You are an investor with an investment horizon of one year and a certain degree of risk aversion. Your task is to determine the efficient frontier in the case of two risky securities and one risk-free (T-bill) security and select the optimal portfolio depending on your risk-aversion parameter. You need to do your work on a spreadsheet (use one that you are comfortable with).
Score: plot of efficient frontier and table of calculations [35 points]; plot of efficient frontier and tangent line [35 points]; write up [20 points]; references [10 points]
The following steps will help you accomplish this task:
1- Choose
· A well-diversified risky bond B represented by its E(RB) and SD(B).
· A well-diversified stock fund S represented by its E(RS) and SD(S).
· A T-bill with one-year maturity represented by RF.
Choose the one-year risk-free rate to be 5%. Choose one of the following. (a) E(RB) = 9%, SD(B) = 14%, E(RS) = 14%, SD(S) = 20% (b) E(RB) = 10%, SD(B) = 15%, E(RS) = 16%, SD(S) = 22% (c) E(RB) = 12%, SD(B) = 16%, E(RS) = 20%, SD(S) = 25%
2- Choose a correlation coefficient between B and S.
Choose one of the following: (a) Corr(B,S) = 0.20 (b) Corr(B,S) = 0.30 (c) Corr(B,S) = 0.40 (d) Corr(B,S) = 0.50 (e) Corr(B,S) = 0.60
3- Make simulations on standard deviation SD(P) and expected rate of return E(RP) of a "complete" portfolio (formed with B and S) by varying the weights allocated on B and S.
4- Construct and graph the opportunity set (feasible set) for B and S from your simulations.
5- Compute the weights of the tangent portfolio (T).
6- Compute the SD(T) and E(RT) of the tangent portfolio (T).
7- Add the T-bill to your portfolio and redo step 3.
8- Repeat step 4 with the T-bill rate.
9- Write up to two page summary of your results