位置16的问题 You are comparing Stock A to Stock B. Given the following information, what is the difference in the expected returns of these two securities? [table]
State of Economy | Probability of State of Economy | Rate of Return if State Occurs Stock A | Stock B
Normal | .75 | .13 | .16 Recession | .25 | −.05 | −.21
[/table] 5.25%1.75%1.55%3.05%2.45%清除选择

Question

BlackTom AI · Accepted Answer

We need to determine the difference between the expected returns of Stock A and Stock B using the provided state-by-state returns and probabilities.
First, compute the expected return for Stock A: E[A] = (Probability of Normal × Return of A in Normal) + (Probability of Recession × Return of A in Recession) = 0.75 × 0.13 + 0.25 × (−0.05) = 0.0975 − 0.0125 = 0.085, or 8.5%.
Next, compute the expected return for Stock B: E[B] = (0.75 × 0.16) + (0.25 × (−0.21)) = 0.12 − 0.0525 = 0.0675, or 6.75%.
Now find the difference in expected returns (Stock A minus Stock B): 8.5% − 6.75% = 1.75%.
With these calculations in mind, evaluate the answer choices:
- 5.25%: This is much higher than the computed difference and does not match the state-weighted results for either stock, so it is incorrect.
- 1.75%: This exactly matches the calculated difference between E[A] and E[B], so it is the correct value for A minus B.
- 1.55%: This is close but does not align with the precise math from the given probabilities and returns; it likely arises from a miscalculation or rounding error, so it is incorrect.
- 3.05%: This would imply a larger gap than computed; it does not fit the state-by-state weighted outcomes, so it is incorrect.
- 2.45%: This value is also not supported by the computed results; it misrepresents either one stock’s expected return or the difference, so it is incorrect.
In summary, after performing the weighted-average calculations for both stocks and subtracting, the difference in expected returns is 1.75%. The other options do not align with the exact state-probability-weighted outcomes.

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