# You are planning to invest \$200,000. Two securities are available, A and B, and you can invest in…

You are planning to invest \$200,000. Two securities are available, A and B, and you can invest in either of them or in a portfolio with some of each. You estimate that the following probability distributions of returns are applicable for A and B:

a. The expected return for Security B is r^B = 20%, and σB = 25.7%. Find r^A and σA:

b. Use Equation 24-3 to find the value of wA that produces the minimum risk portfolio. Assume ρAB = −0.5 for parts b and c.

c. Construct a table giving r^p and σp for portfolios with wA = 1.00, 0.75, 0.50, 0.25, 0.0, and the minimum risk value of wA. ( Hint: For wA = 0.75, r^p = 16.25% and σp = 8.5%; for wA = 0.5, r^p = 17.5% and σp = 11.1%; for wA = 0.25, r^p = 18.75% and σp = 17.9%.)

d. Graph the feasible set of portfolios and identify the efficient frontier of the feasible set.

e. Suppose your risk–return trade-off function, or indifference curve, is tangent to the efficient set at the point where r^p = 18%. Use this information, together with the graph constructed in part d, to locate (approximately) your optimal portfolio. Draw in a reasonable indifference curve, indicate the percentage of your funds invested in each security, and determine the optimal portfolio’s σp and r^p. ( Hint: Estimate σp
and r^p graphically; then use the equation for r^p to determine wA.)

f. Now suppose a riskless asset with a return rRF = 10% becomes available. How would this change the investment opportunity set? Explain why the efficient frontier becomes linear.

g. Given the indifference curve in part e, would you change your portfolio? If so, how? (Hint: Assume that the indifference curves are parallel.)

h. What are the beta coefficients of Stocks A and B? (Hint: Recognize that ri = r RF + bi(rM −rRF) and then solve for bi; assume that your preferences match those of most other investors.)

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