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

$$\begin{aligned} W_{\text{Aave}} &: \text{ idle liquidity in Aave (earns }\text{IR}_{\text{SOFR}}\text{)} \\[2pt] W_{n} &: \text{ weight of merchant }n \\ &: \bigl(\sum_{n} W_{n}=1-W_{\text{Aave}}\bigr) \end{aligned}$$

Cash-flows are then split between the senior and junior tranches:

$$W_{\text{USD3}}\;\text{IR}_{\text{USD3}} + W_{\text{sUSD3}}\;\text{IR}_{\text{sUSD3}} = \text{IR}_{\text{Pool}},\qquad W_{\text{USD3}} = 0.85,\; W_{\text{sUSD3}} = 0.15$$

USD3 and sUSD3 APY

$$\text{IR}_{\text{USD3}} = \frac{\text{IR}_{\text{Pool}} - W_{\text{sUSD3}}\;\text{IR}_{\text{sUSD3}}} {W_{\text{USD3}}}$$

USD3 receives interest first and benefits from a real-time cash reserve that enables most redemptions to clear instantly.

$$\text{IR}_{\text{sUSD3}} = \text{IR}_{\text{USD3}} + \frac{\bigl(\text{Excess Spread} - \text{Reserve Accrual}\bigr)} {W_{\text{sUSD3}}}$$

sUSD3 earns every remaining basis-point of spread after senior distributions and reserve top-ups, but it also absorbs first losses.

Merchant Discount Factor Rate

3Jane gives you an upfront advance and, in return, buys a fixed specified amount of your future yield. The Discount Factor Rate (DFR) is a discount that reduces the specified amount if you repay the advance amount early, effectively charging you less. The discount shrinks towards zero over time as the days since funding increases.

$$\text{RP}(N) = A \times \left( 1 + \sum_{n=1}^{N} \text{P}_{n} \right)\\[2em] \text{DFR}(N) = 1 - \frac{\mathrm{RP}(N) - A}{\mathrm{A} \times (F-1)}$$

$$\begin{aligned} N &: \text{days since funding} \\[2pt] A &: \text{advance amount at funding} \\[2pt] \text{F} &: \text{fixed Factor (set at funding)} \\[2pt] \text{RP} &: \text{repurchase amount by day N} \\[2pt] \text{DFR} &: \text{discount factor rate by day N} \\[2pt] \text{P}_{n} &: \text{daily pacing increment} \\[2pt] \end{aligned}$$

Each day, a tiny pacing increment is applied:

(1) base factor: the pool’s baseline conditions (utilization)

(2) credit risk factor: your credit risk profile

(3) urgency factor: whether you were late that day

Those three slices add up to your daily fraction P_n​.

$$\begin{aligned} \text{P}_{n} &: \text{B}_{n} + \text{C}_{n} + \text{L}_{n} \\[2pt] \text{B}_{n} &: \text{implied base apy, expressed as a (1) day factor, pool-wide. Derived from the pool’s utilization curve} \\[2pt] \text{C}_{n} &: \text{implied credit risk apy, expressed as a (1) day factor, per-user. Derived from the 3CA algorithm} \\[2pt] \text{L}_{n} &: \text{implied urgency apy, expressed as a (1) day factor, per-user. Applied on days flagged late} \\[2pt] \end{aligned}$$

Note: DFR according to the formula is updated daily (as of 11:59 p.m. UTC). Your real-time DFR (and hence early payoff amount) will be updated to include time elapsed from last day DFR prior to payment.

Example:

• Advance: A = 100,000

• Factor: F = 1.15

• Specified Amount: A⋅F = 115,000

D	Bn	Cn	Ln	Pn	Sum Pn	RP(N)	DFR(N)
1	0.000115	0.000049	0	0.000164	0.000164	100,016	99.8904%
2	0.000112	0.000052	0	0.000164	0.000328	100,032	99.7808%
3	0.000117	0.000046	0.000136	0.000301	0.000630	100,063	99.5799%
4	0.000109	0.000050	0	0.000160	0.000790	100,079	99.4731%
5	0.000120	0.000053	0	0.000173	0.000964	100,096	99.3571%