Currently the risk-free rate equals 5% and the expected return on the market portfolio equals 11%. An investment analyst provides you with the following information:
Stock beta Expected return
A 1.33 12%
B 0.7 10%
C 1.5 14%
D 0.66 9%
Required:
1. Indicate whether each stock is overpriced, underpriced, or correctly priced. (9 marks)
2. For each stock, subtract the risk-free rate from the stock’s expected return and divide the result by the stock’s beta. For example, for asset A this calculation is (12%-5%) divide 1.33. Provide an interpretation for these ratios. Which stock has the highest ratio and which has the lowest? (8 marks)
3. Show how a smart investor could construct a portfolio of stocks C and D that would outperform stock A. (7 marks)
4. Construct a portfolio consisting of some combination of the market portfolio and the risk-free asset such that the portfolio’s expected return equals 9%. What is the beta of this portfolio? What does this say about stock D?
Where is the answer?
1. To determine whether each stock is overpriced, underpriced, or correctly priced, we can compare the expected return of the stock to its required return based on the Capital Asset Pricing Model (CAPM). The required return can be calculated using the formula: Required Return = Risk-Free Rate + Beta * (Expected Market Return - Risk-Free Rate).
For each stock:
- Stock A: Required Return = 5% + 1.33 * (11% - 5%) = 12.98%.
Since the expected return for stock A is 12%, it is underpriced.
- Stock B: Required Return = 5% + 0.7 * (11% - 5%) = 7.4%.
Since the expected return for stock B is 10%, it is overpriced.
- Stock C: Required Return = 5% + 1.5 * (11% - 5%) = 14%.
Since the expected return for stock C is 14%, it is correctly priced.
- Stock D: Required Return = 5% + 0.66 * (11% - 5%) = 7.56%.
Since the expected return for stock D is 9%, it is correctly priced.
2. To calculate the ratio, subtract the risk-free rate from the stock’s expected return and divide the result by the stock’s beta. For example, for stock A: (12% - 5%) / 1.33 = 5.26%. This ratio represents the excess return earned per unit of risk (beta).
- Stock A: (12% - 5%) / 1.33 = 5.26%
Stock A has the highest ratio, indicating it offers the highest excess return per unit of risk.
- Stock B: (10% - 5%) / 0.7 = 7.14%
- Stock C: (14% - 5%) / 1.5 = 6%
- Stock D: (9% - 5%) / 0.66 = 6.06%
Stock D has the lowest ratio among the four stocks.
3. To construct a portfolio of stocks C and D that outperforms stock A, the investor should allocate more funds to stocks C and D relative to stock A. By doing so, the investor can potentially earn a higher overall return.
4. To construct a portfolio with an expected return of 9%, we need to find a combination of the market portfolio and the risk-free asset.
The beta of the portfolio can be calculated using the formula: Portfolio Beta = Weight of Market Portfolio * Beta of Market Portfolio.
Since the portfolio's expected return is equal to 9%:
Required Return = Risk-Free Rate + Beta of Portfolio * (Expected Market Return - Risk-Free Rate)
9% = 5% + Beta of Portfolio * (11% - 5%)
4% = 6 * Beta of Portfolio
Beta of Portfolio = 4% / 6 = 0.67
This implies that the beta of this portfolio is 0.67. Based on the information given, we cannot directly determine what this says about stock D without knowing its beta.