# Account Health

Avoiding liquidation risk

## What is Account health?

In essence, Account health is a proportion between your Borrow Limit(Borrow Capacity) and your Borrow Capacity Used.

$BC_{u} = \sum(CF_a * C_{(u, a)} *Deposit_{(u,a)} * Price_a)$

where, for user u and asset a:

• CF is asset's Collateral Factor

• C is 1 for assets used as collateral, otherwise 0

• Deposit is amount of asset deposited

• Price is the equivalent asset's price in U.S. Dollars

$\\ BCU_{u} = \sum((Borrow_{(u,a)} * Price_a) / LT_a)$

where

• Borrow is amount of asset borrowed

• LT is Liquidation Threshold for the asset a.

Altogether,

$AccountHealth_u = 1 - BCU_u/BC_u$

### Special case: Supply and Borrow in the same asset

It's a completely healthy situation to borrow the same asset as the collateral: Depositing amount D and borrowing amount B should effectively be seen as Deposit D-B, but only until Borrow starts exceeding Deposit. In this moment, a healthy account can become burned-out(with total negative saldo) and there's nothing liquidators can do about it.

To prevent that, an overlap_factor is introduced to smoothen the account health formula while still be tolerable with the same deposit-borrow asset:

If

$Borrow_{(u, a)} > C_{(u,a)} *Deposit_{(u,a)}$

Then

$BC_{u,a} =0 \\ BCU_{(u,a)} =( \frac{(Borrow_{(u, a)} - C_{(u,a)} *Deposit_{(u,a)})}{ LT_a} + OverlapCharge_{(u,a)}) * Price_a$

Otherwise

$BC_{u,a} = CF_a *(Deposit_{(u,a)}- Borrow_{(u,a)}) * Price_a \\ BCU_{(u,a)} = OverlapCharge_{(u,a)} * Price_a$

Given

$OverlapCharge_{(u,a)} = min(Borrow_{(u, a)} , C_{(u,a)} * Deposit_{(u,a)}) * overlap\_factor$

Liquidators can liquidate part of your debt when your Account Health goes below 0.

## Why has my Account health changed?

Even if you don't interact with the protocol, your account health is subject to change:

• Your Deposit increased or decreased its value

• Your Borrows increased or decreased its value

• Interest on your deposits/borrows has been accounted.

• Your debt has been liquidated in order to increase your account health

## What is liquidation?

Liquidators can liquidate part of your debt when your Account Health goes below 0%. This means, when your Account Health goes below 0%, a liquidator can step in and take up to 50% of your debt for one asset and the corresponding amount of your deposit + premium. The related parameters(Liquidation Threshold and Liquidation Penalty) are listed in "Asset Parameters" section.

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