Convexity Is the Only Honest Edge
Most strategies people run are linear.
Fixed position size. Fixed stops. Linear P&L intuition.
Linear thinking works until volatility changes regime.
Then losses stop scaling linearly.
Convexity is the property that breaks this.
Mathematically, convex payoffs benefit from variance:
Translation:
If your payoff is convex, randomness helps you.
Volatility spikes punish linear exposure:
- Mean reversion explodes
- Tight stops become meaningless
- "High win rate" strategies implode
Convex strategies behave differently:
- Small losses most of the time
- Large gains occasionally
- Survival during regime shifts
Convexity is not about being right. It's about not being fragile when the math changes.
This is why trend followers survive crises. This is why volatility sellers eventually blow up. This is why spikes feel unfair - they're asymmetric by design.
Practical Implications
How do you actually build convexity into your trading?
Use position sizing that scales with volatility, not fixed sizes.
Fixed position sizes assume linear risk. When volatility spikes, your risk explodes. Instead, size positions inversely to volatility - smaller positions when volatility is high, larger when it's low. This creates natural convexity.
Prefer strategies with convex payoffs.
Trend following is convex: small losses most of the time, occasional large wins. Long options are convex. Mean reversion is concave: small wins most of the time, occasional large losses. During regime shifts, convex strategies survive; concave ones blow up.
Avoid fixed stops that don't account for volatility changes.
A fixed 2% stop assumes volatility is constant. When volatility doubles, your effective stop becomes 1% in volatility-adjusted terms. Use stops that scale with volatility, or accept that fixed stops will fail during regime shifts.
Accept small frequent losses for occasional large wins.
Convex strategies feel wrong psychologically. You'll lose money most days. You'll feel like you're doing something wrong. But during volatility spikes, you'll be the one still standing. Most traders can't handle this asymmetry - which is why it persists.
Don't optimize for win rate.
High win rate strategies are usually concave. They feel good until they don't. Convex strategies have lower win rates but survive volatility regime changes. Focus on payoff geometry, not win rate.
The practical takeaway: During normal times, convex strategies underperform. During regime shifts, they're the only ones that survive. Most traders quit convex strategies before the regime shift happens. Don't be most traders.
Part II of the series: Trading What Breaks Linear Thinking.
Previous: Part I - Volatility Is Not Risk | Next: Part III - Options Are Volatility Instruments