Both routes deliver the same asset on the same date, so they must cost the same; the forward price reflects the spot price plus the cost of storage and of financing the purchase
F=S0(1+r)T+CT
Illustrative version
An assumption for practice on this page, not the video's formula (that comes later in the course): r is compounded annually over T years and the storage bill CT is paid at delivery
V0=0
Market value at inception
No money changes hands at signing; if the contract were worth more than zero, its holder could sell it to a third party at a profit
Each side values the contract by its own information; both can expect to gain only when their expectations differ
Key Insight: The forward route and the buy-now route end with the same asset on the same date, but only the buy-now route needs cash today and a place to store the goods. That is why an airline that cannot pay for, or house, five years of jet fuel can still lock in its supply with forwards.
IITwo Routes to the Same Copper
Buying now costs the spot price plus financing plus storage; a fair forward price matches that total.
IIIDifferent Information, Same Market Value
Private beliefs can give each side a positive expected value while the contract's market value stays zero.
💡 Over the counter the two parties may legally write any price, even $200 a barrel; a price far from where oil stands gives the contract a large market value to one side and hands the other a spectacularly bad deal, so it is not signed.
IVQuiz Questions
Problem 1 · Features of a Forward
Which statement about forward contracts is false?
✅ Correct! Physical delivery is typical, because people use forwards to get the oil, gas or copper they need, but a forward can also be written as a pure side bet that settles in cash.
❌ That one is true. Forwards are customized and non-standard: each is written for the two parties who sign it, unlike an identical, exchange-traded share.
❌ That one is true. No money changes hands until maturity, which is exactly what makes a forward a no-money-down deal.
❌ That one is true. Non-trivial counterparty risk is the fourth feature: nothing guarantees the other side performs at maturity.
❌ Not quite. Three of the statements are the features the video lists.
Show solution
The four features of a forward contract are: customized (negotiated counterparty by counterparty), non-standard and traded over the counter, no money changes hands until maturity, and non-trivial counterparty risk. Statements (a), (c) and (d) restate them.
Statement (b) is false. Forwards typically assume physical delivery, but they need not: a forward can settle as a side bet with only a cash payment between the parties.
Problem 2 · Price the Forward Route
Given: Corn trades at $5.00 a bushel today, and you need one bushel in one year. Route 1, buy now and store: pay $5.00 today with money that costs 6% for the year (interest settled at delivery), and pay storage of $0.05 a month, billed at delivery. Route 2, buy forward: pay nothing today and the forward price at delivery. Find the one-year forward price at which the two routes cost the same, both counted at the delivery date.
✅ Correct! The buy-now route pays $5.00 today, which grows to $5.30 with a year of financing, plus $0.60 of storage: $5.90.
❌ That is today's spot price. Buying now also ties up $5.00 for a year and needs twelve months of storage; the forward price has to reflect both costs.
❌ Storage is missing. Corn is not costless to store: twelve months at $0.05 add $0.60 to the buy-now route.
❌ Financing is missing. Paying $5.00 today ties up cash for a year; at 6% that costs $0.30, the borrowing or opportunity cost of capital.
❌ Not quite. Add the spot price, a year of financing on it, and the storage bill.
Show solution
Route 1 (buy now and store), per bushel, counted at the delivery date: the $5.00 paid today plus a year's financing on it (6% of $5.00 = $0.30), plus twelve months of storage (12 × $0.05 = $0.60).
route 1=5.00+0.30+0.60=5.90
Route 2 pays the forward price at delivery, so the two routes cost the same when it is $5.90 a bushel. (This one-period sum is the page's illustrative relation F=S0(1+r)T+CT with T=1; the exact pricing formula comes in the next unit.)
Problem 3 · Which Route Is Cheaper?
Given: A wire maker needs 10,000 lb of copper in 3 months. Spot copper is $3.00 per lb. Financing the purchase for the 3 months costs 2% of the amount paid today, and storage costs $0.08 per lb for the 3 months, billed at delivery. A dealer quotes a 3-month forward at $3.10 per lb.
Which route is cheaper, per lb, at the delivery date?
For the 10,000 lb, how much more cash does buying now and storing need today than buying forward?
✅ Correct! Buying now and storing costs $3.00 + $0.06 + $0.08 = $3.14 per lb at delivery, so the $3.10 forward is $0.04 cheaper. Buying now also takes 10,000 × $3.00 = $30,000 of cash today, while the forward takes none.
❌ Storage is missing. $3.00 + $0.06 = $3.06 is below $3.10, but the buy-now route must also pay $0.08 to store the copper, which brings it to $3.14.
❌ Spot alone is not the cost of buying now. Comparing $3.10 with $3.00 ignores the $0.06 of financing and $0.08 of storage that the buy-now route carries.
❌ They differ. Route 1 costs $3.14 per lb at delivery and route 2 costs $3.10.
❌ Check the comparison. Carry the buy-now route to the delivery date: spot + financing + storage.
❌ Only the forward waits until delivery. Buying now pays spot for the copper today: 10,000 × $3.00 = $30,000, against nothing for the forward.
❌ That is the cost gap at delivery. 10,000 × $0.04 = $400 is how much cheaper the forward is in 3 months, not the cash each route needs today.
❌ That is route 1's total cost at delivery. 10,000 × $3.14 = $31,400; the financing and storage are paid later. Today route 1 pays only spot, $30,000, and the forward pays nothing.
❌ Not quite. When does money change hands in a forward contract?
Show solution
Route 1, buy now and store, per lb, carried to the delivery date:
cost=3.00+0.02×3.00+0.08=3.00+0.06+0.08=3.14
Route 2, buy forward: $3.10 per lb, paid at delivery.
The forward is cheaper by $3.14 − $3.10 = $0.04 per lb ($400 on 10,000 lb). Route 1 needs $30,000 of cash today (10,000 × $3.00); the forward needs $0 today, because no money changes hands until maturity. So buying now needs $30,000 more cash today.
Problem 4 · Private Values vs Market Value
Given: A refiner and a producer sign a 6-month oil forward over the counter at $82 a barrel, which is the market forward price that day. The refiner (long) privately expects oil to be at $90 in six months; the producer (short) privately expects $76.
What are the private expected values per barrel (refiner, producer)?
The contract's market value at inception is $0. Which argument shows that, whatever the two parties privately believe?
✅ Correct! Each side expects to gain by its own information ($90 − $82 = $8 and $82 − $76 = $6), yet the contract is worth $0 to the market: if either side were worth more, its holder could sell it to a third party at a profit.
❌ That assumes one belief. With the refiner's belief applied to both sides, the gain would be zero-sum. The producer uses its own $76: $82 − $76 = +$6.
❌ Check the short's sign. The short gains when the price at delivery ends up below the contract price, so its expected value is $82 − $76 = +$6.
❌ Check the long's sign. The long gains when the price at delivery ends up above the contract price, so its expected value is $90 − $82 = +$8.
❌ Not quite. Long: expected price minus contract price. Short: contract price minus expected price.
❌ They do not cancel, and they are not market value. +$8 and +$6 are both expected gains; netted they leave $2, summed $14. Either way they are private views. Market value is what the contract would fetch from market participants in general.
❌ No money down does not pin the value. A contract written at $200 a barrel also costs nothing to sign, yet one side would be making a spectacularly bad deal. What keeps this contract, signed at the market forward price, at $0 is that neither side could be resold at a profit.
❌ They disagree. The refiner expects $90 and the producer $76. The video's point is that the buyer's and seller's motives need no agreement on where oil is heading.
❌ Not quite. What would a third party pay for either side on the day it is signed?
Show solution
Private expected values use each party's own expectation of the price at delivery:
Both are positive because the two expectations differ; their sum is $90 − $76 = $14, the gap between the beliefs. Had both expected the same price, one side's expected gain would be the other's expected loss.
Market value is what the contract would fetch if auctioned to market participants in general, whatever the two parties privately believe. Signed at the market forward price with no money down, it is worth $0 at inception, and the argument is resale: if either side were worth more than zero, its holder could sell it to a third party at a profit. Netting the private values proves nothing (they are private views and leave $2), and no money down alone does not pin the value, since a contract written at $200 a barrel also costs nothing to sign.