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101 Concepts for the Level I Exam

Concept 11: Central Limit Theorem

According to the central limit theorem, if we draw a sample from a population with a mean µ and a variance σ2, then the sampling distribution of the sample mean:

  • will be normally distributed (irrespective of the type of distribution of the original population).
  • will have a mean of µ.
  • will have a variance of σ2/n.

Suppose the average return of the universe of 10,000 stocks is 12% and its standard deviation is 10%. Through central limit theorem, we can conclude that if we keep drawing samples of 100 stocks and plot their average returns, we will get a sampling distribution that will be normally distributed with mean = 12% and variance of 102/100 = 1%.