Yahoo! Finance reported the following market betas for the stocks of selected health insurers: Company Beta UnitedHealth Group 0.70 Humana 1.16 Aetna 0.63 Cigna 0.71 Assume that the risk-free rate, RF, and required rate of return on the market value, R(Rm), were 2.0 percent and 8.5 percent, respectively. What are the required return rates of return on the four stocks? Which of the stocks is riskiest for investors? Explain your answer.
The Correct Answer and Explanation is:
To calculate the required rates of return for the stocks of the four companies, we can use the Capital Asset Pricing Model (CAPM), which is given by the formula:Ri=Rf+βi×(Rm−Rf)R_i = R_f + \beta_i \times (R_m – R_f)Ri=Rf+βi×(Rm−Rf)
Where:
- RiR_iRi is the required rate of return for the stock,
- RfR_fRf is the risk-free rate (2.0%),
- RmR_mRm is the expected return on the market (8.5%),
- βi\beta_iβi is the beta of the stock.
Let’s calculate the required returns for each company:
1. UnitedHealth Group (Beta = 0.70)
RUnitedHealth=2.0%+0.70×(8.5%−2.0%)=2.0%+0.70×6.5%=2.0%+4.55%=6.55%R_{\text{UnitedHealth}} = 2.0\% + 0.70 \times (8.5\% – 2.0\%) = 2.0\% + 0.70 \times 6.5\% = 2.0\% + 4.55\% = 6.55\%RUnitedHealth=2.0%+0.70×(8.5%−2.0%)=2.0%+0.70×6.5%=2.0%+4.55%=6.55%
2. Humana (Beta = 1.16)
RHumana=2.0%+1.16×(8.5%−2.0%)=2.0%+1.16×6.5%=2.0%+7.54%=9.54%R_{\text{Humana}} = 2.0\% + 1.16 \times (8.5\% – 2.0\%) = 2.0\% + 1.16 \times 6.5\% = 2.0\% + 7.54\% = 9.54\%RHumana=2.0%+1.16×(8.5%−2.0%)=2.0%+1.16×6.5%=2.0%+7.54%=9.54%
3. Aetna (Beta = 0.63)
RAetna=2.0%+0.63×(8.5%−2.0%)=2.0%+0.63×6.5%=2.0%+4.10%=6.10%R_{\text{Aetna}} = 2.0\% + 0.63 \times (8.5\% – 2.0\%) = 2.0\% + 0.63 \times 6.5\% = 2.0\% + 4.10\% = 6.10\%RAetna=2.0%+0.63×(8.5%−2.0%)=2.0%+0.63×6.5%=2.0%+4.10%=6.10%
4. Cigna (Beta = 0.71)
RCigna=2.0%+0.71×(8.5%−2.0%)=2.0%+0.71×6.5%=2.0%+4.62%=6.62%R_{\text{Cigna}} = 2.0\% + 0.71 \times (8.5\% – 2.0\%) = 2.0\% + 0.71 \times 6.5\% = 2.0\% + 4.62\% = 6.62\%RCigna=2.0%+0.71×(8.5%−2.0%)=2.0%+0.71×6.5%=2.0%+4.62%=6.62%
Summary of Required Returns:
- UnitedHealth Group: 6.55%
- Humana: 9.54%
- Aetna: 6.10%
- Cigna: 6.62%
Riskiest Stock:
The riskiest stock for investors is Humana, which has the highest beta of 1.16. Beta measures the sensitivity of a stock’s returns to the returns of the market. A higher beta indicates greater volatility compared to the overall market. Since Humana’s beta is greater than 1, it is expected to experience more volatility than the market. This means that investors in Humana are taking on more risk, as its stock price is more sensitive to fluctuations in the broader market. Conversely, Aetna with the lowest beta of 0.63 is the least risky among the four, as its stock is less volatile in relation to market movements.
