Find the optimal portfolio for a target Active Risk of 5% per year, assuming that short-positions are allowed, but now adding the constrains that the beta of the optimal portfolio with respect to the HML Risk Factor (aka Value Risk Factor) has to be "small". More specifically, such beta has to be between -0.1 and +0.1. calculate Information Ratio of such portfolio 

 

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E(alpha) WB SMB BHML V Energy Utilities Energy -2.50% 5% 0.9 0 0.4 Energy Utilities -1.00% 5% 0.4 -0.3 0.2 Tech+Tcom 2.00% 20% 1.3 0 -0.7 Materials -0.50% 5% 1.1 0.1 0.4 Cons Disc 0.50% 15% 1.1 -0.1 0.1 HealthCare 3.00% 15% 0.7 -0.2 -0.3 Industrials 0.25% 10% 1.1 0 0.3 Cons Stap -1.50% 10% 0.6 -0.2 0.15 Utilities Tech+Tcom Materials Cons Disc HealthCare Industrials Cons Stap Financials -4.00% 15% 1.2 0.2 0.7 Financials Tech+Tcom Materials Cons Disc HealthCare Industrials Cons Stap Financials 0.0458 0.0118 0.0195 0.0295 0.0181 0.0122 0.0244 0.0091 0.0223 0.0118 0.0210 0.0067 0.0106 0.0080 0.0076 0.0105 0.0093 0.0101 0.0195 0.0067 0.0530 0.0269 0.0287 0.0195 0.0274 0.0084 0.0252 0.0295 0.0106 0.0269 0.0432 0.0282 0.0180 0.0320 0.0111 0.0302 0.0181 0.0080 0.0287 0.0282 0.0320 0.0173 0.0265 0.0110 0.0287 0.0122 0.0076 0.0195 0.0180 0.0173 0.0194 0.0177 0.0088 0.0183 0.0244 0.0105 0.0274 0.0320 0.0265 0.0177 0.0329 0.0116 0.0302 0.0091 0.0093 0.0084 0.0111 0.0110 0.0088 0.0116 0.0143 0.0133 0.0223 0.0101 0.0252 0.0302 0.0287 0.0183 0.0302 0.0133 0.0473 E(alpha) WB SMB BHML V Energy Utilities Energy -2.50% 5% 0.9 0 0.4 Energy Utilities -1.00% 5% 0.4 -0.3 0.2 Tech+Tcom 2.00% 20% 1.3 0 -0.7 Materials -0.50% 5% 1.1 0.1 0.4 Cons Disc 0.50% 15% 1.1 -0.1 0.1 HealthCare 3.00% 15% 0.7 -0.2 -0.3 Industrials 0.25% 10% 1.1 0 0.3 Cons Stap -1.50% 10% 0.6 -0.2 0.15 Utilities Tech+Tcom Materials Cons Disc HealthCare Industrials Cons Stap Financials -4.00% 15% 1.2 0.2 0.7 Financials Tech+Tcom Materials Cons Disc HealthCare Industrials Cons Stap Financials 0.0458 0.0118 0.0195 0.0295 0.0181 0.0122 0.0244 0.0091 0.0223 0.0118 0.0210 0.0067 0.0106 0.0080 0.0076 0.0105 0.0093 0.0101 0.0195 0.0067 0.0530 0.0269 0.0287 0.0195 0.0274 0.0084 0.0252 0.0295 0.0106 0.0269 0.0432 0.0282 0.0180 0.0320 0.0111 0.0302 0.0181 0.0080 0.0287 0.0282 0.0320 0.0173 0.0265 0.0110 0.0287 0.0122 0.0076 0.0195 0.0180 0.0173 0.0194 0.0177 0.0088 0.0183 0.0244 0.0105 0.0274 0.0320 0.0265 0.0177 0.0329 0.0116 0.0302 0.0091 0.0093 0.0084 0.0111 0.0110 0.0088 0.0116 0.0143 0.0133 0.0223 0.0101 0.0252 0.0302 0.0287 0.0183 0.0302 0.0133 0.0473

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