This article provides the necessary formulas and explanations to calculate and manage the margin requirements of your leveraged derivatives and spot margin positions.
Definitions and Formulas
|
Term |
Definition |
Formulas |
|
Total Account Value |
Total value of the collateral and unrealized PnL within a specific subaccount. |
Total Account Collateral + Unrealized PnL |
|
Position Notional |
Notional size of your position in USD |
Position size * Market price |
|
Margin Fraction (MF) |
Fraction of Total Account Value vs Total Position Notional in the subaccount |
Total Account Value / Total Position Notional |
|
IMF Factor |
Multiplier assigned to each asset on FTX. It is set based on factors such as liquidity or market capitalization. |
See values here. |
|
IMF Weight |
Multiplier of the margin required to open a new leveraged position |
See values here. |
|
MMF Weight |
Multiplier of the margin required to maintain an existing leveraged position |
See values here. |
|
Max Leverage |
Max allowable leverage to open new derivatives or spot margin positions set by the user. |
A subaccount's max leverage can be adjusted on the profile page under the Margin section. Max allowable leverage on spot margin is 10x. |
|
Base IMF |
The minimum Initial Margin Fraction needed to open a new perpetual swap or futures position. |
1 / Maximum account leverage set by user |
|
Position Open Size |
The maximum Total Position Size if your outstanding long or short orders were filled. |
MAX (ABS [position size + open long orders], ABS [position size - open short orders] ) |
|
Position Open Size Notional |
Notional value in USD of your position, including open orders. |
Position Open Size * Mark Price |
|
Total Open Position Notional |
The total notional amount in USD of all open derivatives or spot margin positions if your outstanding long or short orders were filled. |
SUM (Position Open Size1 * Mark Price1, Position Open Size2 * Mark Price2, …) For all positions |
|
Collateral Used |
Collateral currently being used by a single derivatives or spot margin position |
Position IMF * Position Notional |
|
Total Collateral Used |
Total of collateral being used by all open derivatives or spot margin positions in the subaccount, as well as collateral tied up in open orders, including spot. |
= sum (Position1 Open Size Notional * Position1 IMF, Position2 Open Size Notional * Position2 IMF,...) + sum(Spot Order1 Size * Mark Price, Spot Order2 Size * Mark Price,...) |
|
Free Collateral |
Total collateral available that can be used for opening new positions and withdrawn from the exchange, excluding collateral locked in open orders or open positions. |
Total Account Collateral - Total Collateral Used |
|
Short Size and Long Size |
The max long or short you could get for a particular position considering your outstanding open orders. Used to calculate your Position IMF. |
Long Size = max (position size + open long order size, 0)
Short Size = -min (position size - open long order size, 0)
If position is short, position size is negative. Otherwise, positive. |
|
Position Initial Margin Fraction (Position IMF) |
The minimum margin fraction required for a particular derivatives position.
Long positions are capped at 1 plus fees required to exit the position (considering open orders). |
If position is long:
|
|
Position Maintenance Margin Fraction (Position MMF) |
The minimum margin fraction required to avoid liquidation on a derivatives position |
max(3%, 0.6 * IMF Factor * sqrt [position open size in tokens]) * MMF Weight |
|
Spot Margin Base IMF |
Needed to calculate the minimum margin fraction required for a particular position. |
If borrowing USD: = 1 / max account leverage If borrowing non-USD assets (e.g. BTC) = max ( 1 / max account leverage, 1.1 / Total Weight - 1 ) (See asset’s Total Weight here) |
|
Spot Margin IMF |
The minimum margin fraction required to open a spot margin position, applicable to positions of all sizes. |
= max( Spot Margin Base IMF, IMF factor * sqrt [position size in tokens] ) * IMF Weight |
|
Spot Margin MMF |
The minimum margin fraction required to avoid liquidation on a spot margin position |
If borrowing USD: = 3% If borrowing non-USD assets (e.g. BTC) = max ( 1.03 / Total Weight - 1, 0.6 * IMF factor * sqrt [position size in tokens] ) * MMF Weight |
|
Account Initial Margin Fraction (Account IMF) |
The minimum account margin fraction required to increase position size, equal to average of position IMF for all account positions weighed by position open notional |
Sum ( [ Position Notional / Total Position Notional ] * Position IMF ) of all derivatives and spot margin positions in subaccount |
|
Account Maintenance Margin Fraction (Account MMF) |
The minimum account MF needed to avoid getting liquidated, equal to average of positions MMF weighed by the positions notional. |
Sum ( [ Position Notional / Total Position Notional ] * Position MMF ) of all derivatives and spot margin positions in subaccount |
|
Auto Close Margin Fraction (ACMF) |
The minimum margin fraction needed to avoid the assets and positions of a given sub being liquidated via backstop liquidity providers. |
max( Account MMF / 2, Account MMF - 0.06 ) |
|
Open Margin Fraction |
Your current margin fraction, including open positions and open orders (derivatives and spot margin). If OMF = IMF, you can’t open more positions. |
MAX (0, MIN [Total Account Value, Collateral] ) / Total Open Position Notional |
|
Zero Price (ZP) |
This is the mark price (MP) that would set a subaccount’s Total Account Value to 0. |
Mark Price * (1 - Margin Fraction) if long, Mark Price * (1 + Margin Fraction) if short. |
|
Position Margin Per Dollar (PMPD) |
Used for calculating Position Zero Price (PZP) |
[(Position maintenance collateral used) / (sum of Position maintenance collateral used for all account positions)] * Total account value / abs(position notional)
Maintenance collateral = Position notional * Position MMF |
|
Position Zero Price (PZP) |
The fill price a bankrupted account would receive for a particular position. |
MP * (1 - PMPD) if long, MP * (1 + PMPD) if short |
|
Unused Collateral |
Total collateral available that can be used for opening new positions and withdrawn from the exchange, including open orders. |
max(OMF - IMF, 0) * total open position notional |
|
Mark Price (MP) |
Median of best bid, best ask, and last traded price (LTP). |
If futures market is not paused = median(best bid, best offer, last traded price) If futures market is paused = index price + (LTP - index price) |
Examples
This example will walk you through the terms and formulas presented above, and calculate how much margin is required to open new derivatives and spot margin positions, and also determine at which margin fraction the positions and account would be liquidated.
Assume that your subaccount has $50,000 USD and 2.5 BTC in collateral, max leverage has been set to 10x, and also spot margin has been enabled. We will open the following positions in this order and finalize the example by calculating our Account IMF and MMF:
- Buy BTC-PERP (long)
- Short LTC/USD using spot margin
- Sell ETH-9030 (short)
Opening and Managing a Futures Position
Before opening the 20 BTC-PERP long position, here’s an overview your account's collateral.
Total Account Value
The account has the following in collateral:
- USD = $50,000
- BTC = 2.5 ($50,000 at current prices assuming BTC/USD is trading at $20,000)
- Total collateral value (in USD) = $100,000
In theory, your total collateral value in USD is $100,000 when we add up the USD and the current value of the BTC balance. However, FTX accepts a wide variety of non-USD assets as collateral, and each of them have different collateral weights for opening new positions and managing existing positions (more info here).
In the case of BTC, it has an initial collateral weight of 0.95, which means that for opening new positions, your 2.5 BTC would be worth $47,500 rather than the full $50,000 after applying the haircut. However, since spot margin is enabled for this subaccount, BTC’s total weight of 0.975 will be used to determine the value of your collateral to open new positions, as well as when the position is already open once the position is opened (if spot margin is disabled, Total Weight is only used for the latter).
Therefore, the total unused collateral available for opening new positions is $97,500. Here's a full overview of the account's collateral:
|
Collateral Overview |
|||
|
Collateral |
USD |
BTC |
Total |
|
Amount |
50,000 |
2.5 |
50,003 |
|
Mark Price |
$1 |
$20,000 |
- |
|
USD Amount |
$50,000 |
$50,000 |
$100,000 |
|
Initial Weight |
1 |
0.95 |
- |
|
Initial Collateral |
$50,000 |
$47,500 |
$97,500 |
|
Total Weight |
1 |
0.975 |
- |
|
Total Collateral |
$50,000 |
$48,750 |
$98,750 |
Calculating IMF - Determining how much collateral/margin is needed to open a position
To calculate the Initial Margin Fraction for the BTC-PERP position, we use the following formula:
Position IMF = MIN (MAX [Base IMF , IMF Factor * sqrt {position open size in tokens}] * IMF Weight, 1 + fee rate * [short size + long size] )
= MIN (MAX [1/10 , 0.002 * sqrt {20} ] * 1, 1 + 0.0005 * [0 + 20] )
= MIN (MAX [0.1 , 0.004], 1.01)
= 0.1 = 10%
So if we want to go long 20 BTC-PERP and each BTC-PERP is trading at $20,000, for a Position Notional of $400,000, we will need at least $40,000 in collateral to open the position.
The account has enough collateral, so we go ahead and open the position.
Note about factors that influence IMF:
Keep in mind that your position’s IMF can increase (i.e. reducing your max leverage to open that position) based on the factors included in the formula, including position size, IMF factor, and IMF weight.
As an example, imagine you’re trying to open a 5000 BTC-PERP short position worth $100,000,000 (assuming BTC-PERP is trading at $20,000). Using the same formula:
Position IMF = MAX (1/10 , 0.002 * sqrt [5000] ) = MAX (0.1 , 0.141 )
Position IMF = 0.141 = 14.1%
So, even though your max leverage is 10x (making your Base IMF 10%), because you are trying to open a large position worth $100,000,000, your initial margin requirement increases to 14%. There can be cases where the IMF is above 100%. Keep in mind however, that this is only possible with short positions, as the IMF for long positions is capped at 100%.
Managing Position - Calculating Maintenance Margin Fraction
After opening the 20 BTC-PERP position, your Margin Fraction is as follows:
= Total Account Value / Total Position Notional
= $98,750 / $400,000
= 24.69%
Now, let's calculate your Maintenance Margin Fraction to understand at which point the position would start getting liquidated (assuming that’s the only open position in the account. We will explore how multiple positions affect your account's MMF and IMF later on in this example).
MMF = max(3%, 0.6 * IMF Factor * sqrt [position open size in tokens]) * MMF Weight
= max (3%, 0.6 * 0.002 * sqrt[20] )) * 1
= 3%
Opening and Managing Spot Margin Position
Next, we’re now going to short 200 LTC @ $50 on the LTC/USD market using spot margin. Keep in mind that IMF formula for spot margin positions is different than the formula for derivatives.
Calculating Spot Margin IMF
Because you're shorting LTC, that means that you're going to borrow LTC in order to sell it. When borrowing non-USD assets, the Spot Margin Base IMF formula is as follows:
= max ( 1 / max account leverage, 1.1 / Total Weight - 1 )
= max (0.1, 1.1 / 0.95 - 1)
= 15.79%
Now that we know the Base IMF, we can go ahead and calculate the Spot Margin Position's IMF:
= max( Spot Margin Base IMF, IMF factor * sqrt [position size in tokens] ) * IMF Weight
= max (15.79%, 0.0004 * sqrt [200] ) * 1
= max (15.79%, 0.4%)
= 15.79%
This means that we need $1,579 in collateral in order to open the 200 LTC @ $50 spot margin short.
Calculating Spot Margin MMF
Because you’re borrowing LTC in this case and not USD, we use the following formula:
= max ( 1.03 / Total Weight - 1, 0.6 * IMF factor * sqrt [position size in tokens] ) * MMF Weight
= max ( 1.03 / 0.95 - 1, 0.6 * 0.0004 * sqrt [200] )
= max (8.42%, 0.34%)
= 8.42%
Calculating Free Collateral
Let's see how much collateral your two positions are currently taking up and ultimately how much free collateral there is in the account for opening another position.
Starting with the 20 BTC-PERP, assuming each BTC-PERP is still trading at $20,000, this is how much collateral the position is currently taking up:
Collateral Used = Position IMF * Position Notional
= 10% * $400,000
= $40,000
The same is done with the LTC/USD spot margin short:
= 15.79% * $10,000 = $1,579
How Spot Margin positions affect collateral and margin
By opening the 200 LTC/USD spot margin short, you are borrowing 200 LTC, which creates a negative spot balance of -200 LTC. In addition to requiring margin, negative spot positions also decrease your account collateral value (more information can be found in this article). Also, because you essentially sold 200 LTC at a price of $50, your USD balance also increased by $10,000.
This is how your balance currently looks after opening the BTC-PERP and LTC/USD spot margin positions:
|
Current Collateral Overview |
||||||
|
Asset |
Size |
Mark Price |
Initial Weight |
Initial Collateral |
Total Weight |
Total Collateral |
|
USD |
60,000 |
$1 |
1 |
$50,000 |
1 |
$50,000 |
|
BTC |
2.5 |
$20,000 |
0.95 |
$47,500 |
0.975 |
$48,750 |
|
LTC (borrow) |
-200 |
$50 |
- |
-$10,000 |
- |
-$10,000 |
|
Total Collateral |
49,803 |
- |
- |
$97,500 |
- |
$98,750 |
Now, let’s see how much free collateral there is currently on the account:
|
Market |
Position Size |
Mark Price |
Position Notional |
IMF % |
MMF |
Collateral Used |
|
BTC-PERP |
20 |
$20,000 |
$400,000 |
10% |
3% |
$40,000 |
|
LTC/USD |
200 |
$50 |
$10,000 |
15.79% |
8.42% |
$1,579 |
|
Total (sum) |
220 |
- |
$410,000 |
- |
- |
$41,579 |
|
Total Collateral |
$98,750 |
|
Total Collateral Used |
$41,579 |
|
Free Collateral |
$57,171 |
This means that there is $57,171 in free collateral after deducting the amount of collateral being used by your open positions, as well as the negative balance from our LTC/USD spot margin short.
Before calculating the Account IMF and MMF, let’s long 25 ETH-0930 contracts using the remaining free collateral in the subaccount. Assuming each contract is trading at $2000, the Position Notional would be $50,000.
Same as before, let’s calculate the Position IMF:
Position IMF = MIN (MAX [Base IMF , IMF Factor * sqrt {position open size in tokens}] * IMF Weight, 1 + fee rate * [short size + long size] )
= MIN (MAX [1/10 , 0.0004 * sqrt {25} ] * 1, 1 + 0.0005 * [0 + 25] )
= MIN (MAX [0.1 , 0.002], 1.0125
= 0.1 = 10%
That means there must be at least $5,000 in collateral in order to open the position. There is enough collateral, so we go ahead and open the position. Now, let's calculate the position's MMF.
Position MMF:
= max (3%, 0.6 * 0.0004 * sqrt[25] )
= 3%
Account IMF and Account MMF
At this point, we have 3 positions open, equalling to a Total Position Notional of $460,000. The Total Account Value remains at $98,750 (we're assuming prices haven't changed at all).
Calculating Account IMF and Account MMF
These will be equal to the average IMF/MMF of all our open positions within the subaccount, weighted by their position notional size.
To do that, we first calculate the Weighted IMF and MMF for each position:
= (Position notional / total position notional) * Position IMF or MMF
As an example, let’s calculate the Weighted IMF for our BTC-PERP position:
= ($400,000 / $460,000) * 10%
= 8.7%
After we calculate that for each of the positions, we then sum the results. Here’s the final result:
|
Market |
Position Size |
Mark Price |
Position Notional |
IMF % |
MMF |
Collateral Used |
Weighted IMF |
Weighted MMF |
|
BTC-PERP |
20 |
$20,000 |
$400,000 |
10% |
3% |
$40,000 |
8.70% |
2.61% |
|
LTC/USD |
200 |
$50 |
$10,000 |
15.79% |
8.42% |
$1,579 |
0.34% |
0.18% |
|
ETH-0930 |
25 |
$2,000 |
$50,000 |
10% |
3% |
$5,000 |
1.09% |
0.33% |
|
Total (sum) |
245 |
- |
$460,000 |
- |
- |
$46,579 |
10.13% |
3.12% |
Here’s a summary of our account after opening the three positions:
|
Total Collateral |
$98,750 |
Margin Fraction |
21.47% |
|
|
Total Collateral Used |
$46,579 |
Account IMF |
10.13% |
|
|
Free Collateral |
$52,171 |
Account MMF |
3.12% |
Once your subaccount's Margin Fraction dips below 3.12%, liquidation will start. More information about how FTX handles liquidations can be found here.
Auto-Close Margin Fraction (ACMF)
ACMF is the margin fraction at which your account would be completely liquidated. To calculate this, we use this formula:
ACMF = max(MMF / 2, MMF - 0.06)
= max( 0.036 / 2, 0.036 - 0.06 )
= 1.53%
So, if your Margin Fraction drops below 1.53%, all of your positions within the subaccount would be instantly liquidated.
Zero Price
Zero Price (ZP) is the price that would cause your account to get completely liquidated.
ZP = Mark Price * (1 - Margin Fraction) if long, Mark Price * (1 + Margin Fraction) if short.
For each of your positions:
BTC-PERP Long = $20,000 * (1 - 21.47%) = $16,141
LTC/USD Short = $50 * (1 + 21.47%) = $60
ETH-0930 Short = $2000 * (1 + 21.47%) = $1,614
Open Orders & Open Margin Fraction
In all of the examples above, we had no open (unfilled) orders before we tried to open new positions. Open orders affect your free collateral and margin, so it’s important to understand the role they play here. To do this, let’s calculate your Open Margin Fraction.
Let’s assume your 3 positions are still open and prices have not changed at all, which means that your Free Collateral is still $52,171.
Now, we’re going to open the following BTC-PERP limit orders:
- Long 2 BTC-PERP @ $19,500 ($39,000 notional)
- Sell 5 BTC-PERP @ $21,000 ($105,000 notional)
To start, let’s calculate the Open Position Size:
= MAX (ABS [position size + open long orders], ABS [position size - open short orders] )
= MAX ( ABS [20 + 2] , ABS [20 - 5] )
= 22
Using the current mark price for BTC-PERP, we calculate the Position Open Notional:
= Open Position Size * Mark Price
= 22 * $20,000
= $440,000
Then, we aggregate all open orders and open positions in the subaccount to calculate the Total Open Position Notional:
Position Open Notional:
- BTC-PERP = $440,000 (includes our Open Position Size, as explained in the example above)
- LTC/USD = $10,000 (no open orders here, so stays the same)
- ETH-0930 = $50,000 (no open orders here, so stays the same)
Total Open Position Notional = $500,000
Now, using what we calculated above, let’s calculate the Open Margin Fraction (OMF):
= MAX (0, MIN [Total Account Value, Collateral] ) / Total Open Position Notional
= MAX (0, MIN [$98,750, $98,750] ) / $500,000
= $98,750 / $500,000
= 19.75%
The OMF (your Margin Fraction with open orders included) is 19.75%. The Account IMF is 10.13%, which means that you can still open more positions.
Notes:
- sum(value1, value2,..) = sum total of the values within the data set provided
- max(value1, value2,..) = the maximum value within the data set provided
- min(value1, value2,..) = the minimum value within the data set provided
- abs(value) = the absolute value of the data provided
- Open position means that the position has been filled and has not been closed yet. Open order means that that the order has been submitted, but has not been filled yet.
- Mark price = median of best ask, best bid, and last traded price.
- Your margin and collateral is segregated per subaccount. Therefore, throughout this article, account = subaccount.
- Much of this article is an approximation and ignores details, e.g. fees.