Jet Protocol

Margin Accounts Accounting

A margin account a ledger within a ledger, keeping track of assets and liabilities that the user has accrued through their interaction with integrated products. It is via the margin account that a user's deposits as construed as collateral against which the user can borrow or take other risk positions. Margin accounts keep the protocol safe by providing a liquidation mechanism to cover debts when necessary.
A particular user, identified by a public key, may have multiple margin accounts. These can be named for easy reference. The app allows seamless switching between margin accounts and for transferring assets between margin accounts. 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.


From an accounting perspective, a particular margin account can be viewed as a list of assets
A{\cal A}
and a list of liabilities
L{\cal L}
. Margin accounting proceeds in terms of the USD value of these positions.
The assets
and liabilities
of the margin account are given by
A=aAPaA = \sum_{a \in \cal{A}} P_a
L=lLPlL = \sum_{l \in \cal{L}} P_l
Pa0P_a \geq 0
​ and
Pl0P_l \geq 0
​ are the USD values of the corresponding positions. The equity or account value is given by
E=ALE = A - L
​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, denoted
wa w_a
, influence the contribution of assets to weighted collateral, which is given by
Kw=aAwaPaK_w = \sum_{a \in \cal{A}} w_a P_a
Liabilities imply a certain amount of required collateral that depends on the size of the liability and the required collateral factor, denoted
fl f_l
​. The required collateral is given by
Kr=lLPlflK_r = \sum_{l \in \cal{L}} { P_l \over f_l }
​The minimum equity condition is captured implicitly through the relationship between these quantities. A margin account is said to be healthy if the collateral weight- adjusted equity equals or exceeds the required collateral. That is, healthy accounts satisfy
KwLKrK_w - L \geq K_r
​Otherwise the account is considered unhealthy and therefore subject to liquidation.
The following metrics are also used throughout the app and SDK to shed light on the state of a margin account:
Leverage is defined as
leverage=AAL{\rm leverage} = { A \over A - L }
​Although a useful quantity when considering a portfolio, it does not connect directly with account health. A related quantity that does is the adjusted leverage, given by
adjusted leverage=KwKw(L+Kr){\rm adjusted\ leverage} = { K_w \over K_w - (L + K_r) }
The adjusted leverage is defined to be zero when
​ is zero and there are no liabilities, and to be infinity when
KwL+KrK_w \leq L + K_r
The adjusted leverage is equal to one when an account has assets but no liabilities, and increases to infinity at the liquidation threshold.
The account risk indicator is displayed prominently in the app. Account risk is defined to be
ρ=L+KrKw\rho = { L + K_r \over K_w }
​ is zero the account risk is zero if there are no liabilities, or infinity if there are.
The account risk indicator is zero for an account with no liabilities, and increases to one at the liquidation threshold.
This indicator has a direct connection to the change in value of collateral assets that would bring an account to the liquidation threshold. Let
​ denote the return on collateral asset
. We can define the collateral-weighted return as
R=aAwaPaKwraR=\sum_{a \in \cal {A}} {w_a P_a \over K_w} r_a
​If the risk indicator is
​ then the collateral-weighted return that would bring the account to the liquidation threshold is
R=ρ1R = \rho - 1
For example, suppose that a user has a USD loan backed by mSOL collateral. If the account risk indicator is
​, then a
decreased in the price of mSOL will bring the account to the liquidation threshold.
The amount of adjusted equity in excess of required collateral is called available collateral:
available collateral=(KwL)Kr{\rm available\ collateral} = (K_w - L) - K_r
​Available collateral is a USD quantity that expresses how close to liquidation a margin account is. The liquidation threshold lies at zero available collateral.