# Rehypothecation

Rehypothecation is Fira's mechanism for making idle reserves productive. A portion of FW-USDC held in fixed-rate market pools is allocated to a variable-rate vault, where it earns floating yield. That yield flows to Coupon Token (CT) holders.

This creates the bridge between Fira's fixed-rate and floating-rate layers: LPs provide liquidity to the fixed-rate AMM, and the unused portion earns floating-rate yield in the background.

## Reserve Allocation Model

The system manages reserves through a **reserve ratio φ** — the fraction of liquid (unrehypothecated) reserves relative to total FW-USDC in the pool:

$$
\varphi = \frac{\text{USDC}*{\text{reserve}}}{\text{FW-USDC}*{\text{pool}}}\
$$

Three parameters control the allocation:

| Parameter              | Role                                                                    |
| ---------------------- | ----------------------------------------------------------------------- |
| $$\varphi \_{min}$$    | Minimum reserve ratio — below this, the system withdraws from the vault |
| $$\varphi \_{max}$$    | Maximum reserve ratio — above this, the system deposits into the vault  |
| $$\varphi \_{target}$$ | Target ratio — rebalancing restores φ to this value                     |

Currently, these are respectively set to 89.89%, 91% and 90%.

### How Rebalancing Works

The reserve ratio is checked on every market swap. If φ falls outside \[φ\_min, φ\_max]:

* $$\varphi < \varphi \_{min}$$ — Too much capital is rehypothecated. The system withdraws FW-USDC from the variable-rate vault back to liquid reserves.
* $$\varphi > \varphi \_{max}$$ — Too much capital sits idle. The system deposits excess FW-USDC into the variable-rate vault.

In both cases, the system restores φ to φ\_target.

## How CT Holders Earn Yield

All interest earned by rehypothecated liquidity is distributed to outstanding Coupon Token (CT) holders. The mechanism:

1. Rehypothecated USDC earns floating yield in the variable-rate vault
2. This yield increases the FW wrapping rate μ(t) — each FW represents more underlying over time
3. CT holders can claim the difference between the current and previous wrapping rates

### Claimable Yield

$$
\text{CT}*{\text{claim}}(t) = \left(1 - \frac{\mu\_s(t^\*)}{\mu\_s(t)}\right) \times \frac{\text{Balance}*{\text{CT}}(t)}{\mu\_s (t\*)}
$$

Where $$\mu \_s(t)$$ is the modified wrapping rate (see [Token Mechanics](https://docs.fira.money/protocol/token-mechanics)) at the last update and μ(t) is the current rate. The yield is distributed proportionally to CT balances, paid in FW-USDC.

After maturity, CT no longer accrues rehypothecation yield — only active markets generate returns.

## CT Price Dynamics

CT is a hybrid instrument: its cash flows come from a floating-rate source, but it trades in the fixed-rate market. Regardless, a natural price equilibrium can be achieved:

* **CT overpriced** relative to expected future yield → holders sell → FW supply increases in pool → more capital for rehypothecation → higher future yields for remaining CT → price adjusts down
* **CT underpriced** → buyers enter → FW supply decreases → less rehypothecation → lower future yields → price adjusts up

In equilibrium, the CT market price equals the discounted expected value of remaining rehypothecation yield.

## Governance

All rehypothecation parameters (φ\_min, φ\_max, φ\_target) are set by the DAO. Key principles:

* **Liquidity first** — The DAO prioritizes redemption availability over yield maximization
* **Conservative by design** — Parameters are chosen through stress testing to ensure sufficient liquidity under adverse conditions
* **Manual updates** — Parameters are not automated; updates happen no more than monthly or quarterly
* **Future delegation** — The DAO may delegate parameter management to a curator

## Related

* [Fixed-Rate Markets](https://docs.fira.money/protocol/fixed-rate-markets) — Where rehypothecated reserves originate
* [Floating-Rate Markets](https://docs.fira.money/protocol/floating-rate-markets) — Where rehypothecated capital earns yield
* [Token Mechanics](https://docs.fira.money/protocol/token-mechanics) — CT token properties and behavior
* [Whitepaper](https://docs.fira.money/resources/whitepaper) — Full mathematical treatment


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