Margin Accounting Formulas

A margin account is a ledger within a ledger, keeping track of assets and liabilities that the user has accrued through their interaction with integrated products. It is through the margin account that a user's deposits are used as collateral, allowing them to borrow assets or take other risk positions.

Margin accounts also serve a critical role in risk management, ensuring Glow Finance remains solvent by triggering liquidations when an account becomes unhealthy.

Key Properties of Margin Accounts

• Users may open multiple margin accounts under a single wallet.
• Accounts are isolated: Liquidation in one margin account does not impact other accounts.
• Users can switch between accounts seamlessly and transfer assets between them.

A particular user, identified by a public key, may have multiple margin accounts. These accounts can be named for easy reference. The app allows seamless switching between margin accounts and for transferring assets between them.

From a risk perspective, all margin accounts are completely isolated. Liquidations only affect a particular unhealthy account, even if the user being liquidated also owns other margin accounts.

Accounting Overview

From an accounting perspective, a margin account can be viewed as a list of assets and a list of liabilities. Margin accounting proceeds in terms of the USD value of these positions.

Assets and Liabilities

The assets (A) and liabilities (L) of the margin account are given by:

$A = \sum_{a \in A} P_a$

$L = \sum_{i \in L} P_i$

where:

• $P_a \geq 0$ represents the USD value of assets.
• $P_i \geq 0$ represents the USD value of liabilities.

Equity Calculation

The equity (E), also referred to as the account value, is calculated as:

E = A - L

This represents the net value of the account after subtracting liabilities from assets.

Weighted Collateral Calculation

A margin account is required to have a minimum amount of equity in order to be considered healthy. The amount depends on the composition of assets and liabilities.

Collateral weights $w_a$ determine the contribution of assets to weighted collateral, which is given by:

$K_w = \sum_{a \in A} w_a P_a$

where:

• $w_a$ is the collateral weight assigned to each asset.

Required Collateral Calculation

Borrowing creates liabilities that require collateral backing. The required collateral $K_r$ is determined by:

$K_r = \sum_{i \in L} \frac{P_i}{f_i}$

where:

• $f_i$ is the required collateral factor, which varies by asset and risk model.

A margin account is considered healthy if the weighted collateral exceeds the required collateral plus liabilities:

$K_w - L \geq K_r$

If this condition is not met, the account is considered unhealthy and may be subject to liquidation.

Leverage and Risk Metrics

Leverage Calculation

Leverage is a measure of how much an account is borrowing relative to its equity. It is defined as:

$\text{leverage} = \frac{A}{A - L}$

This indicates the multiplier effect of borrowing on the account’s exposure.

Adjusted Leverage

Adjusted leverage accounts for collateral weight and required collateral:

$\text{adjusted leverage} = \frac{K_w}{K_w - (L + K_r)}$

• Adjusted leverage is zero when $K_w$ is zero and there are no liabilities.
• Adjusted leverage increases as an account takes on more debt relative to collateral.
• If $K_w \leq L + K_r$, adjusted leverage approaches infinity, meaning the account is at the liquidation threshold.

Account Risk Indicator

The account risk indicator ($\rho$) helps determine how close an account is to liquidation:

$\rho = \frac{L + K_r}{K_w}$

• If $\rho = 1$, the account is at the liquidation threshold.
• If $\rho > 1$, the account is over-leveraged and at high risk.
• The app prevents users from taking actions that would immediately liquidate their accounts by enforcing setup checks.

Collateral-Weighted Return

The risk indicator is linked to collateral-weighted return ($R$):

R = $\sum_{a \in A} \frac{w_a P_a}{K_w} r_a$

where $r_a$ is the return on collateral asset $a$.

The return required to bring an account to liquidation is given by:

R = $\rho - 1$

For example, if $\rho = 0.90$, then a 10% decrease in collateral value will trigger liquidation.

Available Collateral Calculation

The excess collateral available before liquidation is given by:

$\text{available collateral} = (K_w - L) - K_r$

This represents the buffer before liquidation occurs.

Liquidation occurs when available collateral reaches zero.

For further details, refer to the Liquidation page.