CAIA Quantitative Methods and Statistics 2 — Questions and Answers
Question 1: What is the primary purpose of a Monte Carlo simulation in alternative investment portfolio analysis?
- To calculate historical returns from actual market data
- To model the distribution of possible future outcomes through repeated random sampling (Correct answer)
- To optimize the Sharpe ratio using quadratic programming
- To calculate the covariance matrix from a factor model
Correct answer: To model the distribution of possible future outcomes through repeated random sampling
Monte Carlo simulation generates thousands of random scenarios based on specified return and risk parameters, producing a distribution of possible outcomes useful for stress-testing and portfolio planning.
Question 2: Conditional Value at Risk (CVaR), also known as Expected Shortfall, is best described as:
- The maximum possible loss in a portfolio under any scenario
- The average loss in scenarios where losses exceed the VaR threshold (Correct answer)
- The standard deviation of losses in the tail beyond VaR
- The probability-weighted loss at exactly the VaR confidence level
Correct answer: The average loss in scenarios where losses exceed the VaR threshold
CVaR (Expected Shortfall) answers the question 'given that we are in the tail beyond VaR, what is our expected loss?' — making it a more complete tail-risk measure than VaR alone.
Question 3: In a linear regression of portfolio returns on a benchmark, the R-squared (R²) statistic measures:
- The statistical significance of the alpha (intercept) coefficient
- The proportion of portfolio return variance explained by the benchmark (Correct answer)
- The correlation between the two independent variables in the model
- The slope coefficient (beta) of the regression line
Correct answer: The proportion of portfolio return variance explained by the benchmark
R² indicates how much of the variation in the dependent variable (portfolio returns) is captured by the independent variable (benchmark returns); a high R² means benchmark moves largely explain portfolio moves.
Question 4: Which statistical test is commonly used to assess whether investment return data follows a normal distribution?
- Augmented Dickey-Fuller test
- Durbin-Watson test
- Jarque-Bera test (Correct answer)
- White's heteroskedasticity test
Correct answer: Jarque-Bera test
The Jarque-Bera test uses the skewness and excess kurtosis of a dataset to test the null hypothesis of normality, making it well-suited for evaluating return distributions.
Question 5: Tracking error is most precisely defined as:
- The cumulative difference between portfolio return and benchmark return over a period
- The standard deviation of the difference between portfolio returns and benchmark returns (Correct answer)
- The correlation coefficient between portfolio returns and benchmark returns
- The portfolio beta minus one, scaled by benchmark volatility
Correct answer: The standard deviation of the difference between portfolio returns and benchmark returns
Tracking error is the annualized standard deviation of active returns (portfolio return minus benchmark return), measuring how consistently a manager deviates from the benchmark.
Question 6: The Sortino ratio improves upon the Sharpe ratio for alternative investments by:
- Substituting the geometric mean return for the arithmetic mean
- Using downside deviation (volatility of negative returns only) in the denominator (Correct answer)
- Excluding the risk-free rate to focus on absolute return strategies
- Incorporating skewness directly into the numerator
Correct answer: Using downside deviation (volatility of negative returns only) in the denominator
The Sortino ratio replaces total standard deviation with downside deviation (semi-deviation), penalizing only downside volatility and therefore better capturing the asymmetric return profiles common in alternatives.
Question 7: In a multi-factor regression model, Jensen's alpha represents:
- The weighted average of the factor loadings across all systematic risk factors
- Portfolio return in excess of what the factor model predicts given the portfolio's risk exposures (Correct answer)
- The geometric difference between the portfolio return and the market return
- The beta-adjusted outperformance relative to the risk-free rate
Correct answer: Portfolio return in excess of what the factor model predicts given the portfolio's risk exposures
Alpha is the intercept term in a factor regression, capturing average return attributable to manager skill or unmodeled sources after stripping out all systematic factor exposures.
CAIA Quantitative Methods and Statistics 2
What is the primary purpose of a Monte Carlo simulation in alternative investment portfolio analysis?