CFM Quantitative Methods & Statistics for Fund Management 1 — Questions and Answers
Question 1: What does standard deviation measure in portfolio analysis?
- The average return of a portfolio
- The dispersion of returns around the mean (Correct answer)
- The correlation between two assets
- The maximum drawdown of a portfolio
Correct answer: The dispersion of returns around the mean
Standard deviation measures how much returns deviate from the mean, representing the total risk of an investment.
Question 2: A fund manager calculates a Sharpe ratio of 1.5. What does this indicate?
- The fund lost 1.5% per unit of risk
- The fund earned 1.5 units of excess return per unit of total risk (Correct answer)
- The fund's beta is 1.5
- The fund has 1.5% standard deviation
Correct answer: The fund earned 1.5 units of excess return per unit of total risk
The Sharpe ratio measures excess return above the risk-free rate per unit of standard deviation, so 1.5 means 1.5 units of excess return per unit of total risk.
Question 3: What is the valid range of the correlation coefficient between two assets?
- 0 to 1
- -1 to 0
- -1 to +1 (Correct answer)
- -∞ to +∞
Correct answer: -1 to +1
The correlation coefficient always ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 indicating no linear relationship.
Question 4: Which statistical measure is most useful for comparing risk-adjusted performance across funds with different absolute risk levels?
- Absolute return
- Standard deviation alone
- Coefficient of variation (Correct answer)
- Arithmetic mean return
Correct answer: Coefficient of variation
The coefficient of variation (standard deviation divided by mean) normalizes risk relative to return, allowing comparison across funds with different absolute risk and return levels.
Question 5: In regression analysis, what does R-squared (R²) measure?
- The slope of the regression line
- The proportion of variance in the dependent variable explained by the independent variable(s) (Correct answer)
- The statistical significance of the intercept
- The number of data points in the regression
Correct answer: The proportion of variance in the dependent variable explained by the independent variable(s)
R-squared, the coefficient of determination, represents the proportion of variance in the dependent variable that is predictable from the independent variable(s), ranging from 0 to 1.
Question 6: What is the primary purpose of Monte Carlo simulation in fund management?
- To calculate historical average returns
- To model potential outcomes by running many random simulations based on input distributions (Correct answer)
- To determine the exact future value of an investment
- To calculate the correlation between two assets
Correct answer: To model potential outcomes by running many random simulations based on input distributions
Monte Carlo simulation uses random sampling to model the probability distribution of outcomes, helping fund managers assess risk and uncertainty across complex, multi-variable scenarios.
Question 7: What does a p-value below 0.05 indicate in hypothesis testing for a fund performance study?
- The null hypothesis is definitely true
- There is a 95% chance the alternative hypothesis is wrong
- The result is statistically significant at the 5% significance level (Correct answer)
- The sample size is too small to draw conclusions
Correct answer: The result is statistically significant at the 5% significance level
A p-value below 0.05 means there is less than a 5% probability of observing the results if the null hypothesis were true, indicating statistical significance at the 5% level.
CFM Quantitative Methods & Statistics for Fund Management 1
What does standard deviation measure in portfolio analysis?