The common stock of Flavorful Teas has an expected return of 21.42 percent. The return on the market is 15 percent and the risk-free rate of return is 4.3 percent. What is the beta of this stock?

Question

BlackTom AI · Accepted Answer

First, identify the CAPM relationship: Expected stock return = Risk-free rate + Beta × (Market return − Risk-free rate). This lets us isolate beta when given the other values.
Option 1: 1.45. If beta were 1.45, the expected return would be 4.3% + 1.45 × (15% − 4.3%) = 4.3% + 1.45 × 10.7% ≈ 4.3% + 15.515% ≈ 19.815%, which is lower than the given 21.42%. So this beta understates the required risk premium.
Option 2: 4.00. With beta 4.00, the expected return would be 4.3% + 4.0 × 10.7% = 4.3% + 42.8% = 47.1%, far above the observed 21.42%. This indicates an implausibly high sensitivity to market moves.
Option 3: 1.60. Calculating with beta 1.60 gives 4.3% + 1.60 × 10.7% = 4.3% + 17.12% = 21.42%, which matches the provided expected return exactly. This aligns perfectly with the CAPM equation.
Option 4: 0.63. With beta 0.63, the expected return would be 4.3% + 0.63 × 10.7% ≈ 4.3% + 6.741% ≈ 11.041%, which is far too low relative to 21.42% and suggests insufficient market sensitivity.
Option 5: 0.80. If beta were 0.80, the expected return would be 4.3% + 0.80 × 10.7% = 4.3% + 8.56% = 12.86%, still well below the given 21.42% and implies a moderate but not matching risk exposure.

In summary, by plugging each candidate beta into the CAPM formula and comparing the resulting expected return to the provided 21.42%, only beta 1.60 yields a perfect match. The other beta values produce expected returns that are too high or too low, indicating they do not reflect the stock’s true risk relative to the market.

The common stock of Flavorful Teas has an expected return of 21.42 percent. The return on the market is 15 percent and the risk-free rate of return is 4.3 percent. What is the beta of this stock?单项选择题

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