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Answer: The correlation-weighted approach uses matrix multiplication to adjust historical portfolio returns so that these returns reflect current volatilities and current correlations.
C is correct. The correlation-weighted approach is similar to the volatility-weighted approach in that both approaches adjust past returns that occurred under a different correlation or volatility regime to reflect the current correlation or volatility. In the correlation-weighted approach this is accomplished through matrix multiplication since correlations are represented with a matrix. A is incorrect. This is a description of an equal-weighted approach, not an age-weighted approach. B is incorrect. The volatility-weighted approach does adjust historical returns but does so in a manner that decreases the historical return if the historical volatility forecast was higher than the current volatility forecast, and increases the historical return if the historical volatility forecast was lower than the current volatility forecast. The volatility adjusted returns are given by the following formula: r*_{t,i} = (σ_{T,i} / σ_{t,i}) * r_{t,i} Where σ_{T,i} is the current volatility forecast, σ_{t,i} is the historical volatility forecast, r_{t,i} is the historical return, and r*_{t,i} is the adjusted historical return. D is incorrect. The filtered HS approach is not a simple filter but is a form of semi-parametric bootstrap model that adjusts returns within a conditional volatility framework.
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An analyst at a commercial bank is evaluating how the bank applies historical simulation (HS) to estimate VaR and ES. The analyst focuses on the approaches used for weighting past return observations, including the age-weighted, volatility-weighted, correlation-weighted, and filtered HS approaches. Which of the following statements is correct regarding the given weighting approach?
A
The age-weighted approach typically specifies that observations that occurred after the cutoff date are given an equal weight while observations that occurred before the cutoff date are given a weight of zero.
B
The volatility-weighted approach adjusts historical returns in the sample by increasing them if the historical volatility forecast was higher than the current volatility forecast, and decreasing them if the historical volatility forecast was lower than the current volatility forecast.
C
The correlation-weighted approach uses matrix multiplication to adjust historical portfolio returns so that these returns reflect current volatilities and current correlations.
D
The filtered HS approach allows the historical returns data to be trimmed or customized based on day of the week, magnitude of return, or any other characteristic of the data.