Measuring and Managing Market Risk

Correct Answer: The portfolio's beta coefficient relative to a market index

The portfolio's beta coefficient relative to a market index is the correct answer.

Value at Risk (VaR) is a statistical measure that quantifies the potential loss that a portfolio may incur over a specified period, given a certain confidence level. The key inputs for calculating VaR are:

1. The volatility of the portfolio's returns over a historical period
2. The desired confidence level (e.g., 95% or 99%)
3. The holding period for which VaR is being calculated

The portfolio's beta coefficient, which measures the sensitivity of the portfolio's returns to a market index, is not a direct input for calculating VaR. Beta is used in other risk management contexts, such as assessing the systematic risk of a portfolio or estimating the expected return using the Capital Asset Pricing Model (CAPM).

The other two answers, volatility of the portfolio's returns and the desired confidence level, are essential inputs for calculating VaR and are therefore incorrect choices for factors not incorporated into the VaR calculation.

Correct Answer: Calculate the 10-day Value at Risk (VaR) using the historical simulation method, which involves simulating potential portfolio returns based on the historical distribution of returns and determining the loss at the 5th percentile of the simulated distribution.

The most appropriate method for the portfolio manager to estimate the potential loss over a 10-day period with a 95% confidence level is to calculate the 10-day Value at Risk (VaR) using the historical simulation method. This method involves simulating potential portfolio returns based on the historical distribution of returns and determining the loss at the 5th percentile of the simulated distribution. The historical simulation method is preferred in this case because it does not assume a specific distribution of returns, such as the normal distribution assumed by the variance-covariance method. Instead, it relies on the actual historical return data to estimate the potential loss. The Expected Shortfall (ES) using the variance-covariance method is not the most appropriate because it assumes a normal distribution of returns, which may not accurately reflect the portfolio's risk profile. Additionally, the question specifically asks for the potential loss at a 95% confidence level, which corresponds to VaR, not ES. The Incremental Value at Risk (IVaR) using the Monte Carlo simulation method is not the most suitable because it focuses on the incremental contribution of each position to the overall portfolio VaR, rather than estimating the total potential loss at a given confidence level.

Correct Answer: The relationship between risk factors and asset returns is linear

The delta-normal method assumes that the relationship between risk factors and asset returns is linear. This means that the method uses a linear approximation to estimate the change in asset value for a given change in the underlying risk factors. The other answers are incorrect because: - The delta-normal method does not assume that the probability distribution of asset returns is log-normal or that it accounts for non-linear relationships between risk factors. - The delta-normal method does not accurately capture the risk of non-linear financial instruments such as options and futures contracts, as it relies on a linear approximation.