Risk & Portfolio

A year of month-end equity. The peak of 108 comes in the third month; the trough of 89 five months later: a maximum drawdown of 17.6%. Getting back to 108 needed +21.3%, and took four months after the bottom. The deeper the fall, the steeper the climb: −50% needs +100%.

• Maximum drawdown is one path. A strategy with the same returns in a different order would have a different number, and a longer history almost always shows a deeper one (Magdon-Ismail & Atiya 2004).
• A backtest drawdown is a minimum, not a forecast of the worst.
• Duration matters as much as depth: a long shallow drawdown can be harder to sit through than a short deep one.

equity = pd.Series([100, 104, 108, 103, 97, 91, 94, 89, 95, 99, 104, 110, 113])   # month-end, made up
peak = equity.cummax()
dd = equity / peak - 1
mdd = dd.min()
trough = dd.idxmin()
start = equity[:trough].idxmax()
recovered = equity[(equity.index > trough) & (equity >= peak[trough])].index.min()
to_recover = 1 / (1 + mdd) - 1                             # gain needed from the bottom

Assumes import numpy as np and import pandas as pd. Each snippet carries its own example numbers; the comments say which are made up or simulated.