Holder Behavior Modeling

This page models how economically rational participants might behave given a cobuild's mechanism design—choosing between redeeming, holding, or borrowing based on network outcomes.

Three Available Actions

At any time, a holder with q tokens has three options:

Burn tokens for a share of the treasury (paying the cash-out tax) or sell on an AMM at market price (which arbitrage keeps between floor and ceiling).

Take no action and remain exposed to future changes in floor / AMM price.

Burn tokens as collateral, borrow less than their cash-out value, and optionally repay later to remint. Because loans are priced off the same convex redemption curve, they are always over-collateralized; the system remains solvent even if all loans default.

The stage parameters determine which action is individually rational under different scenarios.

Immediate Liquidity Needs

First, consider a purely myopic scenario where future expectations are ignored. A participant simply asks:

"I need liquidity now. Should I redeem or borrow?"

The relevant variables are:

• Cash-out tax rₖ
• Net loan proceeds factor a (what % of collateral's cash-out value is received after fees)
• Position size as fraction of supply x = q / S

Redemption vs Borrowing

When cash-out tax is below ~39%, redeeming yields more immediate liquidity than borrowing. Most cobuilds use 10–20% tax, so in practice: for immediate liquidity needs, redemption dominates.

Only at very high taxes (40%+) does borrowing begin to compete for large holders seeking immediate liquidity.

Forward-Looking Scenarios

Now consider participants who account for expected outcomes between time t₀ and future time t₁.

Three variables matter:

• External opportunity cost R — alternative yield available elsewhere (DeFi, treasuries, etc.)
• Expected token appreciation — floor / AMM price growth between t₀ and t₁
• Loan fee level a — net proceeds as fraction of collateral value

We model three outcome scenarios:

1. Unsuccessful network — token underperforms alternatives
2. Moderate success — steady but modest appreciation
3. Strong success — sustained compounding over years

Unsuccessful Network Scenario

In this model, participants believe:

• "Alternative opportunities outperform this token."

Formally, redemption beats holding when:

(1 + R) > P_sell(t₁, q) / P_sell(t₀, q)

In this scenario:

• Redemption dominates holding — If expected token appreciation is worse than external yield, rational behavior is to redeem and reallocate.

• Borrowing vs holding — For participants who want to maintain some exposure while reallocating capital, borrowing only beats holding if external return R clears the fee threshold:

  R > (1 − a) / a

  With default loan parameters:

  • 6-month loan (a ≈ 0.94) — Requires ~6% return over 6 months (~12% annualized)
  • 10-year loan (a ≈ 0.63) — Requires ~60% total return over 10 years (~5–6% annualized)

In an unsuccessful network model:

Most rational participants redeem. Borrowing only makes sense if external yield is genuinely attractive and the participant wants to maintain some token exposure.

Moderate Success Scenario

Assume the network performs adequately:

• Floor / AMM price drifts up over time
• But not by large multiples

With minimal external yield (R ≈ 0), the key comparison is borrowing vs redemption.

With no external yield, borrowing only makes sense if expected token appreciation beats the loan fee.

For typical parameters:

• 6-month loan (a ≈ 0.94) — Requires ~6% floor / price growth in 6 months (~11–12% annualized)

• 10-year loan (a ≈ 0.63) — Requires ~37% total floor growth over 10 years (~3–4% annualized)

In a moderate success model where floor growth of ~4–5% annually seems plausible:

• Holding is rational over redeeming
• 10-year loans become viable: slow but steady growth covers the loan fee, and borrowed capital can be deployed elsewhere

If expected growth is below ~3% annually:

• Holding may still be rational for those who value the exposure
• Loans add little value unless external yield R is non-trivial

Strong Success Scenario

This models a network that achieves product-market fit: real revenue and a floor that compounds over years.

Redemption vs Holding

Holding beats redemption when expected appreciation exceeds external opportunity cost:

Hold beats Redeem when:
P_sell(t₁, q) / P_sell(t₀, q) > (1 + R)

In this regime, optimistic participants hold or acquire more. Redemption is for those who believe they can do better elsewhere.

Loan Thresholds

Two thresholds emerge:

• Borrowing vs Holding

  For participants maintaining exposure either way, borrowing beats simply holding when external return on borrowed capital clears:

  R > (1 − a) / a

  For a 10-year window (a ≈ 0.63), that's the ~60% total over 10 years (~5–6%/yr) threshold. Once external yield beats that, "hold + borrow" strictly dominates "just hold".

• Borrowing vs Redemption (with R ≈ 0)

  If external opportunities are limited and loans are mainly used to access liquidity sooner, the relevant condition is that token appreciation beats the fee: roughly ~37% total over 10 years (~3–4%/yr) for long-dated loans.

In other words:

• If token growth of ~1.4× over 10 years (~3–4% annualized) seems plausible, long-dated loans are individually rational vs immediate redemption.
• If external yield of ~5–6% annually is achievable, loans become compelling vs just holding—participants keep exposure and earn yield on borrowed capital.

Both conditions can easily hold in a successful network, so rational behavior in this scenario is:

• Don't redeem
• Do hold
• Use loans opportunistically when good external opportunities or liquidity needs arise

Parameter Effects

Stage parameters don't just change the math—they also signal what kind of behavior the network is designed for.

Cash-out Tax

Higher cash-out taxes discourage immediate redemption, but also require stronger long-term growth to make loans worthwhile versus just leaving.

Issuance Growth

• Faster issuance cuts (steeper ceiling) create more growth potential and make holding + borrowing more attractive if the network succeeds.

• But if the ceiling outruns reality for too long, you enter the "runaway" regime:

  • new issuance effectively stops
  • inbound flows mostly route through the AMM
  • AMM liquidity can thin out if demand is mostly speculative

Calibrating the ceiling so it roughly tracks plausible long-term demand is key to avoiding multi-year runaway.

Summary

Parameter choices implicitly select for certain behavioral patterns:

• High uncertainty and churn expected → tilt toward lower cash-out tax, accept more redemptions, and lean on floor mechanics to reward those who stay.

• Strong long-term growth expected → design for:

  • a modest-high cash-out tax (to reward stayers and enable loans)
  • an issuance schedule that doesn't outpace realistic demand (to avoid runaway)
  • clear UX around loans as the primary liquidity mechanism that preserves exposure