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Answer: 2.1%
## Explanation In volatility-weighted historical simulation, the volatility-adjusted return is calculated using the formula: \[ \text{Adjusted Return} = \text{Actual Return} \times \frac{\text{Current Volatility}}{\text{Past Volatility}} \] Given: - Actual return 30 days ago = 1.5% - Daily volatility estimate 30 days ago = 1.0% - Current daily volatility = 1.4% Calculation: \[ \text{Adjusted Return} = 1.5\% \times \frac{1.4\%}{1.0\%} = 1.5\% \times 1.4 = 2.1\% \] Therefore, the volatility-adjusted return is **2.1%**, which corresponds to option D. This adjustment is used in historical simulation to account for changes in market volatility over time, making the historical returns more relevant to current market conditions.
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Suppose you are using the volatility-weighted historical simulation approach to estimate value at risk (VaR) and expected shortfall (ES) for asset Y. The actual return for the asset 30 days ago was 1.5% with a daily volatility estimate of 1.0%. What is the volatility-adjusted return if the current daily volatility is 1.4%?
A
0.9%
B
1.6%
C
1.8%
D
2.1%
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