# 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%.