Estimate the expected return for each company according to CAPM

Problem 1:

a. Estimate the expected return for each company according to CAPM: Expected return for Victoria Store = 4% + 1.5(6%) = 10% Expected return for Houston Store = 4% + 1.0(6%) = 10%

b. Characterize each company as underpriced, overpriced, or properly priced according to CAPM: Victoria Store – Expected return is 12%, which is higher than the expected return of 10% calculated using CAPM, so it is overpriced. Houston Store – Expected return is 11%, which is equal to the expected return of 10% calculated using CAPM, so it is properly priced.

c. Another company, Sugar Land store, has a beta of 2.0. Assuming efficient market hypothesis (CAPM holds), estimate the expected rate of return for a portfolio consisting of 1/3 Victoria stock, 1/3 Houston stock, and 1/3 Sugar Land store: Expected return for Sugar Land store = 4% + 2.0(6%) = 12% Expected return for the portfolio = (1/3)(12%) + (1/3)(11%) + (1/3)(12%) = 11.67%

Problem 2: a. Construct an appropriate portfolio (Mix of risky asset and risk free asset) for your young client and estimate the expected return and standard deviation of your young client for the coming year: The young client has high risk tolerance, so they can invest more in the risky asset and less in the risk-free asset. Let’s assume the young client invests 90% in the risky asset and 10% in the risk-free asset. Expected return = (90%)(30%) + (10%)(12%) = 27% Standard deviation = (90%)(40%) = 36%

b. Construct an appropriate portfolio for your middle aged client and estimate the expected return and standard deviation of your middle aged client: The middle aged client has medium risk tolerance, so they can invest moderately in the risky asset and moderately in the risk-free asset. Let’s assume the middle aged client invests 60% in the risky asset and 40% in the risk-free asset. Expected return = (60%)(30%) + (40%)(12%) = 21% Standard deviation = (60%)(40%) = 24%

c. Construct an appropriate portfolio for your old client and estimate the expected return and standard deviation of your old client: The old client has low risk tolerance, so they can invest less in the risky asset and more in the risk-free asset. Let’s assume the old client invests 30% in the risky asset and 70% in the risk-free asset. Expected return = (30%)(30%) + (70%)(12%) = 15% Standard deviation = (30%)(40%) = 12%

d. If your middle aged client requires a portfolio with a standard deviation of 30%, what is its expected rate of return? We can use the Capital Market Line (CML) to find the expected rate of return for a given level of standard deviation. The CML is given by: E(rp) = rf + [E(rm) – rf] * (σp / σm) Where E(rp) is the expected return of the portfolio, rf is the risk-free rate, E(rm) is the expected return of the market portfolio, σp is the standard deviation of the portfolio and σm is the standard deviation of the market portfolio.