a. Suppose we form a portfolio invested in Mercedes and BMW stocks. The two stocks are equally weighted in the portfolio. The table below displays each stocks mean return, variance, and standard deviation, as well as their covariance. Estimate the mean and variance of this portfolio, as well as its standard deviation. Show in detail your calculations.

b. The graph below shows the envelope frontier. Based on the graph below do you agree with the statement Portfolio P(1) and P(2) are two efficient portfolios? Explain your answer.

c. Explain in detail all five propositions on envelope portfolios.

d. Consider two portfolios, x and y, whose convex combinations compose the envelope frontier in the graph below (curve ABC). Also marked, are other portfolios, some of which contain short positions of either x or y. Do you agree with the statement Every convex combination of any two efficient portfolios is efficient? Explain your answer.

e. Let us now compute an envelope portfolio with constant = 4%, where the vector z solves the system of simultaneous linear equations () = . Then, this solution produces a portfolio x and y on the envelope of the feasible set. Write down and explain the Excel formula used to calculate the values in Cells A20, F20, F24 (portfolio weights and sum of portfolio weights), F26:F28 (mean, variance and standard deviation), and B30:B31 (covariance, correlation), in the Excel spreadsheet below:

Asset returns Mean return Variance Standard deviation Covariance Mercedes BMW 1.78% -0.48% 0.0456 0.0276 21.35% 16.61% 0.0020 Portfolio Means and Returns 17% A 15% 13% Portfolio expected retrun Erp) 11% P(1) B B 9% P(2) 7% C 5% 30% 35% 40% 45% 70% 75% 80% 85% 50% 55% 60% 65% Portfolio standard deviation op 16% A 14% 12% 10% 8% B 6% 4% 20% 25% 30% 35% 40% 45% 50% 55% 60% H A B C D G 1 CALCULATING THE FRONTIER E(r) Variance covariance, Mean minus returns constan 2 E(1) t 3 0.10 0.01 0.03 0.05 6% 2.00% 4 0.01 0.30 0.06 -0.04 8% 4.00% 5 0.03 0.06 0.40 0.02 10% 6.00% 6 0.05 -0.04 0.02 0.50 15% 11.00% 7 8 Constant, 4.00% 9 10 Computing an envelope portfolio with constant - 0 Envelope Z portfolio 11 12 0.3861 0.3553 13 0.2567 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% Ely 11.30% ? 27 Varix) 0.0862 Vary) 0.1414 ? 28 Sigmax) 29.37% Sigma(y) 37.60% ? 29 30 Covix.) 0.1040 31 Corrix,y) 0.9419 ? 32 Asset returns Mean return Variance Standard deviation Covariance Mercedes BMW 1.78% -0.48% 0.0456 0.0276 21.35% 16.61% 0.0020 Portfolio Means and Returns 17% A 15% 13% Portfolio expected retrun Erp) 11% P(1) B B 9% P(2) 7% C 5% 30% 35% 40% 45% 70% 75% 80% 85% 50% 55% 60% 65% Portfolio standard deviation op 16% A 14% 12% 10% 8% B 6% 4% 20% 25% 30% 35% 40% 45% 50% 55% 60% H A B C D G 1 CALCULATING THE FRONTIER E(r) Variance covariance, Mean minus returns constan 2 E(1) t 3 0.10 0.01 0.03 0.05 6% 2.00% 4 0.01 0.30 0.06 -0.04 8% 4.00% 5 0.03 0.06 0.40 0.02 10% 6.00% 6 0.05 -0.04 0.02 0.50 15% 11.00% 7 8 Constant, 4.00% 9 10 Computing an envelope portfolio with constant - 0 Envelope Z portfolio 11 12 0.3861 0.3553 13 0.2567 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% Ely 11.30% ? 27 Varix) 0.0862 Vary) 0.1414 ? 28 Sigmax) 29.37% Sigma(y) 37.60% ? 29 30 Covix.) 0.1040 31 Corrix,y) 0.9419 ? 32