> For the complete documentation index, see [llms.txt](https://docs.pareto.credit/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.pareto.credit/product/credit-vaults/tranching.md).

# Tranching

Credit Vaults can **optionally** activate a tranching mechanism to allow users to tailor their lending experience to various risk appetites.

<details>

<summary>Senior class</summary>

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).

</details>

<details>

<summary>Junior class</summary>

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.

</details>

### 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

<details>

<summary>Formulae</summary>

#### Liquidity ratios <a href="#liquidity-ratios" id="liquidity-ratios"></a>

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 <a href="#senior-and-junior-yields" id="senior-and-junior-yields"></a>

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.&#x20;

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 <a href="#senior-coverage-and-junior-overperformance" id="senior-coverage-and-junior-overperformance"></a>

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

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

</details>

### Yield and loss scenarios <a href="#liquidity-ratios" id="liquidity-ratios"></a>

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.

<figure><img src="https://4223418165-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FVSPclqPyChB4NMxFfG2X%2Fuploads%2FJRgxizpwPVRUKdov3X1X%2FDocs_credit_vault_tranching_yield_loss.png?alt=media&amp;token=88df7d78-c139-4e43-965f-1c933a7427c6" alt=""><figcaption></figcaption></figure>

#### **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%.&#x20;

#### **Hedge case #1**

Majority of the total vault's liquidity lies on the Senior side (≥ 99%). See the [#formulae](#formulae "mention") section.&#x20;

| 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.&#x20;

| 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%.