IAI Actuarial Core Principles · Actuarial Statistics · Basic univariate distributions and generating samples
A simulation of a portfolio loss gives a standard error of 3.0 with 1,000 runs. Approximately how many runs are needed to reduce the standard error to 1.0, assuming the output standard deviation is unchanged?
About 9,000 runs are needed. Standard error falls in proportion to the inverse square root of the number of simulations, so cutting it to one third needs nine times as many runs. Tripling the runs to 3,000 would only reduce the error by about 42%.
- A3,000
- B6,000
- C9,000Correct
- D10,000
- 27,000
Explanation
Standard error is proportional to 1/sqrt(n). Reducing it by a factor of 3 requires n to be multiplied by 9, so 9,000 runs. 3,000 wrongly assumes a linear relationship.
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