The Contango

Hilary Till, Principal Premia Capital Management, LLC

Hilary Till, Principal Premia Capital Management, LLC

Continuing with Hilary Till’s study, the next interesting find is the roll yield embedded in the term structure of futures contracts. In her own words:

In the past, even if spot commodity prices declined, there was an additional way that a commodity investor could have a positive statistical expectation of profit, and that was through the “roll yield” embedded in certain commodity futures contracts.


By term structure, we mean one should examine the relative price differences of futures contracts across delivery months. When a near-month contract is trading at a premium to more distant contracts, we say that a commodity futures curve is in “backwardation.” Conversely, when a near-month contract is trading at a discount to more distant contracts, we say that the curve is in “contango.”


Forward shifts in crude oil. Source:

The above figure shows how oil future forward curves, for any given month, have evolved for oil futures during 2004-05, from the typical oil backwardation to contango curves. As Howard Simons puts it:

Each ribbon in the chart represents a forward curve beginning with the front month and ending with the December 2005 contract. The near months are on the left of the ribbon; the far months are on the right of the ribbon. As time goes forward and as price rises, the switch from a backwardated structure — front months over the back — switches to a deeper and deeper carry and a bona fide contango.

Let’s back-up a little to go over some basics. The normal (subjective) situation for a forward contract, such as any future’s contract, should be a contango which meets the following:


F = Future
t = number of days from today.
r = daily interest rate.
y = 0, the convenience yield. In special situations, buyers are willing to pay extra to carry inventory on hand (i.e. a refinery worried about oil supplies).
sp = Spot price.
ic = inventory (carry) cost.

It is always possible to buy the spot commodity, pay the cost of carry —or the rents for the investment and storage facilities, which has to equal the future price of sale of the commodity. If not, there is a profitable arbitrage to be made between the two.

OK, but where do we make our money in a roll yield?

In Hilary’s own words:

When a commodity futures contract is in backwardation, an investor has two potential sources of returns. Since backwardation typically indicates scarcity, one is on the correct side of a potential price spike in the commodity by being long at that time.

The other source of return involves a bit more explanation.

In a backwardated futures market, a futures contract converges (or rolls up) to the spot price. This is the “roll yield” that a futures investor captures. The spot price can stay constant, but an investor will still earn returns from buying discounted futures contracts, which continuously roll up to the constant spot price. A bond investor might liken this situation to one of earning “positive carry.”

In a contango market, the reverse occurs: an investor continuously locks in losses from futures contracts converging to a lower spot price. Correspondingly, a bond investor might liken this scenario to one of earning “negative carry.”

In other words, for a backwardation (contango) commodity we buy (sell) a future contract further into the delivery curve and wait for its appreciation (depreciation) as it approaches the higher (lower) spot price.


Source: EDHEC

Another interesting source of potential profits, which is depicted in the above figure, is derived from the notion that backwardated contracts are well correlated to higher (long) returns in these contracts, predominantly in extended holding periods –five years.

Since there is quite a controversy regarding the reasons for the prolonged oil contango, I recommend you read Howard Simons’: It Takes Crude to Contango. The oil contango can be explained away by the recent play on oil futures to counter the ETF funds (i.e. GSCI) requirement to always go long on the rollover to a subsequent delivery month at expiration: savvy players are buying the the required futures in advance to sell to the ETF funds at a premium.