Cash-and-Carry Arbitrage

Futures have a fair price you can calculate

Buying the physical today and holding it to delivery costs interest and storage. So the fair price = spot × (1 + rate × time) + cost of carry. If the futures quote strays from it, someone can make free money.

The profit is locked in the moment you open

Futures rich: borrow to buy the physical + sell futures (cash-and-carry). At expiry the spot and futures legs move opposite ways and cancel exactly, leaving the price gap from when you opened, whatever the expiry price.

Reverse arbitrage is harder than forward

When futures are rich, anyone can borrow money to buy the physical and arbitrage it. When futures are cheap, the reverse trade needs you to sell the physical first: you have to own it or be able to borrow it, and pay a borrowing fee. Commodity holders value the convenience yield and won't sell, so futures can stay below fair value for a long time (backwardation).

Key takeaways

• Futures fair value = spot × (1 + interest rate × time) + carrying costs.
• Futures above fair value: borrow to buy spot + sell futures (cash-and-carry). Below fair value: sell spot + buy futures (reverse cash-and-carry).
• Profit at expiry = futures price − fair value, no matter how high or low spot ends up. That's what makes it risk-free arbitrage.

Try it yourself

You can do these exercises in this lesson's interactive simulation:

1. Click the example: what's the fair price? How much profit is locked in? Compare with the numbers in the quiz.
2. Drag "Spot at expiry" from $60 to $140: how does each of the spot and futures legs change? Did the total change?
3. Drag the futures quote to $100: what happened? Watch how the direction of both cash flow tables flips.
4. Set the rate to 0% and carry cost to $2: what's the fair price now? Which factor makes futures "deserve" to be pricier than spot?

Quiz and explanations

1. Spot is $100, the annual interest rate is 6%, delivery is in 3 months and there's no storage cost. Roughly what's the futures fair value?

Answer: $101.5.$100 × (1 + 6% × 0.25) = $101.5.

2. The futures are quoted at $104 and fair value is $101.5. What should you do?

Answer: Borrow to buy spot and sell futures at the same time.You lock in the $2.5 gap and deliver at expiry; the result doesn't depend on the price at expiry.

3. Spot is $100, the annual interest rate is 4%, delivery is in 6 months and storage costs $1 over the period. What's the futures fair value?

Answer: $103.$100 × (1 + 4% × 0.5) + $1 = $103.

Terms in this lesson

• backwardation (Backwardation): A market where futures (or later months) trade below spot (or nearer months).
• cost of carry (Cost of Carry): The storage, insurance and financing costs of holding a physical commodity.
• cash-and-carry (Cash-and-Carry): When futures are too expensive: borrow to buy the spot asset and sell futures at the same time, locking in the gap at delivery.
• convenience yield (Convenience Yield): The benefit of actually holding the goods (no shortages, ready to use); it makes holders reluctant to sell, so futures can stay below fair value for a long time and reverse arbitrage may not work.
• fair value (Fair Value): The theoretical price implied by “no free money”; for example, futures fair value = spot × (1 + rate × time) + carrying costs.
• reverse cash-and-carry (Reverse Cash-and-Carry): When futures are too cheap: sell the spot asset and buy futures at the same time, taking delivery to restore your position.