FRM一级模拟题
1 . Which type of distribution produces the lowest probability for a variable to exceed a specified extreme value X which is greater than the mean assuming the distributions all have the same mean and variance?
A. A leptokurtic distribution with a kurtosis of 4
B. A leptokurtic distribution with a kurtosis of 8
C. A normal distribution
D. A pjatykurtic distribution
Answer: D
A. Jncorrect. A leptokurtic distribution has fatter tails than the normal distribution. The kurtosis indicates the level of fatness in the tails, th,g higher the kurtosis, the fatter the tails. Therefore, the probability of exceeding a specified extreme value will be higher
B. Incorrect. Since answer A. has a lower kurtosis, a distribution with a kurtosis of 8 will necessarily produce a larger probability in the tails.
C. Incorrect. By definition, a normal distribution has thinner tails than a leptokurtic distribution and larger tails than a platykurtic distribution.
D. Correct. By definition, a platykurtic distribution has thinner tails than both the normal distribution and any leptokurtic distribution. Therefore, for an extreme value X, the lowest probability of exceeding it will be found in the distribution with the thinner tails.
2 .It is ofien said that distributions of returns from financial instruments are leptokurtotic. For such distributions, which of the following comparisons with a normal distribution of the same mean and variance MUST hold?
A. The skewness of the leptokurtotic distribution is greater
B. The kurtosis of the leptokurtotic distribution is greater
C. The skewness of the leptokurtotic distribution is smaller
D. The kurtosis of the leptokurtotic distribution is smaller
Answer: B
A Ieptokurtic distribution is characterized as having fat tails. Kurtosis is a measurement of the flatness of a distribution, or how fat its tails are. A distribution with a higherkurtosis has fatter tails.
3 .What is kurtosis? What is its role in statistical distributions?
A. Kurtosis measures the nature of the spread of the values around the mean. It represents the 4th moment ofa distribution. A large kurtosis indicates a sharp peak in the middle of a distribution. A population with high kurtosis is usually called leptokurtic. The kurtosis plays an important role in distinguishing those distributions that place additional probability on larger values.
B. Kurtosis represents the 3rd moment of a distribution. A small kurtosis indicates flatness in the middle of the distribution. A population with low kurtosis is usually called leptokurtic. Skewness (and not kurtosis) plays an important role in distinguishing those distributions that place additional probability on larger values.
mean of a distribution
D. Kurtosis can be seen in the second and fourth moments of a distribution and measures the standard deviation of a distribution.
Answer: A
Kurtosis measures the nature of the spread of values around th e mean (4th moment).The kurtosis measure for a normal distribution is 3. Excess kurtosis is sometimes used in lieu of the kurtosis itself and is the kurtosis number minus 3.
4 . An analyst collects the data for interest rate expectations. The mean expected rate is 2.5%, the lowest expectation is l% and the highest expectation is 5%. T his distribution is:
A. sparse
B. normal
C. skewed
D. abnormal
Answer: C
In this distribution, the lowest element is l.5% below the mean whereas the highest element is
2.5% above the mean. Thus the distribution is skewed towards the right.
5 . Left-skewed distributions exhibit:
A. greater mass to the left of the expected value
B. greater mass to the right of the expected value
C. a longer tail to the right of the distribution
D. greater mass close to the expected value
Answer: B
Lefi-skewed distributions are those with a longer tail to the Ieft side of the distribution, and whose mass is to the right of the expected value.