# Account Health

## 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

$$
OverlapCharge\_{(u,a)} = min(Borrow\_{(u, a)} , C\_{(u,a)} \* Deposit\_{(u,a)}) \* overlap\_factor
$$

{% hint style="warning" %}
Liquidators can liquidate part of your debt when your Account Health goes below 0.
{% endhint %}

## 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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