
Explanation:
Risk models like VaR and Expected Shortfall are forward-looking and must reflect current market conditions rather than historical averages. Although the analyst observed normally distributed returns within individual market periods, the key insight is that volatility has recently increased from an average of 2% to 3%. Using the current 3% standard deviation ensures that the model captures the heightened risk environment accurately, without underestimating potential losses. Since the normal distribution assumption still holds within these subsets, combining it with the up-to-date volatility makes this the most appropriate and realistic approach.
A is incorrect. Using the average volatility masks current market risk. VaR would be understated, as current volatility (3%) is higher than the historical mean.
B is incorrect. While fat tails can help model extreme risks, the analyst noted normal distributions within subsets. The fat tails arise from volatility variation over time, not inherently fat-tailed data. So this approach misses the true cause of the non-normality.
D is incorrect. This would result in the same problem as (A): understating current volatility. Volatility is not additive or linear, and averaging across regimes distorts current risk measures.
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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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