You are planning to invest $200,000. You estimate the following probability distributions of returns for Stock A and B:

Stock A Stock B

Probability Returns Probability Returns

.1 -10% .1 -30%

.2 5 .2 0

.4 15 .4 20

.2 25 .2 40

.1 40 .1 70

Corr (A,B) = -.5

a. What are the expected return and standard deviation for security A and security B?

b. What is the minimum variance portfolio?

c. Construct a table giving E (R_P) and Standard deviation, and for portfolios with

W = 1.00, 0.75, 0.50, 0.25, 0.0 and the minimum risk portfolio.

d. Graph the feasible set of portfolios and identify the efficient section on the feasible set.

e. Suppose your risk return trade-off function or indifference curve is tangent to the efficient set at the point where E(R_P) = 18%.

i. Use this information plus the graph constructed in Part (d) to locate approximately your optimal portfolio. Draw in a reasonable indifference curve.

ii) Compute the percentage and the dollar amount invested in each stock and determine the optimal portfolios VAR(R_P).

f. Now suppose a riskless asset with a return R_F = 10% becomes available.

i) How would this change the investment opportunity set? Explain why the investment opportunity set becomes linear.

ii) what is the asset allocation if the investor requires an expected rate of return = 22%?