Maximum Drawdown and the Recovery Asymmetry

Maximum drawdown (MDD) is the largest peak-to-trough decline in the value of a portfolio over a period, measured as a percentage of the peak:

MDD = max t(0,T) [ max s(0,t)V s V t max s(0,t)V s ]

In words: for every day, compute how far below the running high-water mark you are; the worst of those is the maximum drawdown. It requires no distributional assumption whatsoever, which is precisely its advantage over everything in section “Volatility” — it is a fact about what happened, not an inference from an assumed shape.

The recovery asymmetry is the whole reason this matters. A drawdown of d requires a subsequent gain of d 1d merely to get back to even. That function is violently convex:

Drawdown Gain needed to recover Years at 7%/yr
10% 11% 1.6
20% 25% 3.3
30% 43% 5.3
50% 100% 10.2
70% 233% 17.8
90% 900% 34.0

Losses and gains of equal percentage are not equal events, and this is the arithmetic behind every warning in this book against leverage, concentration, and forced selling. It is also why time under water — how long you spent below the previous high — often matters more to a real household than the depth itself. A 30% drawdown that recovers in eight months is an inconvenience. The same 30% taking six years is a retirement postponed, and if you are drawing income from the portfolio during those six years (section “The Default Sequence Is Wrong”), it is permanent damage rather than a paper loss.

What the historical record actually looks like. Bessembinder’s study of the greatest wealth creators in U.S. market history found that even the top 200 firm-decades — measured during their winning decade — endured maximum drawdowns averaging 50.2%, against 70.1% for typical firms.50 If you intend to hold individual equities, a halving is not the tail scenario. It is the base case, and your position sizing should say so.

The honest limitation. Maximum drawdown is a single realized number from a single path, and it is sample-size dependent: a longer track record mechanically produces a worse MDD, because there was more time for something bad to happen. Comparing a three-year fund’s MDD against a twenty-year fund’s is meaningless. Compare over identical windows, or use the average of the worst n drawdowns rather than the single worst.