4) Imagine that you have an investment universe consisting of 10 stocks. The stock's expected returns, along with the variance-covariance matrix are given below. The risk-free rate is 2%. A B D A B D Expected Returns 3.50% 4.00% 4.50% 5.00% 5.50% 6.00% 6.50% 7.00% 7.50% 8.00% 0.0020 0.0037 0.0028 0.0015 0.0017 0.0007 0.0020 0.0031 0.0015 0.0011 E 0.0037 0.0380 0.0284 0.0076 0.0111 0.0031 0.0127 0.0176 0.0043 0.0043 Variance Covariance Matrix G 0.0015 0.0017 0.0007 0.0020 0.0076 0.0111 0.0031 0.0127 0.0065 0.0097 0.0031 0.0102 0.0063 0.0049 0.0010 0.0046 0.0049 0.0126 0.0016 0.0049 0.0010 0.0016 0.0026 0.0028 0.0046 0.0049 0.0028 0.0122 0.0079 0.0049 0.0046 0.0163 0.0018 0.0007 0.0011 0.0041 0.00141 0.0020 0.0003 0.0022 0.0028 0.0284 0.0267 0.0065 0.0097 0.0031 0.0102 0.0133 0.0038 0.0039) 0.0031 0.0176 0.0133 0.0079 0.0049 0.0046 0.0163 0.0393 0.0080 0.0017 0.0015 0.0043 0.0038 0.0018 0.0007 0.0011 0.0041 0.0080 0.0041 0.0011 0.0011 0.0043 0.0039 0.0014 0.0020 0.0003 0.0022 0.0017 0.0011 0.0026 F G H 1 J a) Determine the optimal portfolio weights in the 10 stocks when the following constraints are enforced. No short sales No more than 30% invested in a single stock At least 5% invested in each stock The sum of stocks' G though I must be less than 40% (these 4 stocks are all in the same industry) i) What is the expected return, standard deviation, and Sharpe ratio of this portfolio? b) Determine the optimal portfolio weights in the 10 stocks when only the constraint against short sales in is force. i) What is the expected return, standard deviation, and Sharpe ratio of this portfolio? c) How much better is the Sharpe ratio for the unconstrained portfolio? How much extra return does the unconstrained portfolio produce? How much lower is the standard deviation for the unconstrained portfolio? 4) Imagine that you have an investment universe consisting of 10 stocks. The stock's expected returns, along with the variance-covariance matrix are given below. The risk-free rate is 2%. A B D A B D Expected Returns 3.50% 4.00% 4.50% 5.00% 5.50% 6.00% 6.50% 7.00% 7.50% 8.00% 0.0020 0.0037 0.0028 0.0015 0.0017 0.0007 0.0020 0.0031 0.0015 0.0011 E 0.0037 0.0380 0.0284 0.0076 0.0111 0.0031 0.0127 0.0176 0.0043 0.0043 Variance Covariance Matrix G 0.0015 0.0017 0.0007 0.0020 0.0076 0.0111 0.0031 0.0127 0.0065 0.0097 0.0031 0.0102 0.0063 0.0049 0.0010 0.0046 0.0049 0.0126 0.0016 0.0049 0.0010 0.0016 0.0026 0.0028 0.0046 0.0049 0.0028 0.0122 0.0079 0.0049 0.0046 0.0163 0.0018 0.0007 0.0011 0.0041 0.00141 0.0020 0.0003 0.0022 0.0028 0.0284 0.0267 0.0065 0.0097 0.0031 0.0102 0.0133 0.0038 0.0039) 0.0031 0.0176 0.0133 0.0079 0.0049 0.0046 0.0163 0.0393 0.0080 0.0017 0.0015 0.0043 0.0038 0.0018 0.0007 0.0011 0.0041 0.0080 0.0041 0.0011 0.0011 0.0043 0.0039 0.0014 0.0020 0.0003 0.0022 0.0017 0.0011 0.0026 F G H 1 J a) Determine the optimal portfolio weights in the 10 stocks when the following constraints are enforced. No short sales No more than 30% invested in a single stock At least 5% invested in each stock The sum of stocks' G though I must be less than 40% (these 4 stocks are all in the same industry) i) What is the expected return, standard deviation, and Sharpe ratio of this portfolio? b) Determine the optimal portfolio weights in the 10 stocks when only the constraint against short sales in is force. i) What is the expected return, standard deviation, and Sharpe ratio of this portfolio? c) How much better is the Sharpe ratio for the unconstrained portfolio? How much extra return does the unconstrained portfolio produce? How much lower is the standard deviation for the unconstrained portfolio