Tail Risk Analysis AI Prompt

Conduct a comprehensive tail risk analysis for this return series.

Portfolio or asset: {{portfolio}}
Return series: {{returns}}

1. Empirical tail analysis:
   - Left tail: distribution of returns below the 5th and 1st percentile
   - Right tail: distribution of returns above the 95th and 99th percentile
   - Tail asymmetry: is the left tail heavier than the right? (Typical for equity strategies)
   - Comparison to normal: at the 1% quantile, how does the empirical loss compare to the normal distribution prediction?

2. Extreme Value Theory (EVT) for tail estimation:
   Peaks Over Threshold (POT) method:
   - Choose threshold u at the 95th percentile of losses
   - Fit Generalized Pareto Distribution (GPD) to exceedances: F(x) = 1 - (1 + ξx/σ)^(-1/ξ)
   - Report: shape parameter ξ (> 0 = heavy tail, = 0 = exponential, < 0 = bounded tail), scale σ
   - ξ > 0.5 indicates very heavy tails — normal-based risk measures severely underestimate risk
   - Use GPD to estimate VaR and CVaR at extreme quantiles (99.9%) beyond the data

3. Maximum Drawdown analysis:
   - Maximum drawdown (MDD): largest peak-to-trough decline
   - Average drawdown
   - Drawdown duration distribution: how long do drawdowns last?
   - Recovery time distribution: how long does it take to recover to prior peak?
   - Calmar ratio: annualized return / |MDD|
   - Pain index: integral of drawdown curve over time

4. Tail correlation (co-tail risk):
   - For a multi-asset portfolio: does the portfolio tail loss exceed what uncorrelated risks would imply?
   - Tail dependence coefficient: probability that both assets suffer extreme losses simultaneously
   - Clayton copula for lower tail dependence: captures asymmetric dependence in down markets

5. Stress test scenarios:
   Apply historical stress scenarios:
   - 2008 financial crisis (Sept–Nov 2008)
   - COVID crash (Feb–Mar 2020)
   - 2020 interest rate spike (Q1 2022)
   - Dot-com crash (2000–2002)
   For each: what was the portfolio loss? How does it compare to VaR predictions?

6. Reporting:
   - At what loss level does your risk model break down? (Where does the normal approximation stop being conservative?)
   - What tail risk is not captured by standard VaR?

Return: empirical tail analysis, GPD parameter estimates, drawdown metrics, tail correlation analysis, stress test results, and risk model limitation statement.