jb-cash-out-curve

Juicebox V5 Cash Out Bonding Curve

Problem

When displaying cash out / redemption values in Juicebox V5 UIs, it's tempting to show a simple message like "Cashing out returns 90% of proportional treasury share" (for a 10% tax rate). This is incorrect and misleading to users.

The actual redemption amount depends on a bonding curve formula where the percentage of supply being cashed out affects the return.

Context / Trigger Conditions

• Building UI that shows cash out / redemption values
• Explaining to users what they'll receive when cashing out
• Any display of cashOutTaxRate impact on redemptions
• When you see code like retainedPercent = 100 - cashOutTax - this is WRONG

Solution

The Bonding Curve Formula

reclaimAmount = (x * s / y) * ((1 - r) + (r * x / y))

Where:

• x = number of tokens being cashed out
• s = surplus (treasury overflow available for redemption)
• y = total token supply
• r = cash out tax rate as decimal (0 to 1, where 0.1 = 10%)

Normalized Form

When working with fractions (what % of supply is being cashed out):

Let f = x/y (fraction of supply being cashed out)
reclaimFraction = f * ((1 - r) + (r * f))

Where reclaimFraction is the fraction of surplus received.

Key Insight

The return depends on HOW MUCH of the supply is being cashed out, not just the tax rate. Cashing out a larger percentage of supply returns proportionally less per token.

Example Calculation

With 10% cash out tax rate (r = 0.1), cashing out 10% of supply (f = 0.1):

reclaimFraction = 0.1 * ((1 - 0.1) + (0.1 * 0.1))
reclaimFraction = 0.1 * (0.9 + 0.01)
reclaimFraction = 0.1 * 0.91
reclaimFraction = 0.091  // 9.1% of surplus

So cashing out 10% of the supply gets ~9.1% of the surplus (not 9% as simple math would suggest).

Code Implementation

// WRONG - Don't do this:
const retainedPercent = 100 - (cashOutTaxRate / 100)
message = `Cashing out returns ${retainedPercent}% of proportional treasury share`

// CORRECT - Use bonding curve:
function calculateCashOutReturn(
  tokensToRedeem: number,
  totalSupply: number,
  surplus: number,
  cashOutTaxRate: number // 0-10000 basis points
): number {
  const r = cashOutTaxRate / 10000  // Convert basis points to 0-1
  const x = tokensToRedeem
  const y = totalSupply
  const s = surplus

  // Bonding curve formula
  return (x * s / y) * ((1 - r) + (r * x / y))
}

// For UI display with example percentage:
const r = cashOutTaxRate / 10000
const exampleFraction = 0.1  // 10% of supply
const returnFraction = exampleFraction * ((1 - r) + (r * exampleFraction))
const returnPercent = (returnFraction * 100).toFixed(1)
message = `Cashing out 10% of ${tokenSymbol} gets ~${returnPercent}% of treasury`

Verification

Test with known values:

• r = 0 (no tax): reclaimFraction = f (linear, full proportional return)
• r = 1 (100% tax): reclaimFraction = f * f (quadratic, harsh penalty)
• r = 0.1, f = 0.1: reclaimFraction = 0.091 (9.1%)
• r = 0.1, f = 0.5: reclaimFraction = 0.5 * (0.9 + 0.05) = 0.475 (47.5%)

Example

In the RulesetSchedule component's Juicy Summary:

// Cash out - redemption value using bonding curve formula
const cashOutTaxRate = ruleset.cashOutTaxRate / 10000
if (cashOutTaxRate >= 1) {
  actionItems.push({ action: 'caution', message: 'Cash outs disabled' })
} else if (cashOutTaxRate > 0) {
  const x = 0.1 // 10% of supply
  const y = x * ((1 - cashOutTaxRate) + (cashOutTaxRate * x))
  const returnPercent = (y * 100).toFixed(1)
  actionItems.push({
    action: 'cash-out',
    message: `Cashing out 10% of ${tokenSymbol} gets ~${returnPercent}% of treasury`,
  })
}

Notes

• The cashOutTaxRate in Juicebox V5 is stored in basis points (0-10000)
• A rate of 10000 (100%) means cash outs are effectively disabled
• The formula assumes the treasury "overflow" is the redeemable amount
• This bonding curve incentivizes holding - early/small cash outs get better rates
• The CashOutCurve visualization component can show this graphically

References

• Juicebox V5 JBRulesets contract
• Cash out bonding curve formula: y = (o * x / s) * ((1 - r) + (r * x / s))
  • Normalized to: y = x * ((1 - r) + (r * x)) where x is fraction of supply