a) Consider four risky assets having the following expected returns E() and variance- covariance matrix (S), where c is a constant: B D E Variance-covariance, S F G Er) Mean minus returns constan E(r) t 6% 2.00% 4.00% 10% 6.00% 15% 11.00% w N 1 2. 0.10 3 0.01 4 0.03 5 0.05 6 7 Constant, 8 8% 0.01 0.30 0.06 -0.04 0.03 0.06 0.40 0.02 0.05 -0.04 0.02 0.50 4.00% i) Write down the Excel formula on how we estimated the values in Cells G3:G6 below: A F G H J K B D E CALCULATING THE FRONTIER 1 Variance-covariance, S 2 3 0.10 0.01 0.03 0.05 -0.04 Mean E(r) returns minus E(r) constant 6% 2.00% 8% 4.00% 10% 6.00% 15% 11.00% 4 4 0.01 0.30 0.06 ? ? ? ? 0.06 0.40 0.02 Question i -0.04 0.02 0.50 5 0.03 6 0.05 7 8 Constant, 4.00% [3 marks] ii) Let us compute an envelope portfolio with constant c=0, where the vector z solves the system of simultaneous linear equations E(r) - c = Sz. Then, this solution produces a portfolio x on the envelope of the feasible set. Write down the Excel formula on how we estimated the values in Cells A12, F12 and F16, in the Excel spreadsheet below, and explain the rational behing these calculations: F G H K B D E CALCULATING THE FRONTIER 1 E(1) Variance-covariance, S 2 3 0.10 0.01 0.03 0.05 4 0.01 0.30 0.06 -0.04 5 0.03 0.06 0.40 0.02 6 0.05 -0.04 0.02 0.50 7 8 Constant, 4.00% 9 10 Computing an envelope portfolio with constant - 0 Mean E(1) returns minus constant 6% 2.00% 8% 4.00% 10% 6.00% 15% 11.00% z Envelope portfolio 11 12 13 ? ? 0.3861 0.2567 0.3553 0.2362 0.1553 0.2532 14 0.1688 Question ii 15 0.2752 Sum 1.0000 ? 16 17 [6 marks] iii) Let us now compute an envelope portfolio with constant c= 4%. Write down and explain the Excel formula on how we estimated the values in Cells A20, F20, F24, F26:F28, and B30:B31, in the Excel spreadsheet below: F G H B E CALCULATING THE FRONTIER 1 E(1) Mean minus returns constan E() t 6% 2.00% 8% 4.00% Variance-covariance, s 2 3 0.10 0.01 0.03 0.05 4 0.01 0.30 0.06 -0.04 5 0.03 0.06 0.40 0.02 6 0.05 -0.04 0.02 0.50 7 8 Constant, 4.00% 9 10 Computing an envelope portfolio with constant - 0 5 10% 6.00% 15% 11.00% z Envelope portfolio 11 12 13 0.3861 0.2567 0.3553 0.2362 ? 14 0.1688 0.1553 15 0.2752 0.2532 16 Sum 1.0000 17 18 Computing an envelope portfolio with constant - 4.00% Envelope Z portfolio 19 20 0.0404 ? 0.0782 21 0.1386 0.2684 22 0.1151 0.2227 23 0.2224 0.4307 24 Sum 1.0000 25 26 E(X) 9.37% EV 11.30% 27 Var(x) 0.0862 Vary) 0.1414 28 Sigma(x) 29.37% Sigma(y) 37.60% 29 30 Cov(x,y) 0.1040 ? 31 Corr(x,y) 0.9419 ? 32 ? Question iii ? ? ? C iv) Let us now conduct a single portfolio calculation with a proportion of portfolio x equal to 0.3. Estimate the expected return, variance, and standard deviation of the portfolio in Cells B36:B38, in the Excel spreadsheet below: G N A B D E F 18 Computing an envelope portfolio with constant = 4.00% Envelope portfolio 19 y 20 0.0404 0.0782 21 0.1386 0.2684 22 0.1151 0.2227 23 0.2224 0.4307 Sum 1.0000 24 25 Ely) 11.30% 0.1414 Varly) Sigma(y) 37.60% 26 E(X) 9.37% 27 Var(x) 0.0862 28 Sigma(x) 29.37% 29 30 Cov(x,y) 0.1040 31 Corr(x,y) 0.9419 32 33 34 A single portfolio calculation Proportion of 35 X 0.3 ? 37 62 ? 38 Op ? 39 36 Erp) Question iv [4 marks] a) Consider four risky assets having the following expected returns E() and variance- covariance matrix (S), where c is a constant: B D E Variance-covariance, S F G Er) Mean minus returns constan E(r) t 6% 2.00% 4.00% 10% 6.00% 15% 11.00% w N 1 2. 0.10 3 0.01 4 0.03 5 0.05 6 7 Constant, 8 8% 0.01 0.30 0.06 -0.04 0.03 0.06 0.40 0.02 0.05 -0.04 0.02 0.50 4.00% i) Write down the Excel formula on how we estimated the values in Cells G3:G6 below: A F G H J K B D E CALCULATING THE FRONTIER 1 Variance-covariance, S 2 3 0.10 0.01 0.03 0.05 -0.04 Mean E(r) returns minus E(r) constant 6% 2.00% 8% 4.00% 10% 6.00% 15% 11.00% 4 4 0.01 0.30 0.06 ? ? ? ? 0.06 0.40 0.02 Question i -0.04 0.02 0.50 5 0.03 6 0.05 7 8 Constant, 4.00% [3 marks] ii) Let us compute an envelope portfolio with constant c=0, where the vector z solves the system of simultaneous linear equations E(r) - c = Sz. Then, this solution produces a portfolio x on the envelope of the feasible set. Write down the Excel formula on how we estimated the values in Cells A12, F12 and F16, in the Excel spreadsheet below, and explain the rational behing these calculations: F G H K B D E CALCULATING THE FRONTIER 1 E(1) Variance-covariance, S 2 3 0.10 0.01 0.03 0.05 4 0.01 0.30 0.06 -0.04 5 0.03 0.06 0.40 0.02 6 0.05 -0.04 0.02 0.50 7 8 Constant, 4.00% 9 10 Computing an envelope portfolio with constant - 0 Mean E(1) returns minus constant 6% 2.00% 8% 4.00% 10% 6.00% 15% 11.00% z Envelope portfolio 11 12 13 ? ? 0.3861 0.2567 0.3553 0.2362 0.1553 0.2532 14 0.1688 Question ii 15 0.2752 Sum 1.0000 ? 16 17 [6 marks] iii) Let us now compute an envelope portfolio with constant c= 4%. Write down and explain the Excel formula on how we estimated the values in Cells A20, F20, F24, F26:F28, and B30:B31, in the Excel spreadsheet below: F G H B E CALCULATING THE FRONTIER 1 E(1) Mean minus returns constan E() t 6% 2.00% 8% 4.00% Variance-covariance, s 2 3 0.10 0.01 0.03 0.05 4 0.01 0.30 0.06 -0.04 5 0.03 0.06 0.40 0.02 6 0.05 -0.04 0.02 0.50 7 8 Constant, 4.00% 9 10 Computing an envelope portfolio with constant - 0 5 10% 6.00% 15% 11.00% z Envelope portfolio 11 12 13 0.3861 0.2567 0.3553 0.2362 ? 14 0.1688 0.1553 15 0.2752 0.2532 16 Sum 1.0000 17 18 Computing an envelope portfolio with constant - 4.00% Envelope Z portfolio 19 20 0.0404 ? 0.0782 21 0.1386 0.2684 22 0.1151 0.2227 23 0.2224 0.4307 24 Sum 1.0000 25 26 E(X) 9.37% EV 11.30% 27 Var(x) 0.0862 Vary) 0.1414 28 Sigma(x) 29.37% Sigma(y) 37.60% 29 30 Cov(x,y) 0.1040 ? 31 Corr(x,y) 0.9419 ? 32 ? Question iii ? ? ? C iv) Let us now conduct a single portfolio calculation with a proportion of portfolio x equal to 0.3. Estimate the expected return, variance, and standard deviation of the portfolio in Cells B36:B38, in the Excel spreadsheet below: G N A B D E F 18 Computing an envelope portfolio with constant = 4.00% Envelope portfolio 19 y 20 0.0404 0.0782 21 0.1386 0.2684 22 0.1151 0.2227 23 0.2224 0.4307 Sum 1.0000 24 25 Ely) 11.30% 0.1414 Varly) Sigma(y) 37.60% 26 E(X) 9.37% 27 Var(x) 0.0862 28 Sigma(x) 29.37% 29 30 Cov(x,y) 0.1040 31 Corr(x,y) 0.9419 32 33 34 A single portfolio calculation Proportion of 35 X 0.3 ? 37 62 ? 38 Op ? 39 36 Erp) Question iv [4 marks]