Understanding Drawdowns: The Math of Losing and Recovering

The math: measuring from peak to trough

A drawdown is the percentage drop from a portfolio's highest point to its lowest point before a new high. Take an account that starts at $50,000, climbs to $64,000, then sinks to $48,000 before turning up again. The drawdown is $64,000 minus $48,000, divided by $64,000: $16,000 / $64,000 = 25%. The starting balance is irrelevant. Drawdown is always measured from the peak, because the peak is money you had and lost.

Two versions of the number matter. Current drawdown is how far below the most recent peak the account sits today. Maximum drawdown is the deepest such valley across the entire record. Even good systems spend most of their life in some drawdown — new equity highs are the exception, not the rule — but max drawdown is the one printed next to a fund's returns, because it is the worst thing that has actually happened.

Depth is only half the measurement. The 25% drawdown above might have taken three weeks or three years, and the recovery runs on a separate clock. Time under water — the stretch between the old peak and the new one — is frequently longer than the decline itself. The S&P 500 topped in October 2007, bottomed 17 months later in March 2009 down roughly 57%, and did not close above the 2007 peak until March 2013: about five and a half years under water on a price basis.

Why recovery is asymmetric

Losses and the gains that repair them are not mirror images. The gain required to recover a drawdown D is D / (1 - D). A 10% drawdown needs an 11.1% gain (0.10 / 0.90). A 25% drawdown needs 33.3% (0.25 / 0.75). A 50% drawdown needs 100%: half the money is gone, so what remains must double. An 80% drawdown needs 400% (0.80 / 0.20) — a five-fold move on what is left, just to reach the old peak.

Run the $64,000 example forward. Sitting at $48,000, a 10%-a-year average return sounds like a quick repair. But 10% on $48,000 is only $4,800, and three straight years of compounding at 10% takes the account to $48,000 × 1.1 × 1.1 × 1.1 = $63,888 — still below the old peak after three above-average years. The dollars lost were peak dollars; the dollars earned back start from the trough.

The asymmetry is why deep drawdowns dominate long-run compounding. Cutting a strategy's max drawdown from 50% to 25% does not halve the damage; it cuts the required recovery from 100% to 33.3%. Two strategies with identical average returns but different drawdown profiles finish in very different places, because the deeper one keeps restarting its compounding from a lower base.

Max drawdown: the number that ends careers

Professional money dies by drawdown, not by average return. Allocators commonly pull capital somewhere between a 15% and 25% drawdown regardless of the story attached, and prop firms routinely cut traders at 5% to 10%. The manager may be running a sound system through an ordinary bad stretch; the capital leaves anyway, and the recovery that would have vindicated the system happens without them.

Retail accounts run the same mechanism with a different trigger: the account holder quits. Behavior at -40% is not behavior at -10%. The arithmetic of the previous section explains the surrender — at -50% the path back is a double, and a trader who got there by oversizing has no reason to believe the same process will now produce a clean +100%. Max drawdown ends careers because it is the point where either the capital or the conviction runs out, and it rarely announces which one first.

Sizing so your worst streak is survivable

Work backward from the streak, not forward from the win rate. A system that wins 40% of the time will lose ten in a row eventually: the chance of ten straight losses starting from any given trade is 0.6^10, about 0.6%, and across a 400-trade year that streak is more likely than not to appear at least once. The sizing question is what ten straight losses does to the account.

Compound the losses honestly, because each one shrinks the base for the next. Risking 1% of current equity per trade, ten straight losses leave 0.99^10 = 90.4% of the account: a 9.6% drawdown, unpleasant and survivable. At 2% per trade, 0.98^10 = 81.7%, an 18.3% drawdown — already inside the zone where allocators fire managers. At 5% per trade, 0.95^10 = 59.9%, a 40.1% drawdown that requires a 67% gain to repair, delivered by a trader who is now demoralized and under-capitalized.

The rule that falls out: pick the deepest drawdown you could genuinely keep trading through, estimate your realistic worst streak, and let those two numbers set per-trade risk. If 20% is the true tolerance and twelve straight losses is plausible, risk r must satisfy (1 - r)^12 at or above 0.80, which puts r just under 1.85%. Sizing is downstream of survival, not the other way around.

The psychological bill arrives mid-drawdown

Every mistake that deepens a drawdown is easier to make inside one. Revenge sizing — doubling risk to win it back faster — is the direct route from a 20% hole to a 40% one, and the recovery asymmetry punishes it exactly when the impulse is strongest. Cutting winners early to lock in any green day, skipping valid setups after a string of stops, abandoning the system at the bottom of its cycle: each is a rational-feeling response to pain that converts a normal drawdown into a permanent loss.

The defense is to decide things before the drawdown that will not be decided well during it. A written maximum daily loss, a rule that halves position size once the account is down 10%, a pre-committed review threshold (re-evaluate the system after 30 trades, not after 3 bad days): these move decisions from the worst possible moment to a calm one. Traders who last long enough to compound tend to be the ones who treated the drawdown as a scheduled event, because for any real system, it is one.

What drawdown statistics leave out

Max drawdown is one number from one path. A backtest's 18% max drawdown means that specific sequence of trades, in that order, produced an 18% valley; reshuffle the same trades and the max drawdown changes, sometimes by a lot. A live strategy should be expected to exceed its historical figure eventually — the longer the record grows, the more chances the worst case has to get worse. Historical max drawdown is a floor on future pain, not a ceiling.

Measurement frequency hides depth. A drawdown computed from month-end values misses everything inside the month; the same portfolio marked daily shows deeper valleys, and intraday marks deeper still. Two funds holding identical positions can report different max drawdowns purely because one reports monthly. Before comparing the number across track records, check the marking frequency behind it.

And drawdown says nothing about why. A 20% drawdown from a diversified system behaving normally and a 20% drawdown from one concentrated position that gapped down are the same statistic and entirely different situations. The number reports what the pain was, not whether the process that produced it is intact. That judgment still requires reading the trades.