Finance-Theory Β· Unit 10 Β· Video 8 Β· Interactive Practice

One Day's Loss at a Time: How Clearing Houses and Margin Make Futures Safe

IKey Formulas

FormulaNameWhat it needs
V=1,000Γ—FV = 1{,}000 \times FContract value1,000 barrels at the futures price FF per barrel: at $75.06 one contract controls $75,060 of oil
Ξ”V=1,000Γ—Ξ”F\Delta V = 1{,}000 \times \Delta FValue of a price moveOne tick is Ξ”F\Delta F = 1 cent a barrel, so one tick moves the contract by $10
Gt=± 1,000 (Ftβˆ’Ftβˆ’1)G_t = \pm\,1{,}000\,(F_t - F_{t-1})Daily settlementPlus sign for the long, minus for the short; GtG_t is added to the margin account every day
Bt<Mmaintβ€…β€Šβ‡’β€…β€ŠdepositΒ Minitβˆ’BtB_t < M_{\text{maint}} \;\Rightarrow\; \text{deposit } M_{\text{init}} - B_tMargin callA balance below the maintenance margin ($3,000) triggers a call to bring the account back up, on most exchanges to the initial margin ($4,050), as assumed here; unpaid by the end of that business day, the broker closes the position

Key Insight: The clearing house is the counterparty to both sides and settles every day, so the most anyone can lose before the account is topped up or closed is roughly one day's change in value. That is why $4,050 of margin can stand behind a $75,060 position.

IIThe Margin Account, Day by Day

Each day the account gains or loses 1,000 barrels times the price change; below maintenance, a margin call refills it, on most exchanges to the initial margin.

IIIThe Clearing House in the Middle

The clearing house faces every trader, so each day the losers' payments exactly fund the winners' gains.

πŸ’‘ Traders A–D, their trades and their accounts are our illustration: each account is assumed to hold exactly the initial margin, $4,050 per contract, at the start of the day.

IVQuiz Questions

Problem 1 Β· Tick Value and Contract Value

Given (illustrative figures): a grain futures contract covers 5,000 bushels, its tick size is a quarter of a cent ($0.0025) per bushel, and it trades at $4.20 a bushel. Find the value of one tick per contract and the value of the grain one contract controls.

What is one tick worth per contract?

What value of grain does one contract control?

βœ… Correct! Both values scale with the contract size: 5,000 Γ— $0.0025 = $12.50 a tick, and 5,000 Γ— $4.20 = $21,000 of grain.
❌ Check the decimal. A quarter of a cent is $0.0025, not $0.025: 5,000 Γ— $0.0025 = $12.50.
❌ Not quite. One tick changes the contract's value by (contract size) Γ— (tick size) = 5,000 Γ— $0.0025.
❌ Not quite. The contract controls (contract size) Γ— (price) = 5,000 Γ— $4.20; count the zeros.
Show solution

Every price move is multiplied by the number of units in the contract, Ξ”V=5,000Γ—Ξ”F\Delta V = 5{,}000 \times \Delta F.

Tick value: 5,000 Γ— $0.0025 = $12.50 per contract.

Contract value: 5,000 Γ— $4.20 = $21,000.

Entering the contract costs nothing today (its value at inception is zero); the $21,000 is the size of the exposure the margin account has to back.

Problem 2 Β· How Big Is the Margin Call?

Given (illustrative figures): a trader goes long one 1,000-barrel oil contract at $82.40 a barrel, with initial margin $5,000 and maintenance margin $4,000. The settlement prices on the next two days are $81.70 and $80.95. The exchange requires a margin call to restore the initial margin. Find the deposit demanded at the end of day 2.

βœ… Correct! The balance is $3,550 after day 2, below $4,000, and the call restores it to the initial $5,000: $5,000 βˆ’ $3,550 = $1,450.
❌ That only reaches the maintenance margin. $4,000 βˆ’ $3,550 = $450 would leave the account at the minimum; the call restores the initial margin, $5,000.
❌ That is only day 2's loss. The call is set by the balance, which also carries day 1's $700 loss: it stands at $3,550.
❌ That is the gap between the two margins. The deposit depends on where the balance actually is, $3,550, not on the size of the cushion.
❌ Not quite. Settle each day: gain = 1,000 Γ— (price change), then compare the balance with $4,000.
Show solution

Day 1: the price falls $0.70, so the long loses 1,000 Γ— $0.70 = $700. Balance $5,000 βˆ’ $700 = $4,300, which is at least $4,000: no call.

Day 2: the price falls $0.75, a loss of 1,000 Γ— $0.75 = $750. Balance $4,300 βˆ’ $750 = $3,550, below $4,000: margin call.

Deposit: back to the initial margin, $5,000 βˆ’ $3,550 = $1,450.

If it is not wired in by the end of the business day, the broker closes out the contract and the $3,550 is returned.

Problem 3 Β· A Short Position over Three Days

Given (illustrative figures): a trader is short 2 oil contracts of 1,000 barrels each, sold at $68.20 a barrel. Margins are per contract: initial $5,000, maintenance $4,000, so the account opens at $10,000. Settlement prices on the next three days: $68.90, $69.35, $68.60. Every margin call is met by restoring the initial margin.

On which day does the first margin call come?

What is the balance at the end of day 3?

βœ… Correct! The short loses $1,400 and $900 as the price rises, gets a call at $7,700 < $8,000, is topped up to $10,000, then gains $1,500 when the price falls.
❌ Compare like with like. The account holds 2 contracts, so its maintenance level is 2 Γ— $4,000 = $8,000, not $4,000.
❌ You skipped the deposit. The day-2 call adds $2,300, bringing the account back to $10,000 before day 3's gain.
❌ The call restores the initial margin. Topping up only to $8,000 is the maintenance level; the deposit brings the account to $10,000.
❌ Check the sign. That is the long's balance path. A short gains when the price falls and loses when it rises: Gt=βˆ’1,000 (Ftβˆ’Ftβˆ’1)G_t = -1{,}000\,(F_t - F_{t-1}) per contract.
❌ Not quite. Settle each day for 2 contracts, gain = βˆ’2 Γ— 1,000 Γ— (price change), and compare the balance with $8,000.
❌ Not quite. Track deposits as well as gains: final balance = $10,000 + deposits + total gain.
Show solution

For 2 short contracts the daily gain is βˆ’2Γ—1,000Γ—Ξ”F-2 \times 1{,}000 \times \Delta F, and the account levels are 2 Γ— $5,000 = $10,000 (initial) and 2 Γ— $4,000 = $8,000 (maintenance).

Day 1: Ξ”F\Delta F = +0.70, gain βˆ’2,000 Γ— 0.70 = βˆ’$1,400. Balance $10,000 βˆ’ $1,400 = $8,600 β‰₯ $8,000: no call.

Day 2: Ξ”F\Delta F = +0.45, gain βˆ’2,000 Γ— 0.45 = βˆ’$900. Balance $8,600 βˆ’ $900 = $7,700 < $8,000: margin call, deposit $10,000 βˆ’ $7,700 = $2,300, balance back to $10,000.

Day 3: Ξ”F\Delta F = βˆ’0.75, gain βˆ’2,000 Γ— (βˆ’0.75) = +$1,500. Balance $10,000 + $1,500 = $11,500.

Check: total gain βˆ’2,000 Γ— (68.60 βˆ’ 68.20) = βˆ’$800, and $10,000 + $2,300 βˆ’ $800 = $11,500.

Problem 4 Β· What the Clearing House Collects

Given (illustrative figures): one clearing house has recorded three trades in 1,000-barrel contracts: A bought 4 contracts from B, C bought 1 from A, and C bought 2 from D. Today the futures price rises by $0.30 a barrel. Find how much the clearing house collects from the traders who lose.

βœ… Correct! Net positions are A +3, B βˆ’4, C +3, D βˆ’2; the shorts B and D pay $1,200 + $600 = $1,800, which the clearing house passes to A and C.
❌ Zero is the clearing house's net, not what it collects. Longs equal shorts, so it pays out exactly what it collects, but money still moves: the losers pay in.
❌ Net A's positions first. A bought 4 and sold 1, so A is long 3 and gains; it does not pay $300 on the contract it sold. Settlement is on each trader's net position.
❌ That counts both directions. $1,800 comes in from the losers and the same $1,800 goes out to the winners; the question asks for the inflow only.
Show solution

Net positions (long positive): A = +4 βˆ’ 1 = +3, B = βˆ’4, C = +1 + 2 = +3, D = βˆ’2. Longs 3 + 3 = 6 equal shorts 4 + 2 = 6, so the clearing house's own net position is 0.

Settlement at Ξ”F\Delta F = +0.30, gain = position Γ— 1,000 Γ— 0.30:

  • A: +3 Γ— 300 = +$900
  • B: βˆ’4 Γ— 300 = βˆ’$1,200
  • C: +3 Γ— 300 = +$900
  • D: βˆ’2 Γ— 300 = βˆ’$600

The clearing house collects $1,200 + $600 = $1,800 from B and D and pays $900 + $900 = $1,800 to A and C: net 0.

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