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FRM Part I · FRM Exam Part I · Sample Moments

A hedge fund's monthly returns show skewness of -1.2 and excess kurtosis of 4. Compared with a normal distribution with the same mean and variance, which description is most consistent with these statistics?

Positive excess kurtosis implies fatter tails and more frequent extreme outcomes. Negative skewness implies a longer left tail, so large losses are more probable than large gains and the mean is usually pulled below the median. This combination is typical of tail-risk exposure.

  1. AExtreme outcomes are more likely, with large losses more probable than large gains, and the mean typically lies below the medianCorrect
  2. BExtreme outcomes are less likely, with large gains more probable than large losses, and the mean typically lies above the median
  3. CExtreme outcomes are more likely, with large gains more probable than large losses, and the mean typically lies above the median
  4. DThe distribution is symmetric with fat tails, so the mean and median coincide

Explanation

Positive excess kurtosis means fatter tails, so extreme outcomes are more frequent. Negative skewness means a longer left tail, so large losses are more likely than large gains, and the mean is typically pulled below the median. The other options reverse the skew or the kurtosis effect, or ignore the nonzero skewness.

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