CFA Level I · CFA Level I Exam · Simulation of Financial Asset Prices and Returns
A Monte Carlo simulation of a stock's terminal price uses 10,000 trials, and the standard error of the estimated mean price is 0.50. The analyst wants to reduce the standard error to 0.25, holding the other inputs constant. The number of trials required is closest to:
About 40,000 trials are needed. Standard error falls with the square root of the number of trials, so cutting it in half requires four times as many trials. Doubling to 20,000 trials would reduce the standard error only by about 29%.
- A20,000
- B40,000Correct
- C100,000
Explanation
Standard error equals s/√N. Halving it requires √N to double, so N must quadruple: 10,000 × 4 = 40,000. Doubling the trials to 20,000 would reduce the error only by a factor of 1.414.
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