What is the expected return for stock A?

Economic State Probability Return for Stock A
Positive GDP .55 18%
Negative GDP .45 -3%

Question

What is the expected return for stock A?

Economic State	Probability	Return for Stock A
Positive GDP	.55	18%
Negative GDP	.45	-3%

BlackTom AI · Accepted Answer

To evaluate the expected return for stock A, we weigh each possible return by its probability and sum the results.
Option 1: 8.55% — This is the correct computation. Multiply the positive GDP state return by its probability: 0.55 × 18% = 9.9%. Multiply the negative GDP state return by its probability: 0.45 × (−3%) = −1.35%. Add them: 9.9% + (−1.35%) = 8.55%. This matches the standard formula for expected return: E[R] = Σ p_i R_i.
Option 2: 6.25% — This would require a different weighting or a miscalculation, such as averaging without proper probabilistic weighting or using incorrect state values. If you tried 0.55 × 18% and 0.45 × 0% (ignoring the negative state), you’d get 9.9% instead of 6.25%; if you averaged the two returns without probabilities, you’d get (18% + (−3%)) / 2 = 7.5%, which is still not 6.25%. Such approaches misapply probability or misstate the outcomes.
Option 3: 18.00% — This would be the return in the positive state only, not the overall expected return across states. It treats the probability of the positive GDP state as if that return occurred with certainty, which ignores the possibility of the negative GDP state and thus overstates the true expectation.
Option 4: −3.00% — This reflects the outcome in the negative GDP state alone, again ignoring the positive GDP state and its probability. Relying on a single scenario excludes the other probable state and fails to represent the average outcome across all states.
In summary, the correct expected return incorporates both scenarios and their respective probabilities, yielding 8.55% as the combined expectation across states.

What is the expected return for stock A? Economic State Probability Return for Stock A Positive GDP .55 18% Negative GDP .45 -3%单项选择题

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