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FRM Part I · FRM Exam Part I · Simulation and Bootstrapping

An analyst compares two unbiased estimators of the same quantity. Plain Monte Carlo has per-draw variance 9 and costs 1 unit of computing time per draw. A variance reduction method has per-draw variance 3 but costs 4 units of time per draw. For the same total computing budget, which statement is correct?

Plain Monte Carlo is more efficient. For a fixed budget, estimator variance is proportional to per-draw variance times cost per draw: 9×1 = 9 for plain versus 3×4 = 12 for the method. The lower product wins, so the cheaper method beats the apparent variance saving.

  1. AThe variance reduction method gives lower estimator variance, because its per-draw variance is one third as large
  2. BPlain Monte Carlo gives lower estimator variance, because the method's variance×cost product is 12 versus 9Correct
  3. CBoth give the same estimator variance, because the product of variance and cost is equal
  4. DThe comparison cannot be made without knowing the correlation between the two estimators

Explanation

For a fixed budget B, the number of draws is B/cost and the variance is variance×cost/B. Plain: 9×1 = 9. Method: 3×4 = 12. Higher product means higher variance for the same budget, so plain Monte Carlo is better. Option A ignores the cost.

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