As a junior investment manager, your boss instructs you to help a client to invest $100,000 for the next year. Particularly, you are asked to form an investment portfolio for the client by investing in risk-free assets like 90-day bank bill and two stocks: A and B. Stock A has a beta value of 0.8, an expected return of 7% and a standard deviation of 10%; and stock B has a beta value of 1.2, an expected return of 12% and a standard deviation of 15%. The correlation coefficient between the returns for the two stocks is 0. The risk-free rate is 2%. (a) What is the expected return of the risky portfolio with the two stocks that has the least amount of risk? (b) Suppose that the optimal risky portfolio with the two stocks has a weight of 53% in A and 47% in B, and has the expected return of 9.4% and standard deviation of 8.8%. If this client is willing to take a risk measured by standard deviation of 5% for his overall investment portfolio, how much would you recommend to the client to invest in the risk-free asset, stock A and stock B respectively? What are the expected return and the beta of the client’s overall investment portfolio that you recommend? (c) Draw a graph of expected returns on the vertical axis and standard deviation on the horizontal axis. In this graph show Stock A, B and the optimal risky portfolio with the two stocks (P). Also show the three capital allocation lines for Stock A, B and your portfolio P respectively. Which of the three capital allocation lines is preferred by a risk-averse investor? Why?
As a junior investment manager, your boss instructs you to help a client to invest $100,000
for the next year. Particularly, you are asked to form an investment portfolio for the client
by investing in risk-free assets like 90-day bank bill and two stocks: A and B. Stock A has
a beta value of 0.8, an expected return of 7% and a standard deviation of 10%; and stock
B has a beta value of 1.2, an expected return of 12% and a standard deviation of 15%.
The correlation coefficient between the returns for the two stocks is 0. The risk-free rate is
2%.
(a) What is the expected return of the risky portfolio with the two stocks that has the
least amount of risk?
(b) Suppose that the optimal risky portfolio with the two stocks has a weight of 53% in
A and 47% in B, and has the expected return of 9.4% and standard deviation of
8.8%. If this client is willing to take a risk measured by standard deviation of 5% for
his overall investment portfolio, how much would you recommend to the client to
invest in the risk-free asset, stock A and stock B respectively? What are the
expected return and the beta of the client’s overall investment portfolio that you
recommend?
(c) Draw a graph of expected returns on the vertical axis and standard deviation on the
horizontal axis. In this graph show Stock A, B and the optimal risky portfolio with the
two stocks (P). Also show the three capital allocation lines for Stock A, B and your
portfolio P respectively. Which of the three capital allocation lines is preferred by a
risk-averse investor? Why?
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