Answer-first summary for fast verification
Answer: The correlation-weighted approach uses matrix multiplication to adjust historical portfolio returns so that these returns reflect current volatilities and current correlations.
The correct answer is C. The correlation-weighted approach is a method used in historical simulation (HS) to estimate Value at Risk (VaR) and Expected Shortfall (ES). This approach takes into account the current correlation or volatility regime and adjusts past returns accordingly. Unlike the equal-weighted approach described in option A, which incorrectly assigns zero weight to observations before a cutoff date, the correlation-weighted approach uses matrix multiplication to align historical portfolio returns with the current market conditions. This method is similar to the volatility-weighted approach mentioned in option B, but it focuses on correlations rather than volatilities. The volatility-weighted approach incorrectly adjusts historical returns in the opposite direction as described in option B, where it should decrease the historical return if the historical volatility forecast was higher than the current forecast, and increase it if the historical forecast was lower. Option D is incorrect as it mischaracterizes the filtered HS approach, which is not a simple filter but a more complex semi-parametric bootstrap model that adjusts returns within a conditional volatility framework, rather than simply trimming or customizing the data based on various characteristics.
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A financial analyst working at a commercial bank is evaluating the bank's approach to employing historical simulation (HS) for determining Value at Risk (VaR) and Expected Shortfall (ES). The analyst is specifically focused on the different strategies used for assigning weights to past return observations. These strategies include age-weighted methods, where more recent returns are given higher significance; volatility-weighted methods, where returns are weighted based on their volatility; correlation-weighted methods, where weights depend on the correlation of returns; and filtered HS methods, which involve adjusting weights based on various factors. Considering these weighting techniques, which of the following statements is correct?
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.