Microhard Inc.’s management is considering the following three scenarios of their firm stock value in the future. If the economy is booming, the Microhard Inc. share price will increase by 85%; in a bad scenario, the stock price will go down by 35%; and if everything stays as it is, the stock price will increase by 15%. The chances of observing any of the scenarios are equal. What is the expected return of Microhard Inc. shares?[Fill in the blank]单项选择题
A
a. 50.00%
B
b. 15.00%
C
c. 21.67%
D
d. 19.50%

Question

Microhard Inc.’s management is considering the following three scenarios of their firm stock value in the future. If the economy is booming, the Microhard Inc. share price will increase by 85%; in a bad scenario, the stock price will go down by 35%; and if everything stays as it is, the stock price will increase by 15%. The chances of observing any of the scenarios are equal. What is the expected return of Microhard Inc. shares?[Fill in the blank]单项选择题

A

a. 50.00%

B

b. 15.00%

C

c. 21.67%

D

d. 19.50%

BlackTom AI · Accepted Answer

Expected return is the probability-weighted average of possible returns, so use the expected value formula E[R] = Σ p_i * R_i.

1) Relevant concepts:
- Expected (arithmetic) return for a discrete set of outcomes = sum of (probability × return) for each outcome.
- Here probabilities are equal for three scenarios, so p = 1/3 for each.
- Returns are given in percent: +85%, -35%, +15%.

2) Step-by-step reasoning and calculation:
- Assign probabilities: p_boom = 1/3, p_bad = 1/3, p_stable = 1/3.
- Write the formula: E[R] = (1/3)*(85%) + (1/3)*(-35%) + (1/3)*(15%).
- Combine numerators before dividing: 85% + (-35%) + 15% = 85% - 35% + 15% = 65%.
- Divide by 3: E[R] = 65% / 3 = 21.666...%.

3) Intermediate steps shown numerically:
- 85% - 35% = 50%
- 50% + 15% = 65%
- 65% ÷ 3 = 21.6666667% ≈ 21.67%

4) Why this answer is correct:
- Because each scenario is equally likely, the arithmetic mean of the three percentage returns gives the expected return. No compounding or geometric averaging is requested, so the arithmetic expected return is appropriate.

5) Why the other options are incorrect:
- a. 50.00% would be the average of +85% and +15% only (ignoring the -35% outcome) or a mistaken sum/division.
- b. 15.00% is just the “stable” scenario value, not the weighted average across all scenarios.
- d. 19.50% is a result of a calculation error (for example, dividing 58.5% by 3 or other arithmetic mistakes).

Conclusion: The expected return is 21.67%, which matches the provided correct answer.

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