Risk
The gain you need to undo a loss
Losing 20 percent of an account does not take a 20 percent gain to fix. It takes 25. The gap widens fast, and it is the reason serious trading rules are written around drawdown instead of return.
Drop an account from $100,000 to $80,000 and you are down 20 percent. To get back to $100,000 you have to make $20,000 on a smaller base, which is a 25 percent gain. The loss and the recovery are measured against different numbers, so they never match.
Write the account as E. A drawdown of D leaves E(1 − D). The gain g that returns it to E satisfies:
solving for g
the recovery is the drawdown divided by what is left
That denominator is the whole story. While D is small the divisor is close to 1 and recovery tracks the loss almost exactly. As D approaches 1 the divisor approaches zero and the required gain runs away.
What that looks like
| Drawdown | Gain to break even | Ratio |
|---|---|---|
| 5% | 5.3% | 1.05x |
| 10% | 11.1% | 1.11x |
| 20% | 25.0% | 1.25x |
| 30% | 42.9% | 1.43x |
| 40% | 66.7% | 1.67x |
| 50% | 100.0% | 2.00x |
| 70% | 233.3% | 3.33x |
| 90% | 900.0% | 10.00x |
A 10 percent drawdown is an ordinary month. A 50 percent drawdown means doubling the account just to arrive back where you started, and doubling an account is the kind of thing people build entire careers around.
Why this drives the rules, not the returns
A strategy that averages 3 percent a month and never loses more than 8 percent is easier to run than one averaging 6 percent that occasionally gives back 45. The second one spends long stretches climbing out of holes, and during those stretches the operator is under pressure to change something, which is usually when the real damage happens.
This is also why a published maximum drawdown deserves more attention than a published gain. Gain tells you what happened. Drawdown tells you what the account had to survive to get there, and how close it came to a number it could not climb back from.