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

A bootstrap of 1,000 resamples produces estimates of a portfolio's beta. The sorted estimates give the 25th smallest value as 0.82 and the 975th smallest value as 1.31, while the original sample estimate is 1.05. Which statement is the most appropriate use of these results?

Trimming 2.5% from each tail of the 1,000 bootstrap estimates gives a percentile interval of about 0.82 to 1.31, which serves as an approximate 95% confidence interval for beta. The confidence level comes from the tail cut-offs, not from the number of resamples.

  1. AThe percentile interval of approximately 0.82 to 1.31 is an approximate 95% confidence interval for betaCorrect
  2. BThe interval 0.82 to 1.31 is a 99% confidence interval because it uses 1,000 resamples
  3. CThe bootstrap shows the true beta must equal 1.05 because it is the original estimate
  4. DThe interval of 0.82 to 1.31 is a prediction interval for the next observation's return

Explanation

Cutting off 25 of 1,000 estimates in each tail (2.5% each) gives a central 95% percentile interval. The number of resamples does not set the confidence level. The bootstrap does not identify the true parameter, and the interval concerns the estimator, not future returns.

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