CAIA Quantitative Methods and Statistics 2

Question 1

What is the primary purpose of a Monte Carlo simulation in alternative investment portfolio analysis?

Accepted Answer

To model the distribution of possible future outcomes through repeated random sampling

Answer

To calculate historical returns from actual market data

Answer

To optimize the Sharpe ratio using quadratic programming

Answer

To calculate the covariance matrix from a factor model

Question 2

Conditional Value at Risk (CVaR), also known as Expected Shortfall, is best described as:

Accepted Answer

The average loss in scenarios where losses exceed the VaR threshold

Answer

The maximum possible loss in a portfolio under any scenario

Answer

The standard deviation of losses in the tail beyond VaR

Answer

The probability-weighted loss at exactly the VaR confidence level

Question 3

In a linear regression of portfolio returns on a benchmark, the R-squared (R²) statistic measures:

Accepted Answer

The proportion of portfolio return variance explained by the benchmark

Answer

The statistical significance of the alpha (intercept) coefficient

Answer

The correlation between the two independent variables in the model

Answer

The slope coefficient (beta) of the regression line

Question 4

Which statistical test is commonly used to assess whether investment return data follows a normal distribution?

Accepted Answer

Jarque-Bera test

Answer

Augmented Dickey-Fuller test

Answer

Durbin-Watson test

Answer

White's heteroskedasticity test

Question 5

Tracking error is most precisely defined as:

Accepted Answer

The standard deviation of the difference between portfolio returns and benchmark returns

Answer

The cumulative difference between portfolio return and benchmark return over a period

Answer

The correlation coefficient between portfolio returns and benchmark returns

Answer

The portfolio beta minus one, scaled by benchmark volatility

Question 6

The Sortino ratio improves upon the Sharpe ratio for alternative investments by:

Accepted Answer

Using downside deviation (volatility of negative returns only) in the denominator

Answer

Substituting the geometric mean return for the arithmetic mean

Answer

Excluding the risk-free rate to focus on absolute return strategies

Answer

Incorporating skewness directly into the numerator

Question 7

In a multi-factor regression model, Jensen's alpha represents:

Accepted Answer

Portfolio return in excess of what the factor model predicts given the portfolio's risk exposures

Answer

The weighted average of the factor loadings across all systematic risk factors

Answer

The geometric difference between the portfolio return and the market return

Answer

The beta-adjusted outperformance relative to the risk-free rate