Explanation

Fat tails (leptokurtosis) in return distributions mean:

• More extreme observations than predicted by a normal distribution
• Higher probability of large losses than the normal distribution suggests

Delta-Normal Method Assumptions:

• Assumes normal distribution of returns
• Uses mean and variance to estimate risk

Impact of Fat Tails:

• The delta-normal method underestimates the probability of extreme losses
• Since VaR measures potential extreme losses, the delta-normal VaR will be too low
• The true VaR (considering fat tails) would be higher

Key Points:

• Fat tails = more extreme events than normal distribution predicts
• Delta-normal method doesn't capture these extreme events properly
• Therefore, it underestimates the true risk
• More sophisticated methods (historical simulation, Monte Carlo) are needed for fat-tailed distributions

Correct Answer: A - The delta-normal VaR underestimates the true VaR in the presence of fat tails.