Question

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).

The following steps will help you accomplish this task:

1- Choose

• A well-diversified risky bond B represented by its E(R_B) and SD(B).
• A well-diversified stock fund S represented by its E(R_S) and SD(S).
• A T-bill with one-year maturity represented by R_F.

Choose the one-year risk-free rate to be 5%. (a) E(R_B) = 9%, SD(B) = 14%, E(R_S) = 14%, SD(S) = 20%

2- Choose a correlation coefficient between B and S.

Choose one of the following: (b) Corr(B,S) = 0.30

3- Make simulations on standard deviation SD(P) and expected rate of return E(R_P) 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(R_T) 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.

Answer 1

(A)  Simulation of the portfolio with diff weights assign to the bond and stock with excel workbook

SD of Portfolio= W₁²$\sigma$₁²+W₂²$\sigma$₂²+2*W₁*W₂*$\varrho$₁₂$\sigma$₁*$\sigma$₂

Where 1 and 2 is stock and bond and $\sigma$ is Std. Deviation and $\varrho$ is coefficient of correlation and W is Weight

Now for the Portfolio Return = W₁*R₁+W₂*R₂

Now here i snip the clip of excel work book which show you the simulation with different weights of portfolio return and portfolio Std. Deviation.

Weight of B Weight of S E(R) Portfolio SD of Portfolio 9.00% 1 14.00 9.50% 0.9 0.1 13.34 10.00% 0.8 0.2 12.97 10.50% 0.7 0.3 12.94 11.50% 0.5 0.5 13.82 0.4 12.00% 0.6 14.69 12.50% 0.3 0.7 15.78 0.8 13.00% 0.2 17.05 13.50% 0.1 0.9 18.47 14.00% 0 1 20.00

(B) Construction of graph the opportunity set for B and S from Simulation.

Opportunity Set with Diff Weight of S and B 16% 14% 12 % 10% 8% E(R) Portfolio 6 % 4% 2% 0 % 5.00 10.00 15.00 20.00 25.00

(C) In opinion Portfolio weight of 0.7 of B and 0.3 of S is best opportunity set because it has least Risk(SD) and Better Return so, this called as Tangent and SD of Tangent Portfolio is 12.94 and ER of same is 10.5%.

(D) To compute the Portfolio Return and SD with combing T-Bill with 5% rate in this case you return will increase with diff sets of weight combination and important point is that no risk (SD) will further rise because T-Bill is risk free instrument so, we construct the graph and the chart also.