harb/onchain/analysis/staking-based-anchor-width.md

Staking-Based AnchorWidth Recommendations

Understanding Staking as a Sentiment Signal

The Harberger tax staking mechanism creates a prediction market where:

• Tax Rate = Cost to hold a position (self-assessed valuation)
• Percentage Staked = Overall confidence in protocol
• Average Tax Rate = Market's price volatility expectation

Staking Metrics → Market Conditions Mapping

High Staking Percentage (>70%)

Interpretation: Strong bullish sentiment, holders confident in price appreciation

• Market expects upward price movement
• Stakers willing to lock capital despite opportunity cost
• Lower expected volatility (confident holders)

anchorWidth Recommendation: 30-50%

• Moderate width to capture expected upward movement
• Avoid excessive rebalancing during steady climb
• Maintain efficiency without being too narrow

Low Staking Percentage (<30%)

Interpretation: Bearish/uncertain sentiment, holders want liquidity

• Market expects downward pressure or high volatility
• Stakers unwilling to commit capital
• Higher expected volatility (nervous market)

anchorWidth Recommendation: 60-80%

• Wide range to handle volatility without constant rebalancing
• Defensive positioning during uncertainty
• Prioritize capital preservation over fee optimization

Medium Staking Percentage (30-70%)

Interpretation: Neutral market, mixed sentiment

• Balanced buyer/seller pressure
• Normal market conditions
• Moderate volatility expectations

anchorWidth Recommendation: 40-60%

• Balanced approach for normal conditions
• Reasonable fee capture with manageable rebalancing
• Standard operating parameters

Average Tax Rate → Volatility Expectations

High Average Tax Rate (>50% of max)

Interpretation: Market expects significant price movement

• Stakers setting high taxes = expect to be "snatched" soon
• Indicates expected volatility or trend change
• Short-term holding mentality

anchorWidth Recommendation: Increase by 20-30%

• Wider anchor to handle expected volatility
• Reduce rebalancing frequency during turbulent period
• Example: Base 40% → Adjust to 60%

Low Average Tax Rate (<20% of max)

Interpretation: Market expects stability

• Stakers comfortable with low taxes = expect to hold long-term
• Low volatility expectations
• Long-term holding mentality

anchorWidth Recommendation: Decrease by 10-20%

• Narrower anchor to maximize fee collection
• Take advantage of expected stability
• Example: Base 40% → Adjust to 30%

Proposed On-Chain Formula

function calculateAnchorWidth(
    uint256 percentageStaked,  // 0 to 1e18
    uint256 avgTaxRate        // 0 to 1e18 (normalized)
) public pure returns (uint24) {
    // Base width starts at 40%
    uint24 baseWidth = 40;
    
    // Staking adjustment: -20% to +20% based on staking percentage
    // High staking (bullish) → narrower width
    // Low staking (bearish) → wider width
    int24 stakingAdjustment = int24(20) - int24(uint24(percentageStaked * 40 / 1e18));
    
    // Tax rate adjustment: -10% to +30% based on average tax
    // High tax (volatile) → wider width
    // Low tax (stable) → narrower width
    int24 taxAdjustment = int24(uint24(avgTaxRate * 30 / 1e18)) - 10;
    
    // Combined width
    int24 totalWidth = int24(baseWidth) + stakingAdjustment + taxAdjustment;
    
    // Clamp between 10 and 80
    if (totalWidth < 10) return 10;
    if (totalWidth > 80) return 80;
    
    return uint24(totalWidth);
}

Staking Signal Interpretations

Scenario 1: "Confident Bull Market"

• High staking (80%), Low tax rate (20%)
• Interpretation: Strong holders, expect steady appreciation
• anchorWidth: ~25-35%
• Rationale: Tight range for fee optimization in trending market

Scenario 2: "Fearful Bear Market"

• Low staking (20%), High tax rate (70%)
• Interpretation: Nervous market, expect volatility/decline
• anchorWidth: ~70-80%
• Rationale: Wide defensive positioning

Scenario 3: "Speculative Frenzy"

• High staking (70%), High tax rate (80%)
• Interpretation: Aggressive speculation, expect big moves
• anchorWidth: ~50-60%
• Rationale: Balance between capturing moves and managing volatility

Scenario 4: "Boring Stability"

• Medium staking (50%), Low tax rate (10%)
• Interpretation: Stable, range-bound market
• anchorWidth: ~30-40%
• Rationale: Optimize for fee collection in stable conditions

Key Advantages of Staking-Based Approach

1. On-Chain Native: Uses only data available to smart contracts
2. Forward-Looking: Tax rates reflect expectations, not just history
3. Self-Adjusting: Market participants' actions directly influence parameters
4. Sybil-Resistant: Costly to manipulate due to tax payments
5. Continuous Signal: Updates in real-time as positions change

Implementation Considerations

1. Smoothing: Average metrics over time window to prevent manipulation
2. Bounds: Always enforce min/max limits (10-80% recommended)
3. Hysteresis: Add small threshold before adjusting to reduce thrashing
4. Gas Optimization: Only recalculate when scraping/repositioning

Summary Recommendations

For the on-chain Optimizer contract:

• Use percentageStaked as primary bull/bear indicator
• Use averageTaxRate as volatility expectation proxy
• Combine both signals for sophisticated width adjustment
• Default to 40% width when signals are neutral
• Never exceed 80% or go below 10% for safety