Futures Margin Cash Flows And Daily Settlement

Daily Settlement: Price Changes Become Cash Flows

A futures position is settled in cash each business day using that day’s settlement price. A price change therefore creates a cash payment or receipt for the position holder, rather than accumulating as an unpaid gain or loss until the contract expires. The margin account records those daily transfers and any additional deposits required by the margin rules.

The quoted futures price is not the same thing as the amount in the margin account, nor is it the current value of a contract that has just been settled. The futures price is a market quote per unit of the underlying asset. The daily settlement cash flow depends on the change in that quote, the position direction, and the contract size.

Definition: Suppose a position consists of $n$ identical futures contracts, each covering $M$ units of the underlying asset. Let $F_t$ be the settlement price per unit on day $t$, and let $F_{t-1}$ be the previous day’s settlement price. Define $h=1$ for a long position and $h=-1$ for a short position. The day-$t$ variation margin is $$ \text{VM}_t=h\,nM(F_t-F_{t-1}). $$ A positive result is cash received by the position holder; a negative result is cash paid by the holder.

This formula assumes the position is unchanged over the settlement interval, the quoted price is per unit, and all contracts have the same multiplier. It also assumes daily settlement at the stated prices. Commissions, taxes, interest on the margin balance, and any intraday cash flows are excluded unless the problem specifies them.

Initial margin is collateral required to open or maintain a position; it is not the purchase price of the underlying asset. A maintenance-margin rule specifies a balance threshold. Under the convention used here, if the account balance after daily settlement is below the maintenance level, the holder deposits enough to restore the balance to the initial-margin level. A problem may specify different call rules, so use its stated convention.

Why the Daily Cash Flow Uses a Price Change

Immediately before settlement on day $t$, the position’s value relative to the previous settlement price is the signed exposure times the price change. For a long position, a rise from $F_{t-1}$ to $F_t$ is favorable; for a short position, it is unfavorable. Multiplying the per-unit change by the number of contracts and the units per contract gives the cash amount transferred at settlement.

After this amount is paid or received, the futures position is marked to the new settlement price $F_t$. Its value relative to that new reference price is zero immediately after settlement. That daily reset explains why the current settlement transfer uses $F_t-F_{t-1}$, not the full quoted price $F_t$. It also explains why one should not treat the quoted price itself as the balance due on the contract.

\text{VM}_t = h\,nM(F_t-F_{t-1}) \qquad\text{and}\qquad \sum_{t=1}^{k}\text{VM}_t = h\,nM(F_k-F_0),

The second equality holds when the position remains unchanged and the settlement intervals form a consecutive sequence from $F_0$ through $F_k$. It follows by adding the daily changes: the intermediate prices cancel. The equality checks cumulative variation margin; it does not imply that the margin account balance equals cumulative variation margin, because the account also contains initial collateral and any margin-call deposits or withdrawals.

Worked Examples

Worked Example: A Long Position Through Three Settlements

A trader is long 4 futures contracts on a hypothetical metal, with 1,000 units covered by each contract. Settlement prices are $ \$52.40$, $ \$53.10$, $ \$51.80$, and $ \$52.65$ per unit on days 0 through 3. The trader deposits initial margin of $ \$18{,}000$; maintenance margin is $ \$15{,}000$. Assume no interest, fees, or withdrawals, and a margin call only when the post-settlement balance is below maintenance. Find each day’s variation margin, the account balance, and any margin call.

Method. Use the long-position sign $h=1$, and multiply each daily price change by the total unit exposure: $$ nM=4(1{,}000)=4{,}000\text{ units}. $$

On day 1, the price change is $53.10-52.40=0.70$, so variation margin is $4{,}000(0.70)=\$2{,}800$. The account balance becomes $18{,}000+2{,}800=\$20{,}800$.

On day 2, the price change is $51.80-53.10=-1.30$, so variation margin is $4{,}000(-1.30)=-\$5{,}200$. The balance becomes $20{,}800-5{,}200=\$15{,}600$.

On day 3, the price change is $52.65-51.80=0.85$, so variation margin is $4{,}000(0.85)=\$3{,}400$. The balance becomes $15{,}600+3{,}400=\$19{,}000$. None of the three post-settlement balances is below $ \$15{,}000$, so there is no margin call.

Check. Total variation margin is $2{,}800-5{,}200+3{,}400=\$1{,}000$. Directly, the overall change is $4{,}000(52.65-52.40)=\$1{,}000$, as required. The final balance is $18{,}000+1{,}000=\$19{,}000$.

Common mistake avoided: Adding the full futures price to the account would incorrectly use $F_t$ instead of the daily price change.

Worked Example: A Short Position and a Margin Call

An investor is short 3 futures contracts on a hypothetical crop, with 250 units per contract. The initial settlement price is $ \$81.20$. The next two settlement prices are $ \$80.40$ and $ \$82.10$, followed by a third-day settlement at $ \$81.60$. Initial margin is $ \$5{,}000$ and maintenance margin is $ \$4{,}500$. Assume a call restores the account to initial margin and that there are no other cash flows. Calculate the daily transfers and deposits.

Method. The short position has $h=-1$, and its total exposure is $3(250)=750$ units. A price decline benefits the short; a price increase creates a payment.

From day 0 to day 1, the price change is $80.40-81.20=-0.80$. Thus $$ \text{VM}_1=(-1)(750)(-0.80)=\$600. $$ The balance rises from $ \$5{,}000$ to $ \$5{,}600$.

From day 1 to day 2, the change is $82.10-80.40=1.70$. Therefore $$ \text{VM}_2=(-1)(750)(1.70)=-\$1{,}275. $$ The balance falls to $5{,}600-1{,}275=\$4{,}325$, which is below the $ \$4{,}500$ maintenance level. The investor must deposit $5{,}000-4{,}325=\$675$ to restore the account to initial margin.

From day 2 to day 3, the price change is $81.60-82.10=-0.50$, so $$ \text{VM}_3=(-1)(750)(-0.50)=\$375. $$ After the deposit and this settlement receipt, the balance is $5{,}000+375=\$5{,}375$.

Check. The cumulative variation margin is $600-1{,}275+375=-\$300$. The short position’s overall result is also $(-1)(750)(81.60-81.20)=-\$300$. The account balance equals the original $ \$5{,}000$, plus $ -\$300$ in trading transfers, plus the $ \$675$ deposit: $ \$5{,}375$.

Common mistake avoided: A short position does not receive cash when the futures price rises. The sign $h=-1$ makes that price increase a payment.

Worked Example: Separating a Margin Deposit from a Trading Gain

A trader is long 5 futures contracts on a hypothetical industrial material. Each contract covers 200 units. Initial margin is $ \$12{,}000$, maintenance margin is $ \$10{,}000$, and the initial settlement price is $ \$44.00$ per unit. Subsequent settlement prices are $ \$42.80$, $ \$43.50$, $ \$39.70$, and $ \$40.10$. A margin call restores the account to initial margin. Find the daily variation margins, any call, and the final account balance.

Method. The long position has $5(200)=1{,}000$ units of exposure. Begin with $ \$12{,}000$ in the account and apply each price change in sequence.

Day 1: $42.80-44.00=-1.20$, so variation margin is $1{,}000(-1.20)=-\$1{,}200$. The account is $12{,}000-1{,}200=\$10{,}800$.

Day 2: $43.50-42.80=0.70$, so variation margin is $1{,}000(0.70)=\$700$. The account is $10{,}800+700=\$11{,}500$.

Day 3: $39.70-43.50=-3.80$, so variation margin is $1{,}000(-3.80)=-\$3{,}800$. The account falls to $11{,}500-3{,}800=\$7{,}700$, below maintenance. The required deposit is $12{,}000-7{,}700=\$4{,}300$, restoring the balance to $ \$12{,}000$.

Day 4: $40.10-39.70=0.40$, so variation margin is $1{,}000(0.40)=\$400$. The final account balance is $12{,}000+400=\$12{,}400$.

Check. The total variation margin is $-1{,}200+700-3{,}800+400=-\$3{,}900$. The overall price change also gives $1{,}000(40.10-44.00)=-\$3{,}900$. Including the $ \$4{,}300$ margin deposit, the balance is $12{,}000-3{,}900+4{,}300=\$12{,}400$.

Common mistake avoided: The $ \$4{,}300$ deposit is not a trading gain. It is additional collateral. The position’s cumulative trading result remains a loss of $ \$3{,}900$.

Account Balances, Contract Values, and Exam Traps

A useful account identity is $$ \text{Ending balance} =\text{opening balance} +\text{variation margin} +\text{deposits} -\text{withdrawals}, $$ where each item covers the period being analyzed. Variation margin is the position’s settlement cash flow. Deposits and withdrawals change the account balance but are not gains or losses from the futures position.

A futures contract’s quoted settlement price is stated per underlying unit. It is not the cash amount transferred that day. For example, a quote of $ \$40.10$ per unit does not mean the holder pays or receives $ \$40.10$ at settlement. The transfer is based on the difference between the current and previous settlement prices, multiplied by the signed contract exposure.

The same distinction matters when discussing contract value. Immediately after a daily settlement, the contract has been reset to the current settlement price, so its value relative to that price is zero. The holder may have a positive or negative margin-account balance, but that balance is collateral plus accumulated settlement cash flows; it is not the contract’s value. Before the day’s settlement, the change from the previous settlement price determines the value being settled for that interval.

For a constant position over multiple days, daily price changes telescope: $$ \sum_{t=1}^{k}(F_t-F_{t-1})=F_k-F_0. $$ Thus cumulative variation margin can be checked from the first and last settlement prices. This check does not replace the daily account ledger: the ledger is still needed to determine whether a maintenance threshold was crossed and how much collateral was deposited.

Set the position sign and exposure.
Use $h=1$ for long and $h=-1$ for short; multiply the number of contracts by the units per contract.

Compute each daily price change.
Subtract the previous settlement price from the current settlement price, using the same quoted units.

Calculate and post variation margin.
Multiply the signed price change by the total contract exposure and update the account balance.

Apply the stated margin rule.
Compare the post-settlement balance with maintenance margin; if a call is triggered, calculate the deposit using the specified restoration target.

Reconcile the result.
Check cumulative variation margin against the overall signed price change, then account separately for deposits and withdrawals.

The most frequent errors are reversing the short-position sign, omitting the contract multiplier, using the original opening price for every day’s transfer, and treating a margin call as a position gain. A further trap is to compare the balance with the maintenance level before posting that day’s variation margin. Under the convention in this tutorial, compare the balance after settlement, then determine any call.

These distinctions are useful whenever a problem asks for a sequence of futures cash flows rather than only a final price comparison. Correctly tracking the timing and direction of settlement is aligned with the SOA Exam FM (Financial Mathematics) syllabus.

Check Your Understanding

For each problem, calculate daily variation margin using the stated contract size and position direction. Apply the specified margin rule and check cumulative trading cash flows separately from collateral deposits.

A trader is long 2 futures contracts, each covering 500 units. Settlement prices move from $ \$63.20$ to $ \$63.75$, then to $ \$63.10$. Initial margin is $ \$8{,}000$, maintenance is $ \$7{,}000$, and no interest or fees apply. Find both daily transfers, the ending balance, and whether a call occurs. (Answer: $+\$550$, then $-\$650$; ending balance $ \$7{,}900$; no call.)
An investor is short 4 contracts of 100 units each. The settlement price moves from $ \$27.50$ to $ \$28.10$, then to $ \$27.20$. Initial margin is $ \$9{,}000$, maintenance is $ \$8{,}000$, and the account starts at initial margin. Find the daily transfers and ending balance. (Answer: $-\$240$, then $+\$360$; ending balance $ \$9{,}120$; no call.)
A long position has 5 contracts, each covering 200 units. The price moves from $ \$105.00$ to $ \$103.50$, then to $ \$102.00$. Initial margin is $ \$15{,}000$, maintenance is $ \$13{,}000$, and a call restores the account to initial margin. Find the call and the ending balance after the second settlement. (Answer: transfers of $-\$1{,}500$ each; a $ \$3{,}000$ call after the second settlement; ending balance $ \$15{,}000$.)
A trader is short 3 contracts, each covering 1,000 units. The settlement prices are $ \$9.80$, $ \$9.65$, $ \$10.05$, and $ \$9.90$. Initial margin is $ \$6{,}000$, maintenance is $ \$5{,}000$, and the initial balance equals initial margin. Find each daily transfer, the ending balance, and whether a call occurs. (Answer: $+\$450$, $-\$1{,}200$, $+\$450$; ending balance $ \$5{,}700$; no call.)
A long position has 2 contracts, each covering 250 units. The settlement price rises from $ \$71.40$ to $ \$72.00$, then falls to $ \$70.80$, when the position is closed. Initial margin is $ \$5{,}000$, maintenance is $ \$4{,}000$, and there are no deposits or withdrawals. Find each settlement transfer, cumulative trading result, and final balance. (Answer: $+\$300$, then $-\$600$; cumulative result $-\$300$; final balance $ \$4{,}700$; no call.)

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