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harb/onchain/analysis/anchor-width-calculations.md
johba f3047072f6 feat: Dynamic anchorWidth based on staking metrics 
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>
2025-08-19 11:41:02 +02:00

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AnchorWidth Price Range Calculations

Understanding the Formula

From the code:

int24 anchorSpacing = TICK_SPACING + (34 * int24(params.anchorWidth) * TICK_SPACING / 100);

Where:

  • TICK_SPACING = 200 (for 1% fee tier pools)
  • anchorWidth ranges from 1 to 100

Tick to Price Conversion

In Uniswap V3:

  • Each tick represents a 0.01% (1 basis point) price change
  • Price at tick i = 1.0001^i
  • So a tick difference of 100 = ~1.01% price change
  • A tick difference of 10,000 = ~2.718x price change

AnchorWidth to Price Range Mapping

Let's calculate the actual price ranges for different anchorWidth values:

Formula Breakdown:

  • anchorSpacing = 200 + (34 * anchorWidth * 200 / 100)
  • anchorSpacing = 200 + (68 * anchorWidth)
  • anchorSpacing = 200 * (1 + 0.34 * anchorWidth)

The anchor position extends from:

  • Lower bound: currentTick - anchorSpacing
  • Upper bound: currentTick + anchorSpacing
  • Total width: 2 * anchorSpacing ticks

Price Range Calculations:

anchorWidth anchorSpacing (ticks) Total Width (ticks) Lower Price Ratio Upper Price Ratio Price Range
1% 268 536 0.974 1.027 ±2.7%
5% 540 1080 0.947 1.056 ±5.5%
10% 880 1760 0.916 1.092 ±9.0%
20% 1560 3120 0.855 1.170 ±16%
30% 2240 4480 0.800 1.251 ±25%
40% 2920 5840 0.748 1.336 ±33%
50% 3600 7200 0.700 1.429 ±42%
60% 4280 8560 0.654 1.528 ±52%
70% 4960 9920 0.612 1.635 ±63%
80% 5640 11280 0.572 1.749 ±74%
90% 6320 12640 0.535 1.871 ±87%
100% 7000 14000 0.500 2.000 ±100%

Key Insights:

  1. Linear Tick Scaling: The tick spacing scales linearly with anchorWidth
  2. Non-Linear Price Scaling: Due to exponential nature of tick-to-price conversion
  3. Asymmetric Percentages: The percentage move down is smaller than up (e.g., 100% width = -50% to +100%)

Practical Examples:

anchorWidth = 50 (Common Default)

  • If current price is $1.00:
    • Lower bound: $0.70 (-30%)
    • Upper bound: $1.43 (+43%)
    • Captures moderate price movements in both directions

anchorWidth = 100 (Maximum)

  • If current price is $1.00:
    • Lower bound: $0.50 (-50%)
    • Upper bound: $2.00 (+100%)
    • Price can double or halve while staying in range

anchorWidth = 10 (Narrow)

  • If current price is $1.00:
    • Lower bound: $0.92 (-8%)
    • Upper bound: $1.09 (+9%)
    • Highly concentrated, requires frequent rebalancing

Important Notes:

  1. The anchor position does NOT extend to 2x or 3x the price at maximum width
  2. At anchorWidth = 100, the upper bound is exactly 2x the current price
  3. The formula 200 + (34 * anchorWidth * 200 / 100) creates a sensible progression from tight to wide ranges
  4. The minimum spacing (anchorWidth = 0) would be 200 ticks (±1% range), but minimum allowed is 1