Free CFA Level I Quantitative Methods Practice Questions
Quantitative methods on the CFA Level I exam cover time value of money, statistical concepts, probability distributions, sampling, hypothesis testing, and regression basics. This topic is weighted 6-9% of the exam (CFA Institute).
Sample Questions
Question 1
Easy
The excess kurtosis of a normal distribution is:
Solution
A is correct.
A normal distribution has a kurtosis of 3. Excess kurtosis is defined as kurtosis minus 3, so for a normal distribution, excess kurtosis = 3 - 3 = 0. A distribution with excess kurtosis greater than 0 is leptokurtic (fatter tails), while one with excess kurtosis less than 0 is platykurtic (thinner tails).
A normal distribution has a kurtosis of 3. Excess kurtosis is defined as kurtosis minus 3, so for a normal distribution, excess kurtosis = 3 - 3 = 0. A distribution with excess kurtosis greater than 0 is leptokurtic (fatter tails), while one with excess kurtosis less than 0 is platykurtic (thinner tails).
Question 2
Medium
In the bias-variance tradeoff, increasing model complexity most likely:
Solution
B is correct.
As model complexity increases, the model fits training data more closely, reducing bias (the error from overly simplistic assumptions). However, the model becomes more sensitive to the specific training data used, increasing variance (the error from sensitivity to small fluctuations in the training set). This is the fundamental bias-variance tradeoff.
As model complexity increases, the model fits training data more closely, reducing bias (the error from overly simplistic assumptions). However, the model becomes more sensitive to the specific training data used, increasing variance (the error from sensitivity to small fluctuations in the training set). This is the fundamental bias-variance tradeoff.
Question 3
Hard
A simple linear regression uses 25 observations with SST = 450 and SSR = 360. What is the F-statistic for this regression?
Solution
B is correct.
For simple linear regression: SSE = SST - SSR = 450 - 360 = 90. df_regression = 1 (one independent variable); df_residual = n - 2 = 25 - 2 = 23. MSR = SSR / df_regression = 360 / 1 = 360. MSE = SSE / df_residual = 90 / 23 = 3.913. F = MSR / MSE = 360 / 3.913 = 92.0.
For simple linear regression: SSE = SST - SSR = 450 - 360 = 90. df_regression = 1 (one independent variable); df_residual = n - 2 = 25 - 2 = 23. MSR = SSR / df_regression = 360 / 1 = 360. MSE = SSE / df_residual = 90 / 23 = 3.913. F = MSR / MSE = 360 / 3.913 = 92.0.