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FRM Part I · FRM Exam Part I · Common Univariate Random Variables

A risk analyst models daily trading P&L of a desk as independent and identically distributed draws with mean USD 50,000 and standard deviation USD 200,000. Using the Central Limit Theorem, what is the approximate standard deviation of the sample mean P&L over 100 trading days?

The standard deviation of the sample mean is the population standard deviation divided by the square root of the sample size. Here 200,000 divided by 10 gives USD 20,000. Dividing by 100 instead of its square root would wrongly understate the dispersion.

  1. AUSD 2,000
  2. BUSD 20,000Correct
  3. CUSD 200,000
  4. DUSD 5,000

Explanation

The standard deviation of the sample mean equals sigma divided by the square root of n: 200,000 / sqrt(100) = 200,000 / 10 = 20,000. USD 2,000 results from dividing by n instead of sqrt(n) (200,000/100 = 2,000). USD 200,000 ignores averaging.

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