Economics 413 Problem Set #2 Rules: Please post your answers on Canvas under Quizzes. I. Efficient Two Asset Portfolios Assume that the expected return on asset 1 is 5% and the expected return on asset 2 is 4%. The standard deviation of asset 1 is 3.0% and 1.5% for asset 2. Assume the correlation of both assets is -0.5 W1 W2 ER,] , Sharpe 1.00 0.00 0.75 0.25 0.50 0.50 0.25 0.7 0.00 1.00 1. The expected portfolio return in the first row is: (a) 5.0; (b) 4.0; (c) 4.50; (d) 0.25; 2. The expected portfolio return in the second row is: (a) 0.95; (b) 4.75; (c) 0.12; (d) -5.00; 3. The expected portfolio return in the third row is: (a) 0.10; (b) 0.20; (c) 4.50; (d) 6.70; 4. The expected portfolio return in the fourth row is: (a) 4.25; (b) 0.25; (c) 0.99; (d) 0.00; 5. The expected portfolio return in the fifth row is: (a) 4.0; (b) -4.50; (c) 0.33; (d) 5.00; 6. The portfolio standard deviation in the first row is: (a) 1.0; (b) 0.2; (c) 3.0; (d) -1.0; 7. The portfolio standard deviation in the second row is: (a) 5.12; (b) 4.33; (c) 6.29; (d) 2.09; 8. The portfolio standard deviation in the third row is: (a) 1.30; (b) 3.45; (c) 4.29; (d) 5.67; 9. The portfolio standard deviation in the fourth row is: (a) 1.67; (b) 4.00; (c) 3.97; (d) 0.99; 10. The portfolio standard deviation in the fifth row is: (a) 1.25; (b) 3.59; (c) 1.50; (d) 6.29; Assume that the risk free rate of return is 0%. 11. The Sharpe ratio in the first row is: (a) 1.67; (b) 0.23; (c) 3.01; (d) -1.00; 12. The Sharpe ratio in the second row is: (a) 2.28; (b) 4.33; (c) 6.29; (d) 8.23; 13. The Sharpe ratio in the third row is: (a) 1.30; (b) 3.46; (c) 4.29; (d) 5.67; 14. The Sharpe ratio in the fourth row is: (a) 1.67; (b) 4.28; (c) 3.97; (d) 0.99; 15. The Sharpe ratio in the fifth row is: (a) 1.50; (b) 3.59; (c) 2.20; (d) 2.67; 16. What is the weight on asset 1 in the maximum Sharpe ratio portfolio: (a) -0.50; (b) 0.15; (c) 0.30; (d) -0.25; 17. What is the weight on asset 2 in the minimum variance portfolio: (a) 0.71; (b) 0.25; (c) 0.35; (d) -0.35; 18. Why is the point w2 = 1.0 not on the efficient frontier: (a) it is never optimal to hold 100% of your money in a single asset; (b) all portfolios with negative variances require holdings of both assets; (c) the portfolio is stochastically dominated; (d) it is on the frontier; II. Value at Risk Find the value at risk for different time horizons and confidence levels of a 1, 000$ portfolio in Dell and Microsoft stocks. Assume that E[RDeli] = 0.15%, and E[RMsft] = 0.05%, andthat their daily percentage returns have the following covariance matrix, Dell Microsoft Dell 0.400 -0.300 Microsoft -0.300 0.250 Assuming you hold an equal weighted portfolio 19. What is the expected return: (a) 0.325; (b) 0.25; (c) 0.10; (d) 0.44; 20. What is the variance: (a) 0.567; (b) 1.234; (c) 0.013; (d) 0.112; 21. What is the 1-day value at risk at a 95% confidence level: (a) $-1.56; (b) $2.90; (c) $-0.84; (d) $0.41; 22. What is the 1-day value at risk at a 99% level: (a) $-3.64; (b) $-1.60; (c) $0.93; (d) $2.72; 23. What is 30-day value at risk at a 95% confidence level: (a) $-4.60; (b) $2.16; (c) $-0.59; (d) $-7.92; 24. What is the 30-day value at risk at a 99% level: (a) $1.96; (b) $-8.77; (c) $-0.89; (d) $-1.32; Now try to find the minimum variance weight between Dell and Microsoft 25. The optimal weight on Dell is (a) 0.25; (b) 0.73; (c) 0.44; (d) 0.32; Assuming the optimal weighting you found in 25 and a $1,000 portfolio: 26. What is the expected return: (a) 0.42; (b) 0.21; (c) 0.72; (d) 0.09; 27. What is the standard deviation: (a) 0.56; (b) 0.45; (c) 0.23; (d) 0.089; 28. What is the 1-day value at risk at a 95% confidence level: (a) $0.53; (b) $-0.53; (c) $1.98; (d) $-0.23; 29. What is the 1-day value at risk at a 99% level: (a) $-6.24; (b) $0.32; (c) $0.02; (d) $-1.14; 30. What is 30-day value at risk at a 95% confidence level; (a) $-2.91; (b) $2.33; (c) $-0.93; (d) $-3.97; 31. What is the 30-day value at risk at a 99% level: (a) $-2.04; (b) $-1.93; (c) $-6.25; (d) $-23.97;Problem Set #2 1 point The expected portfolio return in therst row is 5.0 4.0 4.50 0000 0.25 1 point The expected portfolio return in the second row is O 0.95 The expected portfolio return in thethird row is 0.10 0.20 4.50 0000 6.70 1 point The expected portfolio return in the fourth row is 4.25 0.25 0.99 0000 0.00 5 1 point The expected portfolio return in the fifth row is O 4.0 O 4.5 O 0.33 O 5.00 6 1 point The portfolio standard deviation in the first row is O 1.0 O 0.2 O 3.0 O -1.0 7 1 point The portfolio standard deviation in the second row is O 5.12 O 4.33 O 6.29 O 2.09 8 1 point The portfolio standard deviation in the third row is O 1.30 O 3.45 O 4.29 O 5.67 9 1 point The portfolio standard deviation in the fourth row is O 1.67 4.00 OO 3.97 O 0.9910 1 point The portfolio standard deviation in the fifth row is O 1.25 O 3.59 O 1.50 O 6.29 11 1 point The Sharpe ratio in the first row is O 1.67 O 0.23 O 3.01 O -1.00 12 1 point The Sharpe ratio in the second row is O 2.28 O 4.33 O 6.29 O 8.23 13 1 point The Sharpe ratio in the third row is O 1.30 O 3.46 4.29 OO 5.67 14 1 point The Sharpe ratio in the fourth row is O 1.67 O 4.28 O 3.97 O 0.99- 1 point The Sharpe ratio in the fth row is 1.50 3.5 9 2.20 2.67 What is the weight on asset 1 in the maximum Sharpe ratio portfolio -0.5 0000 0.15 0.30 0000 -0.25 1 point What is theweight on asset2 in the minimum variance portfolio 0 0.71 O 0.25 O 0.35 O 0.35 1 point Why is the point W2=1.0 not on the efcient frontier 0 it is never optimal to hold 100% of your money in a single asset 0 all portfolios with negative variances require holdings of both assets 0 the portfolio is stochastically dominated 0 it is on the frontier; 1 point What is the expected return 0.325 0.25 0.10 0000 0.44 20 1 point What is the variance O 0.567 O 1.234 0.013 OO 0.112 21 1 point What is the 1-day value at risk at a 95% confidence level O $-1.56 $2.90 OOO $-0.84 $0.41 22 1 point What is the 1-day value at risk at a 99% level $-3.64 OO $-1.60 $0.93 OO $2.72 23 1 point What is 30-day value at risk at a 95% confidence level $-4.60 OOO $2.16 $-0.59 O $-7.92 24 1 point What is the 30-day value at risk at a 99% level O $1.96 $-8.77 OOO $-0.89 $-1.3225 1 point The optimal weight on Dell is O 0.25 O 0.73 O 0.44 O 0.32 26 1 point What is the expected return O 0.42 O 0.21 O 0.72 O 0.09 27 1 point What is the standard deviation 0.56 OO 0.45 0.23 OO 0.089 28 1 point What is the 1-day value at risk at a 95% confidence level O $0.53 O $-0.53 $1.98 OO $-0.23 29 1 point What is the 1-day value at risk at a 99% level O $-6.24 $0.32 OO $0.02 O $-1.1430 1 point What is 30-day value at risk at a 95% confidence level O $-2.91 O $2.33 O $-0.93 O $-3.97 31 1 point What is the 30-day value at risk at a 99% level O $-2.04 O $-1.93 O $-6.25 O $-23.97