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CFA Level I · CFA Level I Exam · Simulation of Financial Asset Prices and Returns

An analyst has 60 monthly returns and wants to estimate the standard error of the sample median using a bootstrap. Which approach is most appropriate?

The most appropriate approach is to repeatedly draw 60 returns with replacement, compute the median of each resample, and take the standard deviation of those medians. This gives an empirical standard error for a statistic lacking a simple formula.

  1. AApply the standard error formula for the mean, s divided by the square root of 60
  2. BRepeatedly draw 60 returns with replacement, compute each median, and take the standard deviation of those mediansCorrect
  3. CDraw 60 returns without replacement once and use the median as the standard error

Explanation

The bootstrap standard error is the standard deviation of the statistic across many resamples drawn with replacement. The mean formula does not apply to the median, and sampling without replacement 60 of 60 reproduces the same sample every time.

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