The Mathematics of Destruction
- Leverage multiplies moves linearly — 10x leverage means 3% becomes 30%
- Convexity multiplies losses exponentially — the further you go, the faster you die
- Gamma accelerates everything — options exposure can flip from manageable to fatal in minutes
- Correlation spikes during stress — your "diversification" disappears when you need it most
- Liquidity vanishes at the worst moment — you can't exit at any price
- Small moves trigger margin calls — which trigger selling, which triggers more margin calls
The Needle That Pops The Balloon
On March 26, 2021, ViacomCBS stock dropped 9%.
Not 50%. Not a crash. Just 9%. A normal bad day for a stock that had tripled in three months.
Within 48 hours, $20 billion in wealth had evaporated. Credit Suisse lost $5.5 billion. Nomura lost $3 billion. Goldman Sachs nearly lost billions but sold first. Archegos Capital — the family office at the center — was completely destroyed.
Nine percent. That's all it took.
Welcome to the mathematics of nonlinear destruction.
The Leverage Amplifier
What a 3% market move becomes at different leverage levels:
At 25x leverage, a 4% move wipes you out completely.
Leverage: The Linear Killer
Leverage is the most obvious amplifier. It's simple multiplication. 10x leverage means a 1% move becomes a 10% move in your equity. Nothing complicated here.
What makes leverage deadly isn't the math — it's the psychology of false safety.
When markets are calm, leverage feels free. You're running 20x leverage, collecting 2% monthly, and nothing bad happens. Month after month, the P&L grows. You start thinking you've figured something out.
Then comes the day when volatility wakes up. A 3% move that would have cost you 3% now costs you 60%. Your entire year's profits — and probably your entire account — gone in an afternoon.
"Leverage is a lot like alcohol. A little enhances the experience. Too much, and you wake up wondering what happened to your life."
— Anonymous Hedge Fund Manager
The Death Table
This is the table every leveraged trader should have tattooed on their forearm:
| Leverage | 1% Move | 3% Move | 5% Move | 10% Move | Kill Zone |
|---|---|---|---|---|---|
| 2x | -2% | -6% | -10% | -20% | 50% move |
| 5x | -5% | -15% | -25% | -50% | 20% move |
| 10x | -10% | -30% | -50% | -100% 💀 | 10% move |
| 20x | -20% | -60% | -100% 💀 | -200% 💀 | 5% move |
| 50x | -50% | -150% 💀 | -250% 💀 | -500% 💀 | 2% move |
💀 The Kill Zone
The "Kill Zone" is the move size that completely wipes out your equity. At 50x leverage (common in forex), a 2% move kills you. Two percent. That's noise. That happens before breakfast.
Under The Magnifying Glass
When leverage acts as a magnifying glass, a 3% move doesn't just become bigger — it becomes impossible to survive. The same move that a long-term investor shrugs off becomes an extinction event for a leveraged fund.
This is why the same market can simultaneously create record profits for index funds and total destruction for hedge funds. They're not playing the same game.
Convexity: The Exponential Killer
Leverage is linear. Convexity is exponential. And exponential always wins.
Convexity means the relationship between price moves and your P&L is curved. Each additional percent of loss hurts more than the one before. The deeper in the hole you go, the faster you fall.
This happens naturally in many trading situations:
Short Options
You collect premium but your losses accelerate as price moves against you. Gamma turns what looks like a manageable loss into catastrophe.
Mortgage Bonds
As rates rise, prices fall — but also duration extends, making them fall faster. Negative convexity is built into the structure.
Carry Trades
Borrow low, invest high. Works until the currency moves. Then the leverage AND the currency loss compound together.
Volatility Selling
Short VIX products can return 50% annually — until a spike. XIV lost 96% in one day. Convexity in its purest form.
Real Deaths From Small Moves
These aren't hypotheticals. These are real funds, real billions, destroyed by moves that most investors would barely notice:
Credit spreads widened by a few percentage points after Russia defaulted. At 25x leverage with $1.25T in derivatives exposure, "a few percent" became $4.6 billion and nearly collapsed the global financial system.
VIX doubled in one afternoon. A product designed to go up when volatility is calm lost 96% of its value in hours. Billions in retail wealth — gone. The product was terminated the next week.
ViacomCBS dropped 9% after a stock offering. At Archegos's leverage, 9% meant margin call. Margin call meant forced selling. Forced selling meant 50-70% drops in multiple stocks and $10B+ in bank losses.
UK government bond yields rose about 1% quickly. "Conservative" pension funds using leveraged derivatives for "liability matching" faced margin calls. The Bank of England had to buy £65B in bonds to prevent collapse.
The Mathematics They Don't Teach You
The academic view of risk is Gaussian — normal distributions, bell curves, standard deviations. Reality is different. Reality is fat-tailed, nonlinear, and mean.
Crisis Correlation → 1.0
Crisis Spread = $0.50 (or no bid at all)
The Domino Effect
Small moves don't just kill individual positions. They trigger chains of destruction. Click the first domino to see what happens:
Click the green domino to start the cascade
Survival Protocol
You can't control market moves. But you can control your exposure to them. Here's how survivors survive:
Size for the Worst Case
Don't size for the likely move. Size for the 6-sigma move that "shouldn't happen." It happens.
Halve Your Maximum Leverage
Whatever leverage feels comfortable, cut it in half. That cushion is your survival margin.
Know Your Convexity
Are your losses linear or exponential? If you're short options or in carry trades, you have negative convexity.
Assume Liquidity Vanishes
Can you exit 80% of your position in one day? If not, you're vulnerable to liquidity traps.
Stress Test Correlations
In your stress test, assume all correlations go to 1. Because in a crisis, they do.
Keep Cash Reserves
Cash meets margin calls. Cash lets you survive the drawdown. Cash is the ultimate hedge.
The Small-Move Survival Rule
- If a 3% move would hurt you badly — reduce position size now
- If a 5% move would trigger margin calls — you're already dead, you just don't know it
- If a 10% move would wipe you out — you're gambling, not trading
"Rule #1: Never lose money. Rule #2: Never forget Rule #1. The math of recovery is brutal — a 50% loss requires a 100% gain just to break even."
— Warren Buffett