Problem 1: Return Computations [32 points]
Use the monthly returns data provided in the spreadsheet. The spreadsheet contains monthly returns to a stock fund and a bond fund as well as the risk-free return from January 2000 to September 2019. Please see attached file for more info
Microsoft Word - FINA_3101_FALL_2019_PS2 FIN 3101, Fall 2019 Problem Set #2 Deadline: 5pm October 14, 2019 Directions: The problem set is due by 5 PM on Monday October 14, 2019. Problem sets must be submitted on Blackboard by the deadline. Due to the tight deadline with the Midterm Exam, solutions will be posted to Blackboard promptly after the deadline. Late assignments will absolutely not be accepted, but there is no penalty to turning in an assignment early. Any students working together must turn in one set of solutions for that group with all group members’ names on that copy. Group size is limited to no more than 3 students. Using any computer file you did not create originally is expressly prohibited and will result in zero credit. Googling for answers is expressly prohibited, though searching for background information is acceptable. All work submitted is required to be the original work product of the group members. Failure to follow instructions will lead to a reduced grade. Problem 1: Return Computations [32 points] Use the monthly returns data provided in the spreadsheet FINA_3101_FALL_2019_PS2_data.xlsx. The spreadsheet contains monthly returns to a stock fund and a bond fund as well as the risk-free return from January 2000 to September 2019. A. [2 points] Compute the arithmetic average monthly returns for both funds. B. [2 points] Compute the geometric average monthly returns for both. C. [2 points] Computed the monthly return variance and standard deviation for both. D. [2 points] Verify that your geometric average return in part B is approximately the arithmetic average minus 0.5 times the return variance. E. [2 points] Annualize the average monthly returns by multiplying it by 12. Annualize the standard deviations by multiplying by the square root of 12. F. [2 points] Compute the covariance and correlation coefficient. G. [2 points] Compute the Sharpe Ratio for the stock and bond funds. H. Assume you form a portfolio that is 50% in the stock fund and 50% in the mutual fund. In other words, invest 100,000 among the two funds by investing 50,000 in each of the two funds on 12/31/1999. a. [2 points] Compute the ending portfolio value assuming the investment is not rebalanced. This means after the initial investment, the portfolio is not adjusted through September 2019. What are the weights of the stocks and bonds at the end of September 2019? b. [2 points] From your answer to a., compute the holding period return. c. Annualize the holding period return from b. d. [2 points] Compute the ending portfolio value assuming the portfolio is rebalance to the original weights at the end of each year. e. [2 points] Compute the holding period return from d. f. [2 points] Annualize the holding period return from e. g. [2 points] Compute the ending portfolio value assuming the portfolio is rebalance to the original weights at the end of each month. h. [2 points] Compute the holding period return from g. i. [2 points] Annualize the holding period return from h. j. [2 points] What is the impact of rebalancing on the holding period return? i. Problem 2: The Efficient Frontier and the CAL [18 points] Consider the case of 2 risky assets. Use your estimates of annual arithmetic average return and standard deviation (1.E.), and the correlation (1.F.) from Problem 1. Assume the return on the risk-free asset is 4.5%. 1. [8 points] What are the expected return and standard deviations of the following portfolios? a. 80% stocks, 20% bonds b. 60% stocks, 40% bonds c. 40% stocks, 60% bonds d. 20% stocks, 80% bonds 2. [2 points] What are the expected return and standard deviation from allocating our wealth 20% to the risk-free asset and 80% to the (40,60) (stock,bond) portfolio? 3. [2 points] What is the slope of the line formed by all possible combinations of the risk-free asset and the (40,60) portfolio? 4. [2 points] What portfolio (selected from all the possible combinations of stocks and bonds) forms the best possible Capital Allocation Line? The correct answer will define the portfolio according to the weights, e.g. (w1,w2) = (50,50). 5. [2 points] What is the slope of the Capital Market Line (CML)? 6. [2 points] What are the expected return and standard deviation of a portfolio that invests -25% in the risk-free asset and the remainder of the portfolio in the optimal portfolio found in Step #4? Problem 3: 3 risky assets [10 points] Consider three risky assets with the following properties. Use this information to answer the following questions. Expected Return Standard Deviation Asset 1 22.00% 25.00% Asset 2 17.00% 20.00% Asset 3 9.00% 13.00% Covariances: σ1,2 = 0.0375 σ1,3 = 0.0065 σ2,3 = 0.0104 1. [3 points] What are the correlation coefficients for assets (1 & 2), (1 & 3), (2 & 3)? 2. [3 points] What is the expected return for the portfolio that invests 35% in Asset 1, 35% in Asset 2, and 30% in Asset 3? 3. [4 points] Compute the standard deviation for the portfolio that invests 35% in Asset 1, 35% in Asset 2, and 30% in Asset 3?