + ;1 (1 ; =2))] P2 = Pr J2 < ;1 ( =2)] + Pr J2 > ;1 (1 ; =2)] = (; 2 + ;1 ( =2))] + 1 ; ( 2 + ;1 (1 ; =2))]: Evaluation of these expressions for = 0:05 gives P1 = 12:1% and P2 = 15:1%. 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 49 prices. Speci cally, the theoretical price H (0) of the option is evaluated under the assumption that the option allows one to sell the stock at the maximum price observed over the course of the entire year. The estimate H^ (0) was obtained under the assumption that only daily closing prices are used to evaluate the maximum. Obviously, the rst de nition always leads to a higher option price than the second. In the context of this particular problem the second de nition of the option (the one used in Monte Carlo simulations) is more relevant, since it is based on the de nition of the actual option.
Kop are (K 1) vectors of portfolio weights. 4) p2 t p2 t 1 Cov R Kt p R 0 ]! 5) = op + Cov Rt R0Kt ]! 9) Rt = a + BRKt + t 29 30 PROBLEMS IN CHAPTER 6 where a is the (N 1) intercept vector, B is the (N K ) matrix of factor regression coe cients, and t is the time period t residual vector. 12) holds for di erent values of op it must be the case that ( ; B ) = 0, that is the factor regression coe cients for each asset, including asset a, sum to one. 11) we have a = 0, that is the regression intercept will be zero for all assets including asset a.