位置1的问题 The common stock of Xiang Estates has an expected return of 13.3 percent. The expected return on the market is 10 percent, the inflation rate is 1.4 percent, and the risk-free rate of return is 1.3 percent. What is the beta of this stock?1.381.551.331.411.23清除选择Single choice
A
1.38
B
1.55
C
1.33
D
1.41
E
1.23

Question

位置1的问题 The common stock of Xiang Estates has an expected return of 13.3 percent. The expected return on the market is 10 percent, the inflation rate is 1.4 percent, and the risk-free rate of return is 1.3 percent. What is the beta of this stock?1.381.551.331.411.23清除选择Single choice

A

1.38

B

1.55

C

1.33

D

1.41

E

1.23

BlackTom AI · Accepted Answer

We start by identifying the formula that links expected stock return, risk-free rate, market return, and beta. According to the CAPM (Capital Asset Pricing Model), E[R_i] = R_f + β_i × (E[R_m] − R_f).

Option-by-option analysis:

Option A: 1.38
- This value yields a close match to the given data. Compute beta: β = (E[R_i] − R_f) / (E[R_m] − R_f) = (0.133 − 0.013) / (0.10 − 0.013) = 0.120 / 0.087 ≈ 1.3793, which rounds to 1.38. Therefore this option is consistent with CAPM using the provided numbers.

Option B: 1.55
- If beta were 1.55, the expected return would be E[R_i] = R_f + β × (E[R_m] − R_f) = 0.013 + 1.55 × (0.10 − 0.013) = 0.013 + 1.55 × 0.087 ≈ 0.013 + 0.13485 ≈ 0.14785, or 14.785%. This is noticeably higher than the given 13.3%, so this beta overstates the stock’s sensitivity.

Option C: 1.33
- With β = 1.33, E[R_i] = 0.013 + 1.33 × 0.087 ≈ 0.013 + 0.11571 ≈ 0.12871, or 12.871%. This is lower than the provided 13.3%, so this beta underestimates the stock’s return relative to the CAPM expectation.

Option D: 1.41
- For β = 1.41, E[R_i] = 0.013 + 1.41 × 0.087 ≈ 0.013 + 0.12267 ≈ 0.13567, or 13.567%. This is higher than 13.3%, so it implies a larger beta than the correct value.

Option E: 1.23
- If β = 1.23, E[R_i] = 0.013 + 1.23 × 0.087 ≈ 0.013 + 0.107 (approximately) ≈ 0.12, or 12.0%. This is well below the given 13.3%, indicating a much weaker (smaller) beta than the actual.

Summary: Only option A yields a beta that aligns with the provided expected return using the CAPM relationship. The remaining options produce expected returns that are either too high or too low relative to 13.3% given the market and risk-free inputs.

位置1的问题 The common stock of Xiang Estates has an expected return of 13.3 percent. The expected return on the market is 10 percent, the inflation rate is 1.4 percent, and the risk-free rate of return is 1.3 percent. What is the beta of this stock?1.381.551.331.411.23清除选择Single choice

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