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

A risk analyst examines a long daily return series for an equity index and finds that the sample kurtosis is 7.5, while the sample skewness is close to zero. Which conclusion is most appropriate?

Kurtosis of 7.5 exceeds the normal value of 3, so the distribution is leptokurtic with fatter tails. Extreme returns are more likely than a normal model suggests. Near-zero skewness only shows symmetry and does not prove normality.

  1. AReturns have fatter tails than a normal distribution, so extreme moves are more likely than normality impliesCorrect
  2. BReturns have thinner tails than a normal distribution, so normal-based VaR overstates risk
  3. CReturns are normally distributed because skewness is near zero
  4. DReturns are positively skewed because kurtosis exceeds 3

Explanation

A normal distribution has kurtosis of 3. A sample kurtosis of 7.5 means excess kurtosis of 4.5, indicating heavy tails (leptokurtosis). Zero skewness alone does not establish normality, since symmetric distributions can still have fat tails.

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