CFA Level IQuantitative MethodsMedium
An analyst models a stock's annual return using three economic scenarios: Boom (probability 0.30, return 20%), Normal growth (probability 0.50, return 10%), and Recession (probability 0.20, return -5%). What is the stock's expected return?
- A15.00%
- B11.67%
- C10.00%
- D8.33%
Show answer & explanationAnswer & explanation
Correct answer: C. 10.00%
Expected return = sum of (probability x outcome) = (0.30 x 20%) + (0.50 x 10%) + (0.20 x -5%) = 6% + 5% - 1% = 10.00%.
Why the other options are wrong
- A. This overstates the boom scenario's weight relative to the others.
- B. This omits the negative contribution from the recession scenario.
- D. This results from an unweighted simple average error, not probability weighting.
Expected Value (Discrete Random Variable)
The expected value of a discrete random variable is the probability-weighted average of all possible outcomes.
- E(X) = sum of [P(X_i) x X_i]
- Probabilities across all scenarios must sum to 1.0
- Used as the basis for calculating variance and standard deviation of returns
Memory trick: Weight, multiply, then add — that's expectation's trade.