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%.