CFM Quantitative Methods & Statistics for Fund Management 2 — Questions and Answers
Question 1: How does the Sortino ratio differ from the Sharpe ratio in risk measurement?
- It uses total standard deviation instead of downside deviation
- It uses downside deviation instead of total standard deviation (Correct answer)
- It measures correlation instead of volatility
- It excludes the risk-free rate from the calculation
Correct answer: It uses downside deviation instead of total standard deviation
The Sortino ratio replaces total standard deviation with downside deviation (only negative return deviations), making it more appropriate for return distributions that are asymmetric.
Question 2: What does Value at Risk (VaR) at a 95% confidence level represent?
- The maximum possible loss in any scenario
- The loss not expected to be exceeded with 95% probability over a given time horizon (Correct answer)
- The average loss over the worst 5% of outcomes
- The standard deviation of returns multiplied by 1.96
Correct answer: The loss not expected to be exceeded with 95% probability over a given time horizon
VaR at 95% confidence means there is only a 5% probability that the actual loss will exceed the VaR estimate over the specified time period.
Question 3: In the Capital Asset Pricing Model (CAPM), what does beta represent?
- The expected return of the market portfolio
- The risk-free rate of return
- A measure of a security's sensitivity to market movements (Correct answer)
- The alpha generated by active management
Correct answer: A measure of a security's sensitivity to market movements
Beta measures systematic risk relative to the market; a beta of 1.0 means the security moves in line with the market, while beta greater than 1 indicates higher sensitivity to market movements.
Question 4: In portfolio optimization, what does the efficient frontier represent?
- The set of portfolios with the highest possible return regardless of risk
- The set of portfolios offering the maximum expected return for a given level of risk (Correct answer)
- The single minimum-risk portfolio only
- The portfolio with the highest Sharpe ratio
Correct answer: The set of portfolios offering the maximum expected return for a given level of risk
The efficient frontier, derived from Modern Portfolio Theory, is the set of optimal portfolios that offer the highest expected return for each defined level of risk.
Question 5: What does positive skewness in a fund's return distribution indicate?
- The distribution has a longer left tail than right tail
- The distribution is perfectly symmetric around the mean
- The distribution has a longer right tail, indicating occasional large positive returns (Correct answer)
- The mean is less than the median
Correct answer: The distribution has a longer right tail, indicating occasional large positive returns
Positive skewness means the right tail is longer, indicating occasional extreme positive returns, with the mean typically exceeding the median.
Question 6: What does high kurtosis (leptokurtosis) indicate about a fund's return distribution?
- The distribution has a flat shape with thin tails
- The distribution has fat tails with more probability of extreme outcomes than a normal distribution (Correct answer)
- The distribution is perfectly normal
- The distribution has negative skewness
Correct answer: The distribution has fat tails with more probability of extreme outcomes than a normal distribution
High kurtosis (leptokurtic) indicates fat tails, meaning the distribution has more extreme outcomes (both gains and losses) than a normal distribution — a key risk consideration for fund managers.
Question 7: In time series analysis, what is autocorrelation?
- The correlation between two different asset return series
- The correlation of a return series with its own lagged values (Correct answer)
- The correlation between a fund's returns and its benchmark
- The average pairwise correlation among all assets in a portfolio
Correct answer: The correlation of a return series with its own lagged values
Autocorrelation (serial correlation) measures the degree to which a time series is correlated with its own past values, revealing patterns such as return momentum or mean-reversion.
CFM Quantitative Methods & Statistics for Fund Management 2
How does the Sortino ratio differ from the Sharpe ratio in risk measurement?