位置7的问题 Consider the following information: [table]
State of Economy | Probability of State of Economy | Rate of Return if State Occurs Stock A | Stock B
Recession | .04 | .097 | .102 Normal | .72 | .114 | .133 Boom | .24 | .156 | .148
[/table] The market risk premium is 7.4 percent, and the risk-free rate is 3.1 percent. The beta of Stock A is _____ and the beta of Stock B is _____.1.47; 1.411.25; 1.411.21; 1.761.47; 1.761.25; 1.89清除选择

Question

BlackTom AI · Accepted Answer

The task asks us to determine the betas of Stock A and Stock B using the given state probabilities and returns, along with the market risk premium and risk-free rate.
First, I’ll compute the expected return for each stock by weighting the state returns by their probabilities:
- Stock A: E(R_A) = 0.04*(0.097) + 0.72*(0.114) + 0.24*(0.156) = 0.00388 + 0.08208 + 0.03744 = 0.1234 (12.34%)
- Stock B: E(R_B) = 0.04*(0.102) + 0.72*(0.133) + 0.24*(0.148) = 0.00408 + 0.09576 + 0.03552 = 0.13536 (13.536%)
Next, recall the CAPM beta formula: beta = (Expected return − Risk-free rate) / Market risk premium.
The given risk-free rate Rf = 3.1% = 0.031, and market risk premium MRP = 7.4% = 0.074.
For Stock A: beta_A = (0.1234 − 0.031) / 0.074 = 0.0924 / 0.074 ≈ 1.25.
For Stock B: beta_B = (0.13536 − 0.031) / 0.074 = 0.10436 / 0.074 ≈ 1.41.
Now evaluating each answer choice:
- Option 1: 1.47; 1.41 — Beta for A is too high here (expected ≈1.25), while B ≈1.41 matches, so this option mismatches A.
- Option 2: 1.25; 1.41 — Both computed betas align with the calculations above, so this is consistent with the data.
- Option 3: 1.21; 1.76 — A’s beta is underestimated compared to 1.25, and B’s beta is greatly overestimated compared to 1.41; both misalign with the computed values.
- Option 4: 1.47; 1.76 — Both A and B betas are overestimated relative to the computed 1.25 and 1.41, respectively.
- Option 5: 1.25; 1.89 — A’s beta is correct, but B’s beta is too high (1.89 vs about 1.41).
In summary, the numbers that match the CAPM-based calculations given the table are around 1.25 for Stock A and 1.41 for Stock B, with other options introducing deviations in one or both betas.

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