Futures expiry and rollover: contango and backwardation

What you will learn

• What happens to a future at expiry and why futures converge to spot
• How cost of carry explains the gap between futures and spot prices
• What contango and backwardation are and how to read a futures curve
• How to calculate the roll cost or roll gain of a long position

Explanation

The spot price is the price for immediate delivery. A future fixes a price for a later date. On the last trading day, a future and the spot price must be almost equal, otherwise anyone could buy the cheaper one and deliver against the more expensive one. This is called convergence.

The basis is the difference between the two. In this course we define basis = spot price − futures price. (Some markets use the opposite sign; always check the definition used.) The basis moves towards zero as expiry approaches.

Cost of carry

Why does a future trade at a different price from spot before expiry? Because holding the underlying until the future date has costs and benefits. This is the cost of carry:

• Costs: financing (interest on the money tied up), storage and insurance for physical goods.
• Benefits: dividends on shares, coupons on bonds, and for commodities sometimes a convenience yield (the benefit of physically holding scarce goods).

For a stock index that does not include dividends, a simple fair value formula is:

Fair value F = S × (1 + (r − d) × days ÷ 360)

where S = spot index level, r = annual interest rate, d = annual dividend yield. If the future trades well above fair value, arbitrageurs buy the index and sell the future, which pushes the prices back together.

The futures curve

If you list the prices of all contract months in order, you get the futures curve (also called the term structure).

• Contango: later contracts are more expensive than nearer ones. Common when carry costs are positive, for example for stored commodities.
• Backwardation: later contracts are cheaper than nearer ones. Often seen when a commodity is scarce now and buyers pay a premium for immediate delivery.

The shape can change from one year to the next; past curve shapes do not predict future ones.

Expiry and rollover

Before expiry you must decide: close the position, or roll it. Rolling means closing the expiring contract (the front month) and opening the same position in a later contract. Many retail brokers do not allow physical delivery and close positions automatically before the last trading day. Check your broker's rules and the exchange's expiry calendar in advance.

When you roll a long position in contango, you sell the cheaper contract and buy the more expensive one. If the spot price does not change, the new contract drifts down towards spot as it approaches expiry, and you lose the difference. This is negative roll yield. In backwardation the effect is reversed. Long-only commodity products that roll futures are affected, so their returns can differ strongly from spot.

Worked example

Hypothetical example, part 1: fair value. A price index (without dividends) stands at 18,000. Interest rate 3% per year, dividend yield 2% per year, 90 days to expiry.

• r − d = 3% − 2% = 1% = 0.01
• 0.01 × 90 ÷ 360 = 0.0025
• F = 18,000 × 1.0025 = 18,045 points

The future should trade about 45 points above spot. A gap of 45 points is not a forecast that the index will rise; it only reflects carry.

Hypothetical example, part 2: roll cost. A commodity future covers 1,000 barrels. You are long the front month, which expires and is at $80.00. The next month trades at $81.20 (contango). You roll: sell the front at $80.00, buy the next at $81.20.

• Assume the spot price stays at $80.00 for the next month and the new contract converges to $80.00 at its expiry.
• Result on the new contract: ($80.00 − $81.20) × 1,000 = −$1,200.
• As a percentage of the front price: $1.20 ÷ $80.00 = 1.5% per month.

Spot did not move, yet the long position lost $1,200. In backwardation, with the next month at $78.80, the result would be +$1,200. Excluded: commissions, the bid-ask spread on both legs of the roll, and currency conversion into euros.

Common mistake

Practice activity

Hypothetical data, no costs.

1. A price index stands at 10,000. Interest rate 4%, dividend yield 1%, 180 days to expiry. Calculate the fair value.
2. You are long 1 commodity future of 100 units. The front month is at €50.00, the next month at €51.50. You roll. If the spot stays at €50.00 until the new contract expires, what is your result in euros and in percent of €50.00?
3. Is the market in question 2 in contango or backwardation?

Key takeaways

• Futures converge to the spot price at expiry; the basis moves towards zero.
• Cost of carry (financing and storage minus income) explains most of the futures-spot gap.
• Contango: later contracts are higher; backwardation: later contracts are lower.
• Rolling a long position in contango costs money even when spot does not move.

Next step

In the next lesson you move from obligations to rights: the basic building blocks of options, namely calls, puts, strike, expiry and premium.