FRM Part I · FRM Exam Part I · Sample Moments
A risk analyst estimates the sample kurtosis of a portfolio's daily returns to be 5.2. Which interpretation is correct?
A kurtosis of 5.2 exceeds the normal benchmark of 3, giving excess kurtosis of 2.2. The distribution is leptokurtic, meaning it has fatter tails and more extreme outcomes than a normal distribution. Kurtosis does not indicate the direction of skewness.
- AThe distribution has fatter tails than a normal distribution, with excess kurtosis of 2.2Correct
- BThe distribution has thinner tails than a normal distribution, with excess kurtosis of 2.2
- CThe distribution is negatively skewed, with excess kurtosis of 5.2
- DThe distribution is approximately normal, because kurtosis is greater than zero
Explanation
A normal distribution has kurtosis of 3. Excess kurtosis is 5.2 - 3 = 2.2, which is positive, so the distribution is leptokurtic with fatter tails. Kurtosis says nothing about the direction of skew, and 5.2 is not close to 3, so the normal approximation is not supported.
Did you get it right without looking?
One question tells you little. A timed set on Sample Moments shows your real accuracy, how long you take and where you lose marks.
More Sample Moments questions
- Observations X1, X2, X3 are i.i.d. with mean mu and variance 36. Estimator A is the sample mean (X1+X2+X3)/3. Estimator B is (X1 + 2*X2 + 3*…
- An analyst records five monthly returns (in %): 2, 4, 6, 8, 10. She wants an estimate of the variance of the underlying return distribution …
- A sample of 5 returns (in %) is: 2, 4, 4, 4, 6. Its sample skewness, defined as the average cubed deviation divided by the cube of the stand…
- Which statement best describes why the sample variance uses a divisor of n-1 rather than n when the population mean is unknown?
- Observations X1, X2, X3, X4 are i.i.d. with mean mu and variance 20. An analyst uses the estimator (X1 + X2 + X3 + X4)/4 for mu. What is the…
- A risk manager estimates the mean of daily returns using n i.i.d. observations with standard deviation 1.5%. She wants the standard error of…