Adaptive Yield Split

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The Adaptive Yield Split is a unique feature of YTs that manages the return distribution dynamically conditional to the liquidity deposited on each side (Senior/Junior) of the Tranche.

Mathematically, the formulas behind this mechanism consider mainly Senior and Junior liquidity ratios to compute Senior and Junior returns.

Please note that the labels used slightly change the naming at the contract level

• The Senior TVL ratio is _AATrancheSplitRatio

• The Senior Yield share is _trancheAPRSplitRatio

Liquidity ratios

First, we define the Senior and Junior TVL ratios as

$$\text{TVL ratio}_{Sr} = \frac{\text{Liquidity}_{Senior}}{\text{Liquidity}_{Senior + Junior}}$$

$$\text{TVL ratio}_{Jr} = \frac{\text{Liquidity}_{Junior}}{\text{Liquidity}_{Senior + Junior}}$$

Senior and Junior yields

The Senior return can be calculated as

$$\text{APY}_{Sr} = \text{Base APY} \times \text{Yield share}_{Sr} \qquad \tag{1}$$

where the Base APY is the underlying Tranches yield and the Yield share of the Senior side is a piecewise function conditional to the liquidity on the Senior tranche.

$$\text{Yield share}_{Sr} = \begin{dcases} 99\% & \text{if } \text{TVL ratio}_{Sr} \geq 99\% \\ \\ \dfrac{\text{Liquidity}_{Senior}}{\text{Liquidity}_{Senior + Junior}} & \text{if } \text{TVL ratio}_{Sr} > 50\% \\ \\ 50\% & \text{if } \text{TVL ratio}_{Sr} \leq 50\% \\ \end{dcases}$$

The Junior return can be calculated as

$$\text{APY}_{Jr} = \frac{(\text{Base APY} - \text{APY}_{Sr}) \times \text{TVL ratio}_{Sr}}{\text{TVL ratio}_{Jr}} + \text{Base APY} \qquad \tag{2}$$

Normal case

When Senior liquidity represents 50-99% of the funds in the Tranche, we use Equation (1) to compute the Yield share of the Senior side.

Alternatively, we use some fixed percentages. There are two hedge cases:

1. The majority of total Tranche's liquidity lying on the Senior side (more than 99%)

2. Less than half of total Tranche's liquidity lying on the Senior side (less than 50%)

$$\text{Yield share}_{Sr} = \begin{dcases} 99\% & \text{if } \dfrac{\text{Liquidity}_{Senior}}{\text{Liquidity}_{Senior + Junior}} \geq 99\% \\ \\ 50\% & \text{if } \dfrac{\text{Liquidity}_{Senior}}{\text{Liquidity}_{Senior + Junior}} \leq 50\% \\ \end{dcases}$$

In the first case, we set the Yield share of Senior Tranches equal to 99% while in the second case, we set it equal to 50%. These two hedge cases link to the principle that

• Senior Tranche receives most of the underlying yield when liquidity is low on the Junior side (i.e. low coverage on Senior funds), or receives a guaranteed minimum portion of the underlying yield when Junior liquidity is high (i.e. high coverage on Senior funds);

• Junior Tranche receives outperforming APYs on the Junior Tranches, no matter what the amount of deposited liquidity on the Senior is.

The guaranteed minimum portion, aka the Yield share of the Senior Tranches, has been set to half the Base APY (see HC#2) when the Senior liquidity is smaller than the Junior one.

Senior coverage and Junior overperformance

The formulas of the Senior coverage provided by the Junior counterparty and the Junior boosted yield vs the underlying return are

$$\text{Coverage}_{Sr} = \frac{\text{Liquidity}_{Junior}}{\text{Liquidity}_{Senior}}$$

$$\text{Overperformance}_{Jr} = \frac{\text{APY}_{Jr}}{\text{Base APY}}$$

The Senior coverage should not be confused with the overall Tranche coverage that is computed in proportion to the whole tranche TVL

$$\text{Tranche coverage} = \frac{\text{Liquidity}_{Junior}}{\text{Liquidity}_{Tranche}}$$

Examples

We compute the returns of the Senior and the Junior sides using the formulas listed previously, assuming

• An average underlying yield, Base APY, of 10%

• The total liquidity of the Tranche, Tranche TVL, equal to $10,000,000

Standard case: between 50 and 99% of the total Tranche's liquidity lying on the Senior side

Side	Liquidity	Expected APY
Senior	$8m	8%
Junior	$2m	18%

The Senior Yield share is equal to 80%.

Senior funds coverage is 25% and the Junior overperformance vs base APY is 1.8x. The Tranche coverage is 20%.

Hedge case 1: the majority of total Tranche's liquidity lying on the Senior side ($\geq$99%)

Side	Liquidity	Expected APY
Senior	$9.9m	10%
Junior	$100	20%

The Senior Yield share is set to 99% (HC#1).

Senior funds coverage is 0% and the Junior overperformance vs base APY is 1.99x. The Tranche coverage is 0% as well.

Hedge case 2: less than half of the total Tranche's liquidity lying on the Senior side ($\leq$50%)

Side	Liquidity	Expected APY
Senior	$4m	5%
Junior	$6m	13%

The Senior Yield share is set to 50% (HC#2).

Senior funds coverage is 150% and the Junior overperformance vs base APY is 1.33x. The Tranche coverage is 60%.