Score drawdown depth and duration as a pain budget

Two axes of an equity decline

An equity decline can be scored along two axes at once: how large the percentage drop is, and how long equity stays below the prior peak.

One episode has a drawdown area equal to the sum of its period-by-period percentage declines while equity remains below its prior peak. Total drawdown area is the sum of those episode areas across the full evaluation window, used as a compact pain score.

Pain multipliers reshape the path

A discomfort response to depth or duration may be linear or nonlinear. A nonlinear mapping can treat a 20 percent decline as more than twice as severe as a 10 percent decline, or a six-month decline as more than twice as severe as a three-month decline.

Self-estimated depth and duration curves can be turned into pain multipliers that reshape an equity path before drawdown areas are compared across candidates. A modified decline for a period is the observed drawdown scaled by a depth multiplier and a duration multiplier.

When summaries match and shapes do not

Two equity paths can share the same start value, end value, and standard deviation of return while still differing in shape. One path can show deep, short declines. The other can show a shallow, long decline.

A bound, a snapshot, and a budget

A drawdown limit is a pre-set bound on acceptable equity-decline depth, duration, or their combined area, used to keep a loss or exposure decision bounded before entry and while the position is open.

A Sharpe ratio is a reward-to-variability baseline that compares excess return with a risk term built from return dispersion over a defined sampling window. It does not by itself credit how long equity stays below a prior peak. Sharpe-style reward-to-risk scores that put only percentage drawdown or return dispersion in the risk term omit the duration component that total modified drawdown area is designed to include.

A modified drawdown-area ratio is investment return minus a guaranteed return rate, divided by total modified drawdown area. It is computed over the same window for each candidate and over a sample long enough to support assessment, with a 30-trade minimum cited as a statistical floor.

Equal pain and combined sleeves

Equal total modified drawdown areas can be read as equal perceived pain, which allows exposure to be scaled until those areas match and then returns to be compared.

A portfolio risk budget is an allocation rule that scales sleeves by capital weight so the combined equity path can be scored as one entity and kept inside a chosen pain or drawdown-area budget. Separate sleeves can be merged by those capital-allocation weights into one equity path and then scored with the same total modified drawdown area and modified drawdown-area ratio used on standalone records.