2012 FRM Calendar

Lognormal distribution L1.T2.119

07 Jan 2011   by David Harper, CFA, FRM, CIPM

Risk (FRM) > Quantitative Analysis

Exam Relevance: Optional

AIM: L1.T2.119. Describe the key properties of the lognormal distribution

Questions:

119.1 If the variable (Y) is a normal random variable, such than Y ~ N(mu, sigma^2), which of the following (X) variables is lognormally (log-normally) distributed?

  • a. X = EXP(Y) = e^Y
  • b. X = LN(Y)
  • c. X = Y(1) + Y(2) + ... Y(n)
  • d. X = LN[Y(2)/Y(1)]

119.2 Assume today’s stock price S(0) is $100, the daily log (continuously compounded) return has mean of 0.0 and standard deviation of 0.10 (10%), and tomorrow’s stock price is lognormally distributed. What is the approximate probability that tomorrow’s stock price will exceed $117.94?

  • a. about 1%
  • b. 1.43%
  • c. 4.46%
  • d. about 5%

119.3 Each of the following is TRUE about the lognormal distribution EXCEPT

  • a. Is always non-negative with positive skew and leptokurtic (heavy tailed)
  • b. If price S(t) is lognormal, then LN[S(t)] is normal
  • c. The sum of lognormal variables is also lognormal
  • d. The product of lognormal random variables is also lognormal

Answers: