DEFINITION of 'Convergence'

Convergence is the movement of the price of a futures contract towards the spot price of the underlying cash commodity as the delivery date approaches. 

BREAKING DOWN 'Convergence'

When a futures contract's delivery date is several months or years in the future, the contract will often trade at a premium to the expected spot price of the underlying commodity on the delivery date. This situation is known as contango​. As the delivery date approaches, the futures contract will depreciate in price; in theory, it will be identical to the spot price on the delivery date.

The chart below shows the prices for wheat futures contracts for different delivery dates, as of October 14, 2015. The upward slope represents contango.

Source: CME Group

The chart below plots the changes in price of wheat futures expiring in December 2015 versus the spot price of wheat, both on the left vertical axis. The basis, or the difference between these two prices, is plotted on the right vertical axis. The fall in the basis as the delivery date nears represents convergence.

Sources: CME Group and

The principle of convergence also applies when a commodity futures market is in backwardation​, that is, when futures contracts are trading at a discount to the expected spot price. In this case, futures prices will appreciate as expiration approaches, equaling the spot price on the delivery date.


That the spot price of a commodity would equal the futures price on the delivery date is fairly straightforward: purchasing the commodity outright on Day X (paying the spot price) and purchasing a contract that requires delivery of the commodity on Day X (paying the futures price) are in essence the same thing. The latter just adds an extra step.

If these prices somehow diverged on the delivery date, there would be an opportunity for arbitrage, that is, to make a functionally risk-free profit by buying the lower-priced commodity and selling the higher-priced futures contract (assuming the market is in contango; vice-versa if the market is in backwardation). While such opportunities may arise briefly due to market inefficiencies, arbitrageurs would in theory drive the price of the commodity up by increasing demand for it and push the price of the futures contract down by increasing the supply. In other words, the prices would converge.

Futures and spot prices do occasionally fail to converge, as happened with wheat, corn and soybeans at different points between 2005 and 2010. There are a number of theories as to why this could happen, but none is generally accepted.

Contango and Backwardation

We may ask why a futures contract would be more expensive than the underlying commodity in the first place, that is, why a futures market would find itself in a state of contango. The commodity itself does not change (unless it is perishable), so why pay extra for the privilege of waiting for it? The answer is in part practical: if you do not need palladium until next October, there is little reason to pay to store, protect and insure it in the mean time. It is easier to leave those expenses, known as the cost of carry, to the counterparty​. Since such convenience does not come for free, there is a premium on the futures contract.

Another way of explaining contango is through the time value of money. If a bond or savings account yields 5% annually, then $1,000 today is theoretically equal to $1,050 next year. Commodities like copper, on the other hand, do not generate interest. As mentioned above, they're more likely to cost money over time. Tying capital up in commodities implies an opportunity cost, which is compensated with higher prices for futures contracts.

The use of futures contracts as a hedge against volatile commodity prices also helps explain contango. The farther away the delivery date, the more time there is for things to go wrong—for wars to start, for crops to fail, for prices to swing. The party signing up for delivery two years from now at a certain price is taking on considerable risk and demands a premium for it. If that same party is signing up for delivery in a week, they will be content with something very close to the spot price.

As for why backwardation occurs, it can be because a commodity producer wants to hedge against future price movements. It is not uncommon for commodities with less predictable supply, such as perishables and oil, to be in backwardation. Farmers and petrostates need to guarantee a measure of revenue; unlike speculators, they are sometimes willing to forgo potential profits in exchange for security.

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