> For the complete documentation index, see [llms.txt](https://docs.3jane.xyz/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.3jane.xyz/usd3-susd3/pool-interest-rates.md).

# Pool Interest Rates

## Pool-Level APY Dynamics

The aggregate variable rate earned by the pool is:

$$
\text{IR}*{\text{Pool}}
\= W*{\text{Aave}};\text{IR}\_{\text{SOFR}}

* \sum\_{n=1}^{N} W\_{n},\text{IR}\_{n}
  $$

where

$$
\begin{aligned}
W\_{\text{Aave}} &: \text{ idle liquidity in Aave (earns }\text{IR}*{\text{SOFR}}\text{)} \\\[2pt]
W*{n}           &: \text{ weight of position }n \text{ (a credit line or facility)} \\
&: \bigl(\sum\_{n} W\_{n}=1-W\_{\text{Aave}}\bigr)
\end{aligned}
$$

Whatever the pool earns is then split between the senior (USD3) and junior (sUSD3) tranches.

## USD3 and sUSD3 APY

In traditional tranching, the senior earns a **fixed** coupon and the junior takes the residual — the junior absorbs all the variance to keep the senior's rate constant. 3Jane works differently. A single **tranche share variant** (`TRANCHE_SHARE_VARIANT`), denoted `s`, splits pool interest in fixed proportions, so **both** tranches earn a variable rate that floats with what the backing generates:

The tranche share variant is a variable protocol parameter and may be adjusted upward or downward by 3Jane. Adjustments take into account realized and expected pool performance, competitive yields for both tranches, and the adequacy of first-loss capital.

$$
\text{IR}*{\text{USD3}}
\= \frac{(1-s),\text{IR}*{\text{Pool}}}{W\_{\text{USD3}}},
\qquad
\text{IR}*{\text{sUSD3}}
\= \frac{s,\text{IR}*{\text{Pool}}}{W\_{\text{sUSD3}}}
$$

$$
\begin{aligned}
s              &: \text{tranche share variant — the junior's fixed fraction of pool interest} \\\[2pt]
W\_{\text{USD3}}, W\_{\text{sUSD3}} &: \text{capital weights of each tranche } (W\_{\text{USD3}}+W\_{\text{sUSD3}}=1) \\\[2pt]
\end{aligned}
$$

The junior receives the fraction `s` of pool interest; the senior receives the remaining `1 − s`. Two consequences follow:

* **The senior (USD3) coupon is variable.** Because USD3 takes a fixed *proportion* rather than a fixed *rate*, its APY rises and falls with pool yield. There is no promised fixed rate to defend.
* **The junior (sUSD3) is more compelling.** The junior never has to give up part of its share to top a fixed senior coupon back up to target. It keeps its full slice of upside when the pool earns more — and, as first-loss capital, bears the downside when the pool earns less or takes losses.

USD3 can be redeemed up to the tranche ratio, and remains senior in the waterfall: losses hit sUSD3 before USD3.

### Example

Take a pool generating **13%**, with capital weights **85% USD3 / 15% sUSD3** and a tranche share variant of **`s = 0.30`** (30% of pool interest to the junior, 70% to the senior):

| Pool yield | → sUSD3 (junior, s = 0.30)                  | → USD3 (senior, 1 − s = 0.70)               |
| ---------- | ------------------------------------------- | ------------------------------------------- |
| 13%        | 30% × 13% over 15% of capital → ≈ **26.0%** | 70% × 13% over 85% of capital → ≈ **10.7%** |
| 15%        | 30% × 15% over 15% of capital → ≈ **30.0%** | 70% × 15% over 85% of capital → ≈ **12.4%** |

The split percentages are fixed; the resulting APYs move with the pool. 3Jane is not promising the senior any particular rate — when the backing generates more, both tranches earn more, and when it generates less, both earn less.

*Figures are illustrative; the tranche share variant and pool yield are parameters that change over time.*