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Homework Solutions 05

# Homework Solutions 05 - IEOR E4007 G Iyengar Nov 29th 2008...

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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 ˆ V x, s.t. n i =1 μ i x i - ( μ 3 + c ) x n +1 = R, n i =1 x i - x n +1 = 1 , x n +1 0 . 5 , x 0 , where ˆ 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

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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-02 1.0000e+01 1.0629e-01 1.0500e+01 1.2044e-01 1.1000e+01 1.3473e-01 1.1500e+01 1.5006e-01 1.2000e+01 1.6669e-01 3. Efficient frontier Consider the portfolio selection problem described in Exercise 8.8 – the last problem of the previous homework. Construct the efficient frontier for this problem assuming that there is no risk-free asset in the market. Compute r min and σ 2
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Homework Solutions 05 - IEOR E4007 G Iyengar Nov 29th 2008...

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