# Tranching
Credit Vaults can **optionally** activate a tranching mechanism to allow users to tailor their lending experience to various risk appetites.
Senior class
This class offers **intrinsic protection on funds**, given by Junior deposits. \
Senior Tranche LPs intrinsically **have a first lien on the underlying assets**, i.e., they are first in line to be repaid in case of default (hack or loss of funds).
Junior class
This class offers a **greater yield** by dragging more exposure to the underlying yield.\
Junior Tranche LPs have a second lien or no lien at all in case of default (hack or loss of funds).
The Junior class is designed to receive a higher share of yield compared to the Senior one, to proportionally compensate for the higher risk taken.
### Yield split
The Tranching feature relies on a unique mechanism that manages the return distribution dynamically conditional to the liquidity deposited on each side (Senior, Junior) of the Credit Vault.
* **Senior class** receives most of the underlying yield when liquidity is low on the Junior side (low coverage), or receives a guaranteed minimum portion of the underlying yield when Junior liquidity is high (high coverage)
* **Junior class** receives outperforming APYs, no matter the Senior class liquidity
Formulae
#### 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
$$\text{APY}*{Jr} = \frac{(\text{Base APY} - \text{APY}*{Sr}) \times \text{TVL ratio}*{Sr}}{\text{TVL ratio}*{Jr}} + \text{Base APY} \qquad \tag{2}$$
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 the vault's liquidity lying on the Senior side (more than 99%)
2. Less than half of the vault'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 the Senior class equal to 99% while in the second case, we set it equal to 50%. These two hedge cases link to the principle that
> * **Senior class** receives most of the underlying yield when liquidity is low on the Junior side (low coverage), or receives a guaranteed minimum portion of the underlying yield when Junior liquidity is high (high coverage)
> * **Junior class** receives outperforming APYs, no matter the Senior class liquidity
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
$$\text{Tranche coverage} = \frac{\text{Liquidity}*{Junior}}{\text{Liquidity}*{Tranche}}$$
### Yield and loss scenarios
Let's assume to have a Credit Vault generating a 10% yield (base APY), where users deposit 10,000,000 DAI split as follows: 70% on the Senior class, and 30% on the Junior class.
#### **Standard case**
Between 50 and 99% of the total vault's liquidity lying on the Senior side
| Side | Liquidity | Expected APY |
| ------ | ------------- | ------------ |
| Senior | 8,000,000 DAI | 8% |
| Junior | 2,000,000 DAI | 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**
Majority of the total vault's liquidity lies on the Senior side (≥ 99%). See the [#formulae](#formulae "mention") section.
| Side | Liquidity | Expected APY |
| ------ | ------------- | ------------ |
| Senior | 9,999,900 DAI | 10% |
| Junior | 100 DAI | 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 vault's liquidity lies on the Senior side (≤ 50%). See the [#formulae](#formulae "mention") section.
| Side | Liquidity | Expected APY |
| ------ | ------------- | ------------ |
| Senior | 4,000,000 DAI | 5% |
| Junior | 6,000,000 DAI | 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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