In commodity futures, when does the pattern in which prices are lower for more distant expiries (backwardation) tend to appear?
Quiz: Commodity Derivatives
Last reviewed: September 25, 2026
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6 questions to check your understanding of the chapter “Commodity Derivatives”. Choose an answer and select “Check answer” to see the answer and explanation. You can also open “Answer and explanation” to see the answer first.
Question 1
Answer and explanation
Answer: D
When inventories are low and supply and demand are tight, holding the physical commodity is worth more even after paying the storage cost, so the convenience yield, the benefit of having the physical commodity on hand expressed as a yield, is higher. The futures price is set at the spot price plus the funding cost and the storage cost, minus this benefit, so a large benefit lowers the price of more distant months and backwardation tends to appear. Backwardation appears when the convenience yield is larger than the sum of the funding cost and the storage cost.
When futures prices are higher for more distant (deferred) contract months, the shape is called contango. A rise in storage costs or the funding cost increases the amount added to the futures price, so it moves toward contango. When inventories are high and supply and demand are loose, holding the physical commodity is worth less and the convenience yield is also low, so contango tends to appear.
Learn more: Overview of Commodity Derivatives
Question 2
On April 20, 2020, the front-month (nearest-expiry) WTI crude oil futures contract on the New York Mercantile Exchange (NYMEX) traded at a negative price for the first time since trading began in 1983. Which statement correctly describes the background?
Answer and explanation
Answer: A
NYMEX WTI crude oil futures settle by physical delivery: if you hold them to expiry, you deliver or take delivery of crude oil at Cushing, Oklahoma. As COVID-19 spread, consumption of crude oil dropped sharply, and surplus crude oil went into storage, leaving little room for storage at Cushing. Some of the unused storage was likely already under contract, so buyers of futures without a storage contract faced high costs to rent it. As a result, some buyers who wanted to avoid delivery sold their futures, even paying the other side to take them. At a negative price, the seller pays money and the buyer receives it.
The futures that are cash-settled against the monthly average price are Platts Dubai Crude Oil Futures on Tokyo Commodity Exchange. The negative prices occurred in the futures for May 2020 delivery, whose last trading day was approaching. Brent crude oil futures for June 2020 delivery closed at a positive price on April 21. WTI crude oil futures for contract months with distant last trading days also had positive prices.
A futures buyer loses money when the price falls. When the price falls below zero, the buyer's loss is larger than the full price paid. A seller, on the other hand, gains when the price falls and loses when it rises.
Learn more: Energy: Crude Oil and Natural Gas
Question 3
A retail electricity supplier plans to buy electricity next month on the spot market of the Japan Electric Power Exchange (JEPX). It hedges this by buying Tokyo Commodity Exchange power futures (baseload) for the same area. Whether spot prices rise or fall, a gap remains between the cost fixed with the futures and the actual procurement cost. Which statement correctly gives the cause of this gap?
Answer and explanation
Answer: C
What futures fix is the cost of buying a constant volume of electricity in the covered area through the period at the period's average price. A retail electricity supplier's actual demand changes every 30 minutes, so if prices are also high when demand is high, the actual procurement cost is higher than the amount calculated at the average price. The supplier can also fix the lowest volume in the period with baseload and add peakload for the extra volume on weekdays from 8:00 to 20:00. Even then, gaps from the 30-minute demand shape remain.
Tokyo Commodity Exchange power futures are cash-settled futures on JEPX spot market prices, with no physical delivery of electricity. On the spot market, after bidding closes, JEPX combines all buy and sell bids and sets a single clearing price, and every participant trades at that price regardless of the price it bid. The final settlement price of power futures is the average of the covered area price. If the futures area differs from the area where the supplier actually trades, a separate gap arises: when market splitting makes area prices diverge, the futures payments and the spot market payments do not offset each other.
Learn more: Power
Question 4
As a hypothetical example, suppose that in the precious metals market the currency (US dollar) borrowing rate is 8% a year and the gold lending rate is 3% a year. In the precious metals market, forwards and swaps that exchange gold and currency are quoted with a one-year swap rate. By that convention, what is the swap rate?
Answer and explanation
Answer: B
The swap rate is 5%. The precious metals market quotes the price of a forward as the currency interest rate minus the metal interest rate. In this example, 8% − 3% = 5%. Prorating this 5% by the number of days and adding it to the spot price gives the forward price for the period to maturity.
11% is the sum of the two rates. The metal rate is subtracted from the currency rate, not added. 8% looks only at the currency rate, and 3% looks only at the metal rate, so neither is the difference between the two. For base metals and foreign exchange, the forward price is quoted in "points" added to the spot price, but the precious metals market does not use this form.
Learn more: Metals
Question 5
As a hypothetical example, a company that makes animal feed plans to buy 50 tonnes of corn in the physical market in three months, and has bought one corn futures contract (50 tonnes) at 40,000 yen per tonne. Three months later, the futures price is 45,000 yen per tonne, and the price paid for the physical corn is the futures price plus 1,000 yen. What is the combined cost of the physical purchase and the gain or loss on the futures (ignoring fees)?
Answer and explanation
Answer: C
The combined cost is 2.05 million yen. The physical purchase price is 45,000 yen + 1,000 yen = 46,000 yen, so the purchase cost is 46,000 yen × 50 tonnes = 2.30 million yen. The futures give a gain of (45,000 yen − 40,000 yen) × 50 tonnes = 250,000 yen, so 2.30 million yen − 250,000 yen = 2.05 million yen.
2.30 million yen leaves out the gain or loss on the futures. 2.00 million yen counts only the futures price of 40,000 yen × 50 tonnes as the cost. 1.80 million yen counts the futures gain as 500,000 yen. The gain or loss on the futures is found by multiplying (futures price − purchase price) by 50 tonnes.
When the gap between the physical purchase price and the futures price (the basis) changes, the cost changes too. If the basis widened to 3,000 yen, the physical purchase price would be 48,000 yen and the purchase cost 2.40 million yen, and after subtracting the futures gain of 250,000 yen the cost would be 2.15 million yen. If the basis narrowed, the cost would be smaller than 2.05 million yen. The risk that the basis changes unexpectedly between putting the hedge on and taking it off is called basis risk.
Learn more: Agricultural Commodities
Question 6
As a hypothetical example, a business with an installation covered by the EU Emissions Trading System (EU ETS) expects to be short of 5,000 tonnes' worth of allowances in one year. It buys 5 EU Allowance (EUA) futures contracts (1,000 allowances per contract, maturing in one year) at 50 euros per tonne, and the price at maturity is 40 euros per tonne. What is the effective cost, combining the futures payments and the cost of buying in the market (ignoring fees and interest on margin)?
Answer and explanation
Answer: D
The effective cost is 250,000 euros. The cost of buying in the market is 40 euros × 5,000 = 200,000 euros. The futures payments, as a total from the trade date to delivery, come to (40 − 50) × 5,000 = −50,000 euros, so the business pays 50,000 euros. Together, 200,000 euros + 50,000 euros = 250,000 euros, or 50 euros per tonne.
200,000 euros leaves out the futures payments. 150,000 euros treats the 50,000 euros on the futures as a receipt and subtracts it from 200,000 euros. 50,000 euros looks only at the futures payments. When the price falls, buying in the market without futures would have cost 200,000 euros, so the difference of 50,000 euros is the burden of having bought the futures. Conversely, if the market price rose to 60 euros, the cost of buying in the market would increase to 300,000 euros, but the business would receive (60 − 50) × 5,000 = 50,000 euros on the futures, and the effective cost would again be 250,000 euros.
Learn more: Emissions