Drawdown Math: Why −50% Needs +100% to Get Even
The asymmetry, in one table
A loss of x% requires a gain of x / (1 − x) just to return to even. It looks linear at small numbers and turns vicious as the loss deepens:
| Drawdown | Gain needed to recover |
|---|---|
| −10% | +11% |
| −20% | +25% |
| −33% | +50% |
| −50% | +100% |
| −75% | +300% |
| −90% | +900% |
This is arithmetic, not opinion. It's also why "survive first, win second" is the entire job description of a risk manager. A portfolio that avoids the −50% hole compounds from a higher base for the next cycle; the one that takes it spends years just clawing back to where it started.
Why markets hand out big holes more often than the models say
The textbook assumption is that returns are normally distributed — a tidy bell curve where a −20% day is a once-in-a-millennium event. Real markets have fat tails: extreme moves happen far more often than the normal distribution predicts, and they cluster (volatile days follow volatile days). 1987, 2008, March 2020 were all "impossible" under a normal model and all happened inside a single working lifetime.
This is why the risk metric matters. Value at Risk (VaR) tells you the threshold a loss won't exceed on, say, 95% of days — but says nothing about how bad the other 5% get. Conditional VaR (CVaR / expected shortfall) answers the question that actually matters: when things break the threshold, how bad is the average outcome? A portfolio can look calm on VaR and be a time bomb on CVaR.
Convexity and the barbell
If the deep hole is the enemy, the defense is convexity — owning a small allocation to things that pay off disproportionately precisely when everything else is falling apart. The barbell construction makes this explicit: hold the large majority of the book in genuinely safe, liquid assets, and a small sleeve in convex, crisis-positive positions (deep-out-of-the-money index puts, long volatility, certain tail hedges). The safe side ensures you survive; the convex side turns a crash from a wealth-destroyer into a buying opportunity.
The discipline that ties it together
- Set a maximum-drawdown limit before you need it — a pre-committed line that triggers de-risking, not a decision made mid-panic.
- Watch correlation regimes. Diversification evaporates in crises — assets that were uncorrelated for years all fall together. Monitor whether your "diversifiers" still diversify.
- Judge the book on survival-weighted returns, not headline averages. Staying in the game through the next cycle beats a higher average that includes a portfolio-ending hole.
QuantLogix surfaces the regime and drawdown context the framework above depends on — the macro regime tag and ±5 macro adjustment in the signal engine, plus the Economy tab's 24 FRED indicators and the Portfolio risk view.