FRM Quantitative Analysis

Question 1

In a normal distribution, approximately what percentage of observations fall within two standard deviations of the mean?

Accepted Answer

95%

Answer

68%

Answer

90%

Answer

99%

Question 2

Which statistical measure describes the asymmetry of a probability distribution?

Accepted Answer

Skewness

Answer

Kurtosis

Answer

Variance

Answer

Standard deviation

Question 3

A leptokurtic distribution compared to a normal distribution has:

Accepted Answer

Excess kurtosis greater than 0

Answer

Excess kurtosis less than 0

Answer

Excess kurtosis equal to 0

Answer

Negative skewness

Question 4

The covariance between two assets is 0.006, and their standard deviations are 0.10 and 0.15. What is their correlation coefficient?

Accepted Answer

0.40

Answer

0.20

Answer

0.30

Answer

0.60

Question 5

Which statement best describes the Central Limit Theorem (CLT)?

Accepted Answer

The distribution of sample means approaches normality as sample size increases regardless of the underlying distribution

Answer

All financial returns are normally distributed

Answer

The mean of a population always equals the mean of its samples

Answer

Large samples always have lower variance than small samples

Question 6

In hypothesis testing, a Type I error occurs when:

Accepted Answer

We reject a true null hypothesis

Answer

We fail to reject a false null hypothesis

Answer

We accept a false alternative hypothesis

Answer

The p-value exceeds the significance level

Question 7

For a two-asset equal-weighted portfolio where each asset has variance 0.04 and the assets have a correlation of 0.50, the portfolio variance is:

Accepted Answer

0.03

Answer

0.02

Answer

0.04

Answer

0.06