# Adaptive Yield Split
> 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](#liquidity-ratios) to compute [Senior and Junior returns](#senior-and-junior-yields).
{% hint style="info" %}
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`
{% endhint %}
### 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) ](#senior-and-junior-yields)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%.
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