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Unformatted text preview: IEOR E4007 G. Iyengar Nov. 29th. 2008 Homework 5 Due: Wednesday, December 3rd 1. Exercise 8.5 in Optimization Methods in Finance Let x n +1 denote the negative part of the investment in the money market asset. Then the optimal frontier is given by the solution of the QP min x prime V x, s.t. n i =1 i x i- ( 3 + c ) x n +1 = R, n i =1 x i- x n +1 = 1 , x n +1 . 5 , x , where V = cov ([ R,- R (: , 3]). The MATLAB code hw4p7.m solves this and the next problem. Return (R) sigma(NoLev) sigma(Lev) sigma(Lev+cost) 6.5000e+00 3.1969e+00 3.1969e+00 3.1643e+00 7.0000e+00 3.4087e+00 3.4087e+00 3.4087e+00 7.5000e+00 4.2106e+00 4.2106e+00 4.2106e+00 8.0000e+00 5.3048e+00 5.3048e+00 5.3048e+00 8.5000e+00 6.5464e+00 6.5464e+00 6.5464e+00 9.0000e+00 7.8664e+00 7.8664e+00 7.8664e+00 9.5000e+00 9.2333e+00 9.2333e+00 9.2333e+00 1.0000e+01 1.0629e+01 1.0629e+01 1.0629e+01 1.0500e+01 1.2044e+01 1.2044e+01 1.2044e+01 1.1000e+01 1.3473e+01 1.3472e+01 1.3473e+01 1.1500e+01 1.5006e+01 1.4909e+01 1.5006e+01 1.2000e+01 1.6669e+01 1.6353e+01 1.6669e+01 2. Exercise 8.8 in Optimization Methods in Finance The Black-Litterman shrinkage shifts the mean as follows: mu mu_BL Change 1.2057e-01 1.2992e-01 9.3508e-03 7.8502e-02 8.0620e-02 2.1170e-03 6.3230e-02 2.0365e-02-4.2865e-02 1.2899e-01 1.7037e-01 4.1376e-02 1 Does the change in means make sense given the views? The new frontier is given by R sigma 6.5000e+00 3.1969e-02 7.0000e+00 3.4087e-02 7.5000e+00 4.2106e-02 8.0000e+00 5.3048e-02 8.5000e+00 6.5464e-02 9.0000e+00 7.8664e-02 9.5000e+00 9.2333e-029....
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This note was uploaded on 06/02/2010 for the course IEOR IEOR E4007 taught by Professor Optimizationmodelsandmethods during the Summer '09 term at Columbia.
- Summer '09