At present, suppose the risk-free rate is 10 percent and the expected return on the market portfolio is 15 percent. The expected returns for four stocks are listed together with their expected betas.
Stock Expected Return Beta NIC 18% 1.3 EIC 14 0.8 UIC 16 1.1 NIBC 17 1.7
Required: a. Determine the required rate of return according to CAPM b. Based on the information given and your result in (a), which stocks are overvalued? Which are undervalued? c. If the risk-free rate were to rise to 12% and the expected return on the market portfolio rose to 16%, will the stock of NIC be overvalued or undervalued? (Assume the expected returns and the betas stay the same)
At present, suppose the risk-free rate is 10 percent and the expected return on the market portfolio is 15 percent. The expected returns for four stocks are listed together with their expected betas.
Stock Expected Return Beta NIC 18% 1.3 EIC 14 0.8 UIC 16 1.1 NIBC 17 1.7
Required: a. Determine the required rate of return according to CAPM b. Based on the information given and your result in (a), which stocks are overvalued? Which are undervalued? c. If the risk-free rate were to rise to 12% and the expected return on the market portfolio rose to 16%, will the stock of NIC be overvalued or undervalued? (Assume the expected returns and the betas stay the same)
student
6. At present, suppose the risk-free rate is 10 percent and the expected return on the market portfolio is 15 percent. The expected returns for four stocks are listed together with their expected betas.
Stock Expected Return Beta
NIC 18% 1.3
EIC 14 0.8
UIC 16 1.1
NIBC 17 1.7
Required:
a. Determine the required rate of return according to CAPM
b. Based on the information given and your result in (a), which stocks are overvalued? Which are undervalued?
c. If the risk-free rate were to rise to 12% and the expected return on the market portfolio rose to 16%, will the stock of NIC be overvalued or undervalued? (Assume the expected returns and the betas stay the same)
For knowledge
To determine the required rate of return (RRR) according to the Capital Asset Pricing Model (CAPM), we can use the formula:
RRR = Risk-Free Rate + Beta * (Expected Return on Market Portfolio - Risk-Free Rate)
a. Using the given information, with a risk-free rate of 10% and an expected return on the market portfolio of 15%, we can calculate the RRR for each stock:
RRR(NIC) = 10% + 1.3 * (15% - 10%) = 10% + 1.3 * 5% = 10% + 6.5% = 16.5%
RRR(EIC) = 10% + 0.8 * (15% - 10%) = 10% + 0.8 * 5% = 10% + 4% = 14%
RRR(UIC) = 10% + 1.1 * (15% - 10%) = 10% + 1.1 * 5% = 10% + 5.5% = 15.5%
RRR(NIBC) = 10% + 1.7 * (15% - 10%) = 10% + 1.7 * 5% = 10% + 8.5% = 18.5%
b. Based on the RRR calculated in (a), we can determine whether each stock is overvalued or undervalued. If the expected return on a stock is higher than its RRR, it is considered undervalued, and if it is lower, it is considered overvalued.
According to the RRR:
- NIC: Expected return (18%) > RRR (16.5%) → NIC is undervalued.
- EIC: Expected return (14%) < RRR (14%) → EIC is overvalued.
- UIC: Expected return (16%) < RRR (15.5%) → UIC is overvalued.
- NIBC: Expected return (17%) < RRR (18.5%) → NIBC is overvalued.
c. If the risk-free rate were to rise to 12% and the expected return on the market portfolio rose to 16%, we can calculate the new RRR for NIC while assuming the expected returns and betas stay the same:
New RRR(NIC) = 12% + 1.3 * (16% - 12%) = 12% + 1.3 * 4% = 12% + 5.2% = 17.2%
Comparing the new RRR(NIC) (17.2%) with the expected return for NIC (18%), we see that NIC would still be considered undervalued, as the expected return is higher than the RRR.