CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns
An analyst estimates an option's value with a Monte Carlo simulation of 10,000 trials and obtains a standard error of 0.40. To cut the standard error to 0.10, the number of trials needed is closest to:
About 160,000 trials are needed. The standard error falls with the square root of the number of trials, so cutting it to one quarter requires sixteen times as many trials: 10,000 multiplied by 16 equals 160,000.
- A40,000
- B100,000
- C160,000Correct
Explanation
Standard error is proportional to 1/sqrt(N). Reducing it by a factor of 4 (0.40/0.10) requires N to rise by 4^2 = 16 times. 10,000 x 16 = 160,000. Choosing 40,000 comes from scaling N by 4 instead of squaring it.
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