Finance-Theory · Unit 11 · Video 1 · Interactive Practice

Nothing Paid, Settled Daily: How a $298,200 Futures Position Moves $800 in a Day

IKey Formulas

Formula	Name	What it needs
$\text{Notional} = F \times N \times Q$	Notional value	Futures price $F$ per unit, $N$ contracts, $Q$ units per contract: $0.7455 \times 10 \times 40{,}000$ gives $298,200 for the cattle position, and $0 is paid to enter it
$G_t = N Q\,(F_t - F_{t-1})$	Daily settlement (marking to market)	The long's gain on day $t$ , paid in cash that day; a fall of 0.20¢ a pound on 400,000 lb moves $800
$G_t^{\text{long}} + G_t^{\text{short}} = 0$	Zero-sum transfer	Whatever the long's margin account loses, the short's gains the same day
$\max(L - M,\ 0)$	Loss beyond margin	A one-day loss $L$ larger than the margin $M$ is still owed by the trader; the clearing corporation absorbs it only if the trader cannot pay

Key Insight: A futures position controls the whole notional but pays nothing to enter; what moves each day is only that day's change in value, settled in cash, so credit risk is not allowed to build up beyond roughly one day's price move.

IIMarking to Market, Day by Day

Each day's cash settlement is the change in the notional value, paid by one side and received by the other.

Contracts

IIISizing the Margin

Margin is set to cover about 99% of one-day losses, so it must grow when daily swings grow.

Typical daily swing σ ($) 6,500 Margin rule

💡 The bell curve, its width and the 2.33 multiplier are our illustration of the video's rule of thumb that margin covers about 99% of plausible daily swings.

IVMargin Is Not a Ceiling on Liability

A one-day loss larger than the margin is still owed; the clearing corporation pays only when the trader cannot.

One-day price drop (¢/lb) 0.20 The long trader

💡 The $15,000 margin is our illustration, the low end of the video's 5%–20% range on $298,200 of notional.

VQuiz Questions

Problem 1 · Notional Value and the Price of Entry

Given (illustrative figures): you buy 6 lean-hog futures contracts, each covering 40,000 lb, at a futures price of 82.40¢ per pound. Find the notional value of the position and the amount you pay to enter it.

What is the notional value?

How much do you pay to enter the position?

✅ Correct! The position controls $197,760 of hogs, yet nothing is paid to enter it; the margin posted is your own collateral.

❌ That is one contract.

0.8240 \times 40{,}000

is the value of a single contract; the position has 6 of them.

❌ Check the units. 82.40¢ is $0.8240 per pound; multiplying 82.40 by the pounds treats cents as dollars, a factor of 100 too large.

❌ Not quite. Notional = price per pound × number of contracts × pounds per contract, with the price in dollars.

❌ Not a payment. The initial margin sits in your own brokerage account as collateral; the seller receives nothing when the contract is struck.

❌ Not quite. A futures contract has zero value at inception, so no money changes hands to enter it.

Show solution

The price in dollars is 82.40¢ = $0.8240 per pound, and the position covers $6 \times 40{,}000 = 240{,}000$ lb:

\text{Notional} = F \times N \times Q = 0.8240 \times 6 \times 40{,}000 = 197{,}760

so the notional value is $197,760. You do not own $197,760 of anything: the contract is struck at the price that makes it worth zero, so $0 is paid to enter. The initial margin (typically 5%–20% of notional) is your own money, held as collateral.

Problem 2 · One Day's Settlement for a Short

Given (illustrative figures): you are short 8 live-cattle futures contracts (40,000 lb each). Yesterday's settlement price was 76.10¢ per pound; today it closes at 76.45¢. Find today's cash settlement on your margin account.

✅ Correct! The price rose, so the short pays $1,120 today and the longs on the other side receive exactly $1,120.

❌ Check the side. $1,120 is the long's gain. A rising price hurts the short, whose settlement is the negative of the long's.

❌ Check the units. The change is 0.35¢ = $0.0035 per pound, not $0.35.

❌ That is one contract.

0.0035 \times 40{,}000

covers a single contract; you are short 8.

❌ Not quite. Settlement = −(price change per pound) × total pounds for a short.

Show solution

The price change is $76.45 - 76.10 = 0.35$ ¢, that is $0.0035 per pound, on $8 \times 40{,}000 = 320{,}000$ lb. For the long,

G^{\text{long}} = 0.0035 \times 320{,}000 = 1{,}120

so the long gains $1,120. The short is the other side of the same transfer, $G^{\text{short}} = -G^{\text{long}}$ : −$1,120 leaves your margin account today.

Problem 3 · Three Days of Marking to Market

Given (illustrative figures): you are long 5 live-cattle contracts (40,000 lb each) entered at 71.20¢ per pound. The next three settlement prices are 70.85¢, 71.40¢ and 71.05¢. Find the day-2 settlement and the net cash moved over the three days.

What is the day-2 settlement on your account?

What is the net cash moved into (+) or out of (−) your account over the three days?

✅ Correct! The daily settlements −$700, +$1,100 and −$700 add to −$300, the same as the change in notional from 71.20¢ to 71.05¢.

❌ Settle against yesterday, not the entry price. Day 1 already settled the move from 71.20¢ to 70.85¢; day 2 settles only 70.85¢ → 71.40¢.

❌ Not quite. Day 2's move is 71.40¢ − 70.85¢ on 200,000 lb, and a rise pays the long.

❌ Include the gain. The day-2 gain of $1,100 is paid into your account too, and offsets part of the two losses.

❌ Not quite. Add the three signed settlements, or equivalently price the whole move from entry to the last close.

Show solution

Total size: $5 \times 40{,}000 = 200{,}000$ lb, so each 1¢ ($0.01) per pound is worth $2,000 to the position.

Day 1: $70.85 - 71.20 = -0.35$ ¢, so $-0.0035 \times 200{,}000 = -700$ : −$700
Day 2: $71.40 - 70.85 = +0.55$ ¢, so $0.0055 \times 200{,}000 = 1{,}100$ : +$1,100
Day 3: $71.05 - 71.40 = -0.35$ ¢, so $-0.0035 \times 200{,}000 = -700$ : −$700

Net: $-700 + 1{,}100 - 700 = -300$ , that is −$300. Check: the whole move from entry is $71.05 - 71.20 = -0.15$ ¢, and $-0.0015 \times 200{,}000 = -300$ . The daily settlements always add up to the change in notional value.

Problem 4 · A Loss That Outruns the Margin

Given (illustrative figures): a trader is long 12 live-cattle contracts (40,000 lb each) with $30,000 of margin posted. On one extreme day the futures price falls from 75.80¢ to 68.55¢ per pound. The loss exceeds the margin by $4,800. Decide who bears that $4,800 and how much the short side is credited.

Who bears the $4,800 beyond the margin?

How much is credited to the short side that day?

✅ Correct! Margin is not a ceiling on liability: the trader owes the full $34,800, and the short is credited the full $34,800 whether or not the trader pays.

❌ Margin is not a ceiling on liability. The margin account is not a non-recourse loan; the broker can pursue the trader's other assets for the rest.

❌ The short is paid in full. The clearing corporation is the short's counterparty, so the short's gain does not depend on this trader's ability to pay.

❌ Only as a last resort. The shortfall lands on the clearing corporation only if the trader cannot pay; otherwise the trader owes it.

❌ Not quite. Ask who is legally liable for the loss, and who steps in only when that party cannot pay.

❌ Not quite. The short gains exactly what the long loses that day: 7.25¢ per pound on 480,000 lb.

Show solution

The position covers $12 \times 40{,}000 = 480{,}000$ lb and the price falls $75.80 - 68.55 = 7.25$ ¢ = $0.0725 per pound, so the day's loss is

L = 0.0725 \times 480{,}000 = 34{,}800

that is $34,800, and $\max(L - M, 0) = 34{,}800 - 30{,}000 = 4{,}800$ , the $4,800 beyond the margin.

Who bears it: the trader. Margin is collateral, not a limit on liability, and the broker can pursue other assets. Only if the trader cannot pay does the shortfall fall on the clearing corporation, which margins sized to cover about 99% of daily swings make rare.

The short side: credited the full $34,800, because the long's loss and the short's gain always sum to zero and the clearing corporation stands between them.

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