Day 25: Quote Distance Optimization
Summary
Result: POSITIVE β Wider quotes outperform.
| Metric | Baseline (6 bps) | Optimal (10 bps) | Change |
|---|---|---|---|
| Expected PnL | 4.63 bps | 5.57 bps | +20.3% |
| Fill Rate | 66% | 51% | -15% |
| Win Rate | 60.5% | 68.1% | +7.6% |
Verdict: Worth deploying β 10 bps quote distance gives meaningful improvement.
The Question
Our maker orders currently sit at 6 bps from mid-price. But is this optimal?
The trade-off: - Closer quotes (e.g., 2 bps): Higher fill rate (~76%), but minimal spread capture (~1 bps) - Wider quotes (e.g., 20 bps): Lower fill rate (~17%), but larger spread capture (~19 bps)
Thereβs a sweet spot. Letβs find it.
Methodology
Theoretical Model
First, a simple theoretical model:
EV = P(fill) Γ (quote_dist - spread/2 + maker_rebate)Where: - P(fill) = fill probability (modeled as logistic function of quote distance) - quote_dist = our distance from mid (bps) - spread/2 = half-spread we capture when filled - maker_rebate = 2 bps (Binance maker rebate)
Fill Probability Model
Empirical calibration (from prior research): - 6 bps β ~71% fill rate - Calibrated logistic: P(fill) = 1 / (1 + exp(0.15 Γ (distance - 8)))
Walk-Forward Backtest
- Data: 5-minute candles, Jan 2022 β Feb 2026
- Train: 2022-2023
- Test: 2024-2025
- Quote distances tested: 2, 3, 4, 5, 6, 7, 8, 10, 12, 15, 20 bps
- Adjustments: Volatility regime adjustment for fill probability
Results
Theoretical Analysis
| Quote Dist (bps) | Fill Prob | Spread Capture | EV (bps) |
|---|---|---|---|
| 2 | 71.1% | 1.0 | -0.71 |
| 4 | 64.6% | 3.0 | 0.65 |
| 6 | 57.4% | 5.0 | 1.72 |
| 8 | 50.0% | 7.0 | 2.50 |
| 10 | 42.6% | 9.0 | 2.98 |
| 12 | 35.4% | 11.0 | 3.19 |
| 15 | 25.9% | 14.0 | 3.11 |
| 20 | 14.2% | 19.0 | 2.41 |
Theoretical optimum: ~12 bps (highest EV).
Walk-Forward Backtest (OOS)
| Quote Dist | Expected PnL | Fill Rate | Win Rate |
|---|---|---|---|
| 2 | 2.28 bps | 76% | 52.3% |
| 3 | 2.96 bps | 74% | 54.4% |
| 4 | 3.59 bps | 72% | 56.4% |
| 5 | 4.15 bps | 69% | 58.5% |
| 6 | 4.63 bps | 66% | 60.5% |
| 7 | 5.03 bps | 63% | 62.5% |
| 8 | 5.34 bps | 59% | 64.5% |
| 10 | 5.57 bps | 51% | 68.1% |
| 12 | 5.48 bps | 42% | 71.3% |
| 15 | 4.94 bps | 31% | 75.6% |
| 20 | 3.54 bps | 17% | 81.4% |
Optimal OOS: 10 bps with 5.57 bps expected PnL per trade.
Key Insights
Wider is better (up to a point): Moving from 6 bps β 10 bps improves expectancy by 20%
The fill-rate penalty is worth it:
- At 6 bps: 66% fill Γ 5 bps = 3.3 bps captured
- At 10 bps: 51% fill Γ 9 bps = 4.6 bps captured
- Net: +1.3 bps per opportunity
Win rate increases with distance:
- Wider quotes filter out adverse selection
- Only βeasyβ fills happen (market moves in our favor)
- At 10 bps: 68% win rate vs 60% at 6 bps
Diminishing returns beyond 10 bps:
- 12 bps: 5.48 bps (slightly worse than 10 bps)
- Fill rate drops too much (42%)
Action Item
Deploy 10 bps quote distance in live trading.
Expected improvement: +0.94 bps/trade (+20.3%) over 6 bps baseline.
Note: This assumes: - Maker rebate of 2 bps (Binance) - ~2 bps spread (BTCUSDT perp) - Slippage assumptions in line with historical data
Files
- research.py β Full backtest code
- backtest_results.csv β Year-by-year results
- theoretical_analysis.csv β Theoretical EV model
- verdict.json β Decision record