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CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns

In a multi-period binomial tree model of a stock price, an analyst increases the number of steps while holding the time horizon fixed and scaling up and down factors to the shorter step length. The resulting distribution of the terminal stock price is most likely to approach:

The terminal price distribution tends toward a lognormal distribution. With many steps the continuously compounded return becomes approximately normal, and the price is the exponential of that return, so it is positive and right-skewed rather than normal or uniform.

  1. Aa lognormal distributionCorrect
  2. Ba normal distribution
  3. Ca uniform distribution

Explanation

As steps increase, the binomial log-return distribution approaches normal, so the price, which is the exponential of the log return, approaches lognormal. Prices are bounded below by zero, which rules out a normal distribution for the price level.

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