Drawdown Series

Peak-to-trough drawdown series plus the maximum drawdown. Input is a returns array (prices also accepted). A standard performance primitive. Edge-first; wired to more than one Price Factor it fans out to per-ticker by_symbol results.

What (One-liner)

A Layer-1 transform: consume a returns series, emit the running drawdown series and its minimum (max drawdown). max_drawdown = -0.23 means a 23% peak-to-trough loss.

Inputs

• returns (array, required) — return series (prices accepted too).

Outputs

• drawdown — drawdown at each point, in (-1, 0].
• max_drawdown — maximum drawdown over the series, in (-1, 0].
• by_symbol — per-ticker map when fed by multiple Price Factors.

How to use

1. Provide a returns array.
2. Read the drawdown array plus the max_drawdown scalar.

Core formulas

cum_t = Π(1 + r_i) for i in 1..t   (starts at 1.0)
running_max_t = max(cum_1, ..., cum_t)
dd_t = (cum_t - running_max_t) / running_max_t   ∈ (-1, 0]
max_drawdown = min(drawdown)

Assumptions & applicability

Assumptions: simple returns (not log) + compounding + starting 1.0.

Applicable: backtest performance, CPPI, fund fact-sheet; any asset class, any frequency, min 2 observations.

Not applicable: price-series input where returns are expected, log returns, n<2.

Known limitations

1. Path-dependent — only reflects the supplied window, not an all-time peak.
2. Says nothing about recovery time or drawdown frequency.
3. Starting point 1.0 (not actual capital).
4. log returns will have second-order error.

References

Magdon-Ismail & Atiya (2004) + Chekhlov et al. (2005) optimization embedding.

Golden Test

tests/golden/fixtures/tier1/drawdown_series/, 1e-12 tolerance, passing as of 2026-05-25. Reference: numpy manual reproduction (cumprod + maximum.accumulate).

Changelog

• 1.1.0 (2026-05-25) — Promoted to Active as Layer-1 transform; merged rich governance fields from the superseded Layer-0 drawdown_series card.
• 1.0.0 (2026-05-23) — Initial edge-first Layer-1 Draft card.