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

An analyst wants to estimate the sampling distribution of the median daily return from a sample of 250 observations without assuming any particular return distribution. Which approach is most appropriate?

Bootstrap resampling is most appropriate. It repeatedly draws observations from the sample with replacement and recalculates the median each time, building an empirical sampling distribution without assuming any return distribution, which suits a statistic like the median that lacks a simple formula.

  1. ABootstrap resampling of the observed returns with replacementCorrect
  2. BMonte Carlo simulation using a normal distribution fitted to the sample mean
  3. CDeriving the standard error from the central limit theorem for the median

Explanation

Bootstrap resampling draws repeatedly from the observed data with replacement and computes the statistic each time, so it needs no distributional assumption. The normal-based Monte Carlo imposes a parametric assumption the analyst wants to avoid. The central limit theorem gives a simple standard error for the mean, not for the median.

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