f3047072f6
Replace hardcoded anchorWidth=100 with dynamic calculation that uses staking data as a decentralized oracle. Changes: - Add _calculateAnchorWidth() function to Optimizer.sol - Base width 40% with adjustments based on staking percentage and average tax rate - Staking adjustment: -20% to +20% (inverse relationship) - Tax rate adjustment: -10% to +30% (direct relationship) - Final range clamped to 10-80% for safety Rationale: - High staking % = bullish sentiment → narrower anchor (20-35%) for fee optimization - Low staking % = bearish/uncertain → wider anchor (60-80%) for defensive positioning - High tax rates = volatility expected → wider anchor to reduce rebalancing - Low tax rates = stability expected → narrower anchor for fee collection The Harberger tax mechanism acts as a prediction market where stakers' self-assessed valuations reveal market expectations. Tests: - Add comprehensive unit tests in test/Optimizer.t.sol - Add mock contracts for testing (MockStake.sol, MockKraiken.sol) - Manual verification confirms all scenarios calculate correctly Documentation: - Add detailed analysis of anchorWidth price ranges - Add staking-based strategy recommendations - Add verification of calculation logic 🤖 Generated with [Claude Code](https://claude.ai/code) Co-Authored-By: Claude <noreply@anthropic.com>
84 lines
No EOL
3.8 KiB
Markdown
84 lines
No EOL
3.8 KiB
Markdown
# AnchorWidth Price Range Calculations
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## Understanding the Formula
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From the code:
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```solidity
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int24 anchorSpacing = TICK_SPACING + (34 * int24(params.anchorWidth) * TICK_SPACING / 100);
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```
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Where:
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- `TICK_SPACING = 200` (for 1% fee tier pools)
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- `anchorWidth` ranges from 1 to 100
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## Tick to Price Conversion
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In Uniswap V3:
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- Each tick represents a 0.01% (1 basis point) price change
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- Price at tick i = 1.0001^i
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- So a tick difference of 100 = ~1.01% price change
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- A tick difference of 10,000 = ~2.718x price change
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## AnchorWidth to Price Range Mapping
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Let's calculate the actual price ranges for different anchorWidth values:
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### Formula Breakdown:
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- `anchorSpacing = 200 + (34 * anchorWidth * 200 / 100)`
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- `anchorSpacing = 200 + (68 * anchorWidth)`
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- `anchorSpacing = 200 * (1 + 0.34 * anchorWidth)`
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The anchor position extends from:
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- Lower bound: `currentTick - anchorSpacing`
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- Upper bound: `currentTick + anchorSpacing`
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- Total width: `2 * anchorSpacing` ticks
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### Price Range Calculations:
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| anchorWidth | anchorSpacing (ticks) | Total Width (ticks) | Lower Price Ratio | Upper Price Ratio | Price Range |
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|-------------|----------------------|---------------------|-------------------|-------------------|-------------|
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| 1% | 268 | 536 | 0.974 | 1.027 | ±2.7% |
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| 5% | 540 | 1080 | 0.947 | 1.056 | ±5.5% |
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| 10% | 880 | 1760 | 0.916 | 1.092 | ±9.0% |
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| 20% | 1560 | 3120 | 0.855 | 1.170 | ±16% |
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| 30% | 2240 | 4480 | 0.800 | 1.251 | ±25% |
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| 40% | 2920 | 5840 | 0.748 | 1.336 | ±33% |
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| 50% | 3600 | 7200 | 0.700 | 1.429 | ±42% |
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| 60% | 4280 | 8560 | 0.654 | 1.528 | ±52% |
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| 70% | 4960 | 9920 | 0.612 | 1.635 | ±63% |
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| 80% | 5640 | 11280 | 0.572 | 1.749 | ±74% |
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| 90% | 6320 | 12640 | 0.535 | 1.871 | ±87% |
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| 100% | 7000 | 14000 | 0.500 | 2.000 | ±100% |
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## Key Insights:
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1. **Linear Tick Scaling**: The tick spacing scales linearly with anchorWidth
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2. **Non-Linear Price Scaling**: Due to exponential nature of tick-to-price conversion
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3. **Asymmetric Percentages**: The percentage move down is smaller than up (e.g., 100% width = -50% to +100%)
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## Practical Examples:
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### anchorWidth = 50 (Common Default)
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- If current price is $1.00:
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- Lower bound: $0.70 (-30%)
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- Upper bound: $1.43 (+43%)
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- Captures moderate price movements in both directions
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### anchorWidth = 100 (Maximum)
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- If current price is $1.00:
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- Lower bound: $0.50 (-50%)
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- Upper bound: $2.00 (+100%)
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- Price can double or halve while staying in range
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### anchorWidth = 10 (Narrow)
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- If current price is $1.00:
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- Lower bound: $0.92 (-8%)
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- Upper bound: $1.09 (+9%)
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- Highly concentrated, requires frequent rebalancing
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## Important Notes:
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1. The anchor position does NOT extend to 2x or 3x the price at maximum width
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2. At anchorWidth = 100, the upper bound is exactly 2x the current price
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3. The formula `200 + (34 * anchorWidth * 200 / 100)` creates a sensible progression from tight to wide ranges
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4. The minimum spacing (anchorWidth = 0) would be 200 ticks (±1% range), but minimum allowed is 1 |