Explanation:
A mixture of normal distributions with different standard deviations (e.g., from different time periods or volatility regimes) results in an overall distribution that exhibits excess kurtosis (fat tails). To accurately capture this underlying characteristic and properly estimate Value at Risk (VaR) and Expected Shortfall (ES), applying a fat-tailed distribution across all historical data is the most appropriate approach. Using a single normal distribution with an averaged standard deviation would significantly underestimate tail risks.
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Q.9 A financial analyst is investigating the historical return distributions of a portfolio. The analyst observes that while the individual market subsets appear to be normally distributed, the overall return distribution exhibits unexpected characteristics when data is pulled from different time points. The historical data shows a standard deviation that averaged 2% over time, but current volatility estimates are at 3%. When constructing a risk model to estimate Value at Risk (VaR) and expected shortfall, which approach would most accurately capture the distribution's underlying characteristics?
A
Use a 2% standard deviation based on historical mean volatility.
B
Apply a fat-tailed distribution across all historical data.
C
Assume a normal distribution with a 3% standard deviation.
D
Average the volatilities from different market environments.
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