Futures Margin Accounts And Maintenance Calls

Why Futures Margin Accounts Need Daily Tracking

A futures contract creates gains or losses as its settlement price changes. Rather than waiting until the contract ends to settle the full result, a futures account is adjusted each trading day through marking to market. Margin is money held in the account to support the position; it is not a down payment on the underlying asset. The account balance rises or falls with daily settlement results, and a sufficiently low balance can require an additional deposit.

The key calculation is the change in settlement price multiplied by the contract's dollar value per price unit and the number of contracts. A long position benefits when the settlement price rises; a short position benefits when it falls. The account must be tracked in order: calculate the day's settlement result, update the balance, compare it with the maintenance requirement, and make any required deposit.

Definition: The initial margin is the amount required to establish the futures position, usually stated per contract. The maintenance margin is the minimum account balance required to avoid a maintenance call, also usually stated per contract. A margin call is a required deposit when the post-settlement account balance is below the applicable maintenance requirement. In the standard convention used here, a call restores the account to the initial margin requirement.

Daily Settlement and the Account-Balance Rule

Assume a position consists of \(N\) identical contracts, each with multiplier \(M\), where \(M\) is the number of dollars gained or lost for each one-unit movement in the quoted futures price. Let \(F_t\) be the settlement price on day \(t\), and let \(B_t\) be the account balance immediately after any margin call on that day. Let \(q=+1\) for a long position and \(q=-1\) for a short position. If the position is unchanged, the day's variation gain or loss is

G_t=qNM(F_t-F_{t-1}).

Before any margin call, the balance is the previous post-call balance plus the day's variation result. If that pre-call balance is below total maintenance margin, the account is brought back to total initial margin.

B_t^{\text{pre-call}}=B_{t-1}+G_t, \qquad C_t= \begin{cases} I_{\text{total}}-B_t^{\text{pre-call}}, & B_t^{\text{pre-call}}<H_{\text{total}},\\ 0, & B_t^{\text{pre-call}}\ge H_{\text{total}}, \end{cases} \qquad B_t=B_t^{\text{pre-call}}+C_t.

Here \(I_{\text{total}}\) is the total initial margin and \(H_{\text{total}}\) is the total maintenance margin. If the requirements are quoted per contract as \(I\) and \(H\), then \(I_{\text{total}}=NI\) and \(H_{\text{total}}=NH\). The deposit \(C_t\) is zero when there is no call. These rules assume that the position size and contract multiplier remain unchanged, that settlement occurs once per day, that margin requirements are fixed, and that fees and interest on the account are ignored. Actual exchange or broker terms may use different call timing or deposit rules, so the stated terms govern in a particular problem.

Threshold convention: A call occurs when the post-settlement balance is below maintenance margin. A balance exactly equal to maintenance margin does not trigger a call under this convention. When a call does occur, the required deposit is the difference between the initial-margin target and the pre-call balance, not merely the difference between maintenance and the balance.

Why the Daily Gain Formula Works

The formula follows from the futures contract's price exposure. For one contract, a long position gains \(M\) dollars for every one-unit increase in the settlement price and loses \(M\) dollars for every one-unit decrease. Thus its result for the price change \(F_t-F_{t-1}\) is \(M(F_t-F_{t-1})\). A short position has the opposite result, represented by multiplying by \(-1\). With \(N\) identical contracts, the one-contract result is multiplied by \(N\), giving \(G_t=qNM(F_t-F_{t-1})\). Daily settlement credits or debits this result to the margin account; it does not change the price-change calculation for later days.

In particular, later daily gains and losses are calculated from the previous settlement price, not from the original futures price. The sum of daily settlement results over a period telescopes to the position's total price-change result, provided the position size and multiplier stay constant:

\sum_{t=1}^{T}G_t =qNM\sum_{t=1}^{T}(F_t-F_{t-1}) =qNM(F_T-F_0).

Margin deposits are separate from trading gains and losses. They add cash to the account but do not reverse or erase the losses that caused a call.

Worked Example: A Long Position That Reaches the Call Threshold

An investor holds two long futures contracts. Each contract has a multiplier of 100 dollars per price unit. Initial margin is 1,500 dollars per contract and maintenance margin is 1,100 dollars per contract. The entry settlement price is 60. Subsequent settlement prices are 56, 55.5, and 57.25. Find the account balance after each settlement and any required deposit.

Method. Total initial margin is \(2(1{,}500)=3{,}000\) dollars, and total maintenance margin is \(2(1{,}100)=2{,}200\) dollars. The position is long, so \(q=+1\); the dollar exposure per price unit is \(NM=2(100)=200\) dollars.

At the first settlement, the price change is \(56-60=-4\). The variation result is \(G_1=(+1)(200)(-4)=-800\) dollars. The balance falls from 3,000 to \(3{,}000-800=2{,}200\) dollars. This is exactly the maintenance requirement, so there is no call.

At the second settlement, use the change from the previous settlement: \(55.5-56=-0.5\). The variation result is \(G_2=(+1)(200)(-0.5)=-100\) dollars. The pre-call balance is \(2{,}200-100=2{,}100\) dollars, which is below the 2,200-dollar maintenance requirement. The call restores the account to 3,000 dollars, so the deposit is \(3{,}000-2{,}100=900\) dollars.

At the third settlement, the price change is \(57.25-55.5=1.75\). The long position gains \(G_3=(+1)(200)(1.75)=350\) dollars. The post-settlement balance is \(3{,}000+350=3{,}350\) dollars, with no call.

Check. From the entry price to the last settlement, the long position's cumulative result is \(200(57.25-60)=-550\) dollars. The account began with 3,000 dollars and received a 900-dollar deposit, so \(3{,}000+900-550=3{,}350\) dollars, matching the daily ledger. The important threshold detail is that equality at 2,200 dollars did not trigger a call; the later balance of 2,100 dollars did.

Worked Examples With Short Positions and Multiple Settlements

Worked Example: A Short Position With a Maintenance Call

A trader holds one short futures contract with a multiplier of 100 dollars per price unit. Initial margin is 2,000 dollars and maintenance margin is 1,500 dollars. The entry settlement price is 90. The next three settlement prices are 94, 96, and 93. Determine the daily account movements, the required call deposit, and the ending balance.

Method. Since the position is short, \(q=-1\). There is one contract, so \(NM=100\) dollars per price unit. The account starts at its 2,000-dollar initial margin.

From 90 to 94, the price rises by 4. The short position loses \(G_1=(-1)(100)(94-90)=-400\) dollars, leaving \(2{,}000-400=1{,}600\) dollars. Since 1,600 is above the 1,500-dollar maintenance requirement, there is no call.

From 94 to 96, the price rises by 2. The loss is \(G_2=(-1)(100)(96-94)=-200\) dollars. The pre-call balance is \(1{,}600-200=1{,}400\) dollars, which is below maintenance. The deposit required to restore initial margin is \(2{,}000-1{,}400=600\) dollars. After the deposit, the balance is 2,000 dollars.

From 96 to 93, the price falls by 3. The short position gains \(G_3=(-1)(100)(93-96)=300\) dollars, so the ending balance is \(2{,}000+300=2{,}300\) dollars.

Check. The cumulative short-position result from 90 to 93 is \((-1)(100)(93-90)=-300\) dollars. Adding the 600-dollar deposit to the starting 2,000 dollars and subtracting the 300-dollar cumulative loss gives \(2{,}300\) dollars. The call was 600 dollars, not 100 dollars: the account was restored to initial margin, not merely lifted to maintenance.

Worked Example: Tracking Several Contracts Across Several Days

A fund holds three long commodity futures contracts, each with a multiplier of 20 dollars per price unit. Initial margin is 500 dollars per contract and maintenance margin is 350 dollars per contract. The entry settlement price is 50, followed by settlement prices of 48, 46, 47, 42, and 43. Track the balance and any call.

Method. Total initial margin is \(3(500)=1{,}500\) dollars, and total maintenance margin is \(3(350)=1{,}050\) dollars. The combined exposure is \(NM=3(20)=60\) dollars for each price-unit change. The position is long.

From 50 to 48, the price change is \(-2\), so the result is \(60(-2)=-120\) dollars. The balance is \(1{,}500-120=1{,}380\) dollars.

From 48 to 46, the result is \(60(-2)=-120\) dollars, leaving \(1{,}380-120=1{,}260\) dollars.

From 46 to 47, the result is \(60(1)=60\) dollars, leaving \(1{,}260+60=1{,}320\) dollars.

From 47 to 42, the result is \(60(-5)=-300\) dollars. The pre-call balance is \(1{,}320-300=1{,}020\) dollars, which is below the 1,050-dollar maintenance requirement. The call restores the balance to 1,500 dollars, requiring a deposit of \(1{,}500-1{,}020=480\) dollars.

From 42 to 43, the position gains \(60(1)=60\) dollars, so the ending balance is \(1{,}500+60=1{,}560\) dollars.

Check. Across all five daily price changes, the cumulative result is \(60(43-50)=-420\) dollars. Including the 480-dollar deposit, the account balance is \(1{,}500-420+480=1{,}560\) dollars, as found in the ledger. This reconciliation is useful for detecting missed days or incorrect signs.

Common Mistakes and Practical Checks

Margin questions usually require straightforward arithmetic, but small interpretation errors can change whether a call occurs and by how much. A reliable solution keeps the contract exposure, settlement changes, account balance, and deposits distinct.

Reversing the long and short signs. A price increase is a gain for a long and a loss for a short. Use \(q=+1\) for long and \(q=-1\) for short in the daily result.
Using the entry price every day. Daily settlement uses \(F_t-F_{t-1}\). The entry price is useful for checking the cumulative result, but it is not the reference price for every daily movement.
Forgetting the contract multiplier or number of contracts. A one-unit price movement produces \(NM\) dollars of account change, not just the price movement itself.
Calling at equality. Under the below-maintenance convention in this tutorial, a balance exactly at maintenance does not trigger a call.
Depositing only to maintenance. If the problem specifies that calls restore initial margin, calculate the deposit as initial margin minus the pre-call balance.
Treating a deposit as a gain. A deposit changes the cash balance but does not change the futures position's cumulative profit or loss.

A useful check after a sequence of settlements is to sum the daily gains and losses. For a constant position, that sum must equal \(qNM(F_T-F_0)\). Then add all margin deposits to the starting balance and reconcile to the final account balance. If the two methods disagree, check the daily settlement intervals, the long/short sign, and whether every call was included.

Margin accounts matter because they specify how futures losses are funded before a contract expires. They do not determine the futures price or predict future gains; they govern the cash required to keep a position open under the stated rules. Careful account tracking is therefore distinct from pricing or hedging analysis and is aligned with the SOA Exam FM (Financial Mathematics) syllabus.

Check Your Understanding

For each problem, track the account sequentially. Unless stated otherwise, assume a call occurs only when the post-settlement balance is below maintenance and restores the account to initial margin. Ignore interest and fees.

A trader holds one long contract with multiplier 50 dollars per price unit. Initial margin is 900 dollars, maintenance margin is 650 dollars, and the entry settlement price is 40. Subsequent settlement prices are 37 and 38. Find the ending balance and state whether there is a call. (Answer: No call; ending balance is 800 dollars.)
An investor holds two short contracts, each with multiplier 25 dollars per price unit. Initial margin is 700 dollars per contract and maintenance margin is 500 dollars per contract. The entry price is 64, followed by settlements at 66 and 70. Find the ending balance and state whether a call occurs. (Answer: No call; ending balance is 1,100 dollars.)
A fund is long four contracts with multiplier 10 dollars per price unit. Initial margin is 600 dollars per contract and maintenance margin is 400 dollars per contract. Starting from settlement price 100, the next prices are 98, 95, and 92. Find the ending balance and state whether there is a call. (Answer: No call; ending balance is 2,080 dollars.)
A trader is short one contract with multiplier 100 dollars per price unit. Initial margin is 1,800 dollars and maintenance margin is 1,300 dollars. The entry settlement price is 75, followed by settlements at 78, 80, and 74. State whether any call occurs and find the ending balance. (Answer: No call; the balance reaches exactly 1,300 dollars after the settlement at 80, then ends at 1,900 dollars.)
An investor is long two contracts with multiplier 40 dollars per price unit. Initial margin is 1,000 dollars per contract and maintenance margin is 700 dollars per contract. The entry settlement price is 25, followed by settlements at 17 and 15. Find any required deposit and the ending balance. (Answer: Deposit 640 dollars after the settlement at 17; ending balance is 1,840 dollars.)

What You'll Learn