Drawdown Analysis AI Prompt

Conduct a comprehensive drawdown analysis for this strategy or portfolio.

Return series: {{returns}}
Benchmark (optional): {{benchmark}}

1. Drawdown calculation:
   - Cumulative wealth index: W_t = ∏(1 + r_i) for i = 1 to t
   - Running maximum: M_t = max(W_1, W_2, ..., W_t)
   - Drawdown at time t: DD_t = (W_t - M_t) / M_t
   - Maximum drawdown (MDD): min(DD_t) over full period

2. Drawdown statistics:
   - Maximum drawdown: magnitude and the peak and trough dates
   - Average drawdown: mean of all drawdown episodes
   - Average drawdown duration: average time from peak to trough
   - Average recovery time: average time from trough to new high water mark
   - Number of drawdown episodes exceeding threshold (e.g. >5%, >10%, >20%)
   - Current drawdown: is the strategy currently in a drawdown?

3. Drawdown distribution:
   - Plot all drawdown episodes sorted by severity
   - Are large drawdowns rare events or do they cluster?
   - Drawdown at each percentile (50th, 75th, 90th, 95th) of episode severity

4. Underwater curve analysis:
   - Plot the cumulative return and the underwater curve (time spent in drawdown) on the same chart
   - What fraction of total time was the strategy in a drawdown?
   - Pain index: average drawdown × fraction of time in drawdown

5. Risk-adjusted return ratios involving drawdown:
   - Calmar ratio: annualized return / |MDD|. Higher is better. Benchmark: > 0.5
   - Sterling ratio: annualized return / average of top 3 annual drawdowns
   - Burke ratio: annualized return / sqrt(sum of squared drawdowns)
   - Martin ratio (Ulcer index-based): annualized return / Ulcer_index
     Ulcer index = sqrt(mean(DD²)): penalizes both depth and duration of drawdowns

6. Drawdown comparison to benchmark:
   - Relative drawdown: active drawdown = portfolio DD - benchmark DD
   - Did the strategy protect capital better or worse than the benchmark during major drawdown periods?
   - Maximum relative drawdown and its timing

Return: drawdown statistics table, underwater curve plot, drawdown episode list, ratio comparison, and benchmark relative analysis.