- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Statistical Measures of Asset Returns
- Subject 3. Measures of Shape of a Distribution
CFA Practice Question
Excess kurtosis is a problem for investment researchers using normal distributions because ______
B. it is difficult to calculate.
C. the likelihood of extreme outcomes will be underestimated.
A. historical returns are better modeled with leptokurtic distributions.
B. it is difficult to calculate.
C. the likelihood of extreme outcomes will be underestimated.
Correct Answer: C
Historical returns are better modeled with fat-tailed (or platykurtic) distributions, not leptokurtic ones. If a researcher uses a normal distribution to model a fat-tailed distribution, the estimated probability of an extreme outcome will be underestimated. Thus, the frequency of market crashes will be underestimated (an underestimation of volatility risk).
User Contributed Comments 7
| User | Comment |
|---|---|
| surob | I thought Leptokurtis is fat-tailored. It has larger tails. I am confused. Can anyone please explain? |
| jallado0 | try this link surob http://mathworld/wolfarm.com/leptokurtic.html , i hope it makes it clear for u |
| bobert | If there is excess kurtosis it means bigger tails (leptokurtosis) because the top is pulled higher than would be on a normal distribution. Therefore if there are going to be extreme outcomes, they will be underestimated using the normal because it has shorter tails than a distribution with leptokurtosis. You are using a normal to estimate what is really leptokurtic. There will be more returns centered around the mean but there will also be more extreme values at the tails. Hope that helps. |
| Sumit14 | Normal Curve is Normal Leptokurtosis - pull the normal curve up from the mean so that the whole curve moves up along with the tails. this will make the Leptokurtosis curve thinner at the center. Platokurtosis - push the normal curve down from the mean so that the whole curve moves down along with the tails. this will make the Platokurtosis curve thicker at the center. |
| rfvo | To further elaborate.....Positive values of kurtosis do not indicate a distribution that has fat tails. Positive values of excess kurtosis (kurtosis > 3) indicate fat tails. |
| tschorsch | try this image fractalpress.com/blog/wp-content/uploads/2008/03/standard_symmetric_pdfs.png |
| Teeto | I think that "excess kurtosis" in the question does not mean _positive_ excess kurtosis It is just a value which should me taken into account (that's why it is a problem). And historical returns are better modeled with distributions with negative values of excess curtosis (platycrutic) |