Explanation

When a distribution has fat tails (leptokurtosis), it means there are more extreme values in the tails than predicted by a normal distribution. The delta-normal method for VaR calculation assumes that returns are normally distributed.

Key points:

• Delta-normal VaR uses mean and standard deviation from a normal distribution
• Fat tails indicate higher probability of extreme losses than normal distribution predicts
• Therefore, the delta-normal method will underestimate the true risk because it doesn't account for the increased probability of extreme events

Mathematical reasoning:

• Normal distribution: 99% VaR = μ - 2.33σ
• Fat-tailed distribution: Actual 99% VaR = μ - kσ, where k > 2.33
• Since delta-normal uses k = 2.33, it produces a smaller (less negative) VaR than the true VaR

Thus, the delta-normal VaR underestimates the true VaR in the presence of fat tails.