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

Which statement about the lognormal distribution is correct?

A lognormal variable has a normally distributed logarithm and cannot fall below zero. It is positively skewed, and while products of independent lognormals are lognormal, sums are not, which is why it suits asset prices.

  1. AIt can take negative values when volatility is high
  2. BIt is symmetric about its mean
  3. CIts logarithm is normally distributed and it is bounded below by zeroCorrect
  4. DThe sum of independent lognormal variables is exactly lognormal

Explanation

A variable is lognormal if its natural log is normal, so the variable equals an exponential and is always positive. It is right-skewed, not symmetric, and sums of lognormals are not exactly lognormal (products are).

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