Risk
The Mathematics of Drawdown Recovery
A 50 percent loss does not need a 50 percent gain to recover. It needs 100 percent. The asymmetry behind why controlling drawdown is non-negotiable.
SIGMASEVEN ResearchIn short
Drawdown recovery is asymmetric. A 20 percent loss requires a 25 percent gain to recover. A 50 percent loss requires a 100 percent gain. A 75 percent loss requires a 300 percent gain. This mathematics is why professional investors optimise for drawdown control before return maximisation.
The asymmetry nobody priced in
To recover from a drawdown of size D, the required gain is D divided by one minus D. At 10 percent, you need 11 percent. At 30 percent, you need 43 percent. At 50 percent, you need 100 percent. At 80 percent, you need 400 percent.
This is not advanced mathematics. It is the mathematics most investors refuse to internalise until they experience it once.
Why this changes strategy design
Once you accept the asymmetry, drawdown stops being a cosmetic metric and becomes the central design constraint. A strategy that halves the maximum drawdown of buy and hold, even at the cost of lower peak returns, usually wins on every metric that matters to a human being managing capital.
This is why serious quantitative systems are evaluated on return-per-unit-of-drawdown, not on raw return.
The psychological layer
The mathematical asymmetry has a psychological twin. Large drawdowns do not just require bigger recoveries, they also erode the investor's willingness to stay invested. The strategy that, on paper, recovers from a 70 percent drawdown rarely does so in practice because the human behind the account has already capitulated.
Controlling drawdown is controlling behaviour.
What "acceptable drawdown" means
There is no universal number. An acceptable drawdown is the largest drawdown you will hold through without changing your process. For most private investors, that is materially smaller than they claim in calm markets.
Design strategies around your real tolerance, not your aspirational tolerance. Each of our systems is designed with drawdown as the primary constraint - reducing peak-to-trough exposure while preserving the majority of cycle upside.
Frequently asked questions
- What is a drawdown?
- A drawdown is the percentage decline from a previous equity peak to a subsequent trough, measured on either closed-trade equity or marked-to-market equity.
- What is the formula for drawdown recovery?
- Required gain equals drawdown divided by one minus drawdown. For a 40 percent drawdown, the required gain to recover is 40 percent divided by 60 percent, or 66.7 percent.
- Why do professionals focus so much on drawdown?
- Because drawdown dictates both the mathematical path of recovery and the behavioural path of whether the investor stays in the strategy long enough to recover at all.
- What is a good maximum drawdown for a long-term strategy?
- There is no universal number. A reasonable target for a private investor in risk assets is a maximum drawdown at least 30 to 50 percent smaller than passive buy and hold of the same underlying.