Balance Sheet
Description of the ProbityDAO's balance sheet.

# Accounting Equation

The protocol's key objective is to maintain solvency at all times. We modify the Accounting Equation definition of ASSETS = LIABILITIES + CAPITAL as follows:
$Reserves_{AUR}+Loans_{AUR}=Interest_{TCN}+Supply_{AUR}$

## Equation Variables

The variables are broken down in the table below. The balance sheet is best viewed from the perspective of the suppliers. Since the protocol is trustless, the assets are owned directly by the suppliers and the interest owed is redeemable at any time. The collateral underlying the Aurei supply is also redeemable at any time.
Variable
Description
Type
$Reserves_{AUR}$
Reserve amount of unallocated AUR
Asset
$Loans_{AUR}$
The loan balance due in AUR
Asset
$Interest_{TCN}$
Interest payable in TCN
Liability
$Supply_{AUR}$
The AUR supply
Capital

## Utilization Ratio

We define the utilization ratio U as:
$U=\frac{Loans_{AUR}}{Supply_{AUR}}$
$Loans_{AUR}$
can be retrieved by calling totalDebt() in the Teller contract.
$Supply_{AUR}$
can be retrieved by calling totalSupply() in the Aurei contract.

# Collateral Requirement

We can rewrite the left-hand side like so, where
$P_C$
is the price of the underlying collateral type,
$C$
is the collateral amount, and
$M$
is the minimum collateral ratio for the collateral type:
$Supply_{AUR}=\frac{P_C \cdot C}{M_C}$
We can rewrite the equation as an inequality such that the value of the underlying collateral in the system must be greater than or equal to the amount of Aurei assets:
$Reserves_{AUR}+Loans_{AUR}<=Interest_{TCN}+\frac{P_C \cdot C}{M_C}$

# Example

Take the following variables at the time t = 0:
Left-hand side
RESERVES
LOANS
$1,000,000$9,000,000
Right-hand side
INTEREST PAYABLE
COLLATERAL
COLLATERAL_PRICE
MIN_COLLATERAL_RATIO
$0 15,000,000$1
150%
This gives us the starting inequality:
This system is solvent but unhealthy because if the collateral price drops, the system will be insolvent. If the price drops, underlying collateral is liquidated, in turn reducing the Aurei reserves to maintain the solvency condition. Liquidations reduce the Aurei supply which increases the interest rate, incentivizing borrowers to repay their debt. In the next section, we discuss interest rates.