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FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation

A risk analyst examines 2,000 daily returns on an equity index and finds a sample kurtosis of 6.2 and a skewness close to zero. Compared with a normal distribution, which description of the return distribution is most accurate?

A kurtosis of 6.2 exceeds the normal value of 3, so the distribution is leptokurtic with fat tails. With skewness near zero the tails are symmetric, meaning extreme gains and losses both occur more often than a normal model predicts. Zero skewness alone does not establish normality.

  1. AThinner tails and a flatter peak than the normal, so extreme returns are less likely than a normal model implies
  2. BFatter tails than the normal, so extreme returns of either sign occur more often than a normal model impliesCorrect
  3. CA longer left tail only, so large losses are more likely but large gains are not
  4. DThe same tail behavior as the normal, because skewness near zero implies normality

Explanation

A normal distribution has kurtosis of 3. A sample kurtosis of 6.2 indicates excess kurtosis of 3.2, meaning fat tails (leptokurtosis). With skewness near zero the tails are roughly symmetric, so extreme moves of both signs are more frequent. Zero skewness alone does not imply normality, so the last option is wrong.

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