payoff-symmetry
Payoff Symmetry: Why a Small Hedge Can Outrun a Large Core
🎯 TL;DR
Scaling and hedging often leave traders with uneven exposure. True payoff symmetry isn’t about equal size—it’s about equalized potential, where the smaller position’s possible gain mirrors the larger one’s potential loss. This article breaks down how to design that balance mathematically and psychologically.
🪞 1. The Illusion of Symmetry
Most traders think “balanced” means equal size—e.g., long 300 SOL, short 300 SOL. In reality, that’s just position neutrality, not risk symmetry. If both sides have similar stop distances and volatility, you’re basically flat.
Payoff symmetry means:
A small position can offset a large one—if it moves far enough, fast enough, or during high convexity.
📏 2. The Core Equation
Let:
- ( S_c ) = size of the core position
- ( L_c ) = % loss on core stop
- ( S_h ) = size of the hedge
- ( R_h ) = % move hedge needs to make to offset core loss
Then:
[R_h = \frac{S_c × L_c}{S_h}]
Example:
- Long 300 SOL, stop −2 %
- Short 50 SOL hedge
[ R_h = (300 × 0.02) / 50 = 0.12 = 12 % ]
So a 12 % move on the hedge offsets a 2 % loss on the core.
⚙️ 3. Designing Convexity
Payoff symmetry doesn’t require 1:1 moves—it requires expected asymmetry. You want the small leg to live where volatility expansion or velocity is highest:
| Type | Example | Convexity Source | Target Hedge Move |
|---|---|---|---|
| Event hedge | Short before FOMC | Vol spike | 5–10 × core stop |
| Momentum hedge | Counter-trend scalp | Trend acceleration | 3–6 × core stop |
| Tail hedge | Long vol, options | Gamma | 10–20 × core stop |
This is where the math and psychology align: the small position must be able to travel farther.
📊 4. Structuring Accounts
Separate “books” or accounts let you preserve clarity:
| Account | Purpose | Typical Stop | Target Size | Convexity |
|---|---|---|---|---|
| Core | Directional thesis | 1–3 % | 100 % base | Low |
| Hedge | Counter-trend / Event | 5–15 % | 10–30 % of core | High |
You then design them for payoff symmetry, not position symmetry. If the hedge moves 6× as far as the core’s loss, your PnL distribution is neutral—but convex to volatility.
🔬 5. Testing It Quantitatively
Backtesting payoff symmetry involves:
- Tracking core and hedge pairs historically.
- Measuring net PnL per volatility cluster (e.g., before/after major news).
- Evaluating “break-even move” on hedge vs. average move realized.
- Optimizing hedge size ratio ( S_h/S_c ) to minimize variance without killing convexity.
Eventually, you can model expected convex payoff like:
[ E[\text{Hedge Gain}] = P(\text{Move ≥ } R_h) × (\text{Move Magnitude}) ]
and see if that compensates your core’s expected loss.
🧭 6. Psychological Payoff
This framework reduces emotional noise:
- You want your hedge small, so missing fills doesn’t sting.
- You want it far, so big moves feel meaningful.
- You accept that sometimes it won’t trigger—that’s fine, convexity is optionality, not obligation.
🧩 7. Future Work: Simulation & Visualization
Planned next steps:
- Simulate SOL/USD 2021–2025 data using rolling 15 m–1 h bars.
- Define two legs (core/hedge) with parameterized stop/target/size.
- Measure how often hedges achieve payoff symmetry vs. how often they drag.
- Visualize convexity curves—when small hedges cover large core drawdowns.
✍️ 8. Closing Thoughts
Payoff symmetry is a mindset:
Don’t just size positions. Shape outcomes.
Once you see trades as distributions of potential energy, not just “entries and exits,” scaling and hedging become tools for engineering convexity—where smaller pieces can punch far above their weight.