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.

First: Choose

• A well-diversified risky bond B represented by its E(RB) and STDB.
• A well-diversified stock fund S represented by its E(RS) and STDS.
• A) Choose your own bond and stock and parameters for a company in the real world.
• B) 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%.

Next:

2- Choose a correlation coefficient between B and S.

Choose your own correlation corresponding to Step 1 A.

For Step 1 B choose one of the following: (a) Corr(B,S) = 0.20 (b) Corr(B,S) = 0.30 (c) Corr(B,S) = 0.40

3- Make simulations on STD and E(R) 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 STDTand 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.

The following equations will help you in your computations:

Var (Rp) = WB2x Var (B) + WS2x Var (S) + 2WBx WSx (STDBx STDSx CORR (B, S))

STD = SQRT (Var)

CORR (B, S) = Correlation coefficient between bond and stock

COV (RB, RS) = STDBx STDSx CORR (B, S)

• OPTIMAL TANGENT PORTFOLIO (T) WEIGHTS

* For the bond fund B:

Numerator = [E(RB) - RF] x Var (RS) - [E(RS) - RF] x COV (RB, RS)

Denominator = [E(RB) - RF] x Var (RS) + [E(RS) - RF] x Var (RB) - [E(RB) - RF+ E(RS) - RF] x COV (RB, RS)

WB= Numerator/Denominator

* For the stock fund: WS= 1 - WB

* The last column of step 7: The Capital Market (Allocation) Line:

E(RC) = RF+ ([E(RT) - RF]/STDT) x STDC