Mar 12

Contango

by David Harper, CFA, FRM, CIPM

Risk | Quant |

Contango and backwardation are confusing enough that even the Financial Times got it wrong (Reports - Analysis: All you need to know of contango). We often see the mistaken idea that contango is when futures prices are higher than spot prices, or similarly, when faraway futures are higher priced than nearby futures. That might or might not be a contango situation. Here is a futures curve from last year, for gold futures:

The futures prices are increasing with longer maturity. This is simply called a 'normal' market.

Here is a crude oil futures curve from last year:

This futures curve is normal but then gives way to an 'inverted market.' (And note, the crude oil futures curve above is traditionally characteristic. Due to supply/demand, long-term oil futures have tended down in price. Under this scenario, direct or indirect consumers of crude oil like airlines do well to hedge; i.e., they lock in a lower price. The point of the FT story is that, currently the crude oil futures is 'normal' as distant futures are higher priced. Under such an alternative scenario, hedging becomes less desirable; i.e., why pay a higher price instead of gambling that the spot will remain low?).

So, if we take a snapshot of the futures curve, it's normal if futures prices are higher at longer maturities and inverted if futures prices are lower at distant maturities. So, if gold is $600 today (spot) and the Dec 2007 futures price is $800, that's normal. If the Dec 2007 futures price is $500, that's inverted. But that's all static. Contango and normal backwardation refer to the pattern of prices over time. Specifically, is the Dec 2007 futures price going to rise (normal backwardation) or fall (contango)?

So this gets a  little tricky, but keep in mind two ideas:

  • As we get closer to maturity, the futures price must converge toward the spot price (the difference is the basis). That because, on the maturity date, the futures price must equal the spot price (or you could make a lot of free money with an easy arbitrage).
  • The most rational futures price is the expected future spot price. For example, if you and your counterparty both could forsee that the spot price in crude oil would be $80 in one year, you would probably settle on an $80 futures price (why would one of you commit to a future loss?).

Now we can make definitions:

  • Contango is when the futures price is above the expected future spot price. Because the futures price must converge to the expected future spot price, therefore, contango implies that futures price are falling over time (i.e., as new information brings them into line with the expected future spot price).
  • Normal backwardation is when the futures price is below the expected future spot price. This is desirable for speculators who are "net long" in their positions: they want the futures price to increase. So, normal backwardation is when the futures prices are increasing.

See how it is more precise to say that "in contango, futures are falling. In normal backwardation, futures are rising." This is somewhat independent of the shape of the futures curve because the futures prices is constantly adjusting to consensus expectations about the expected future spot price.

Finally, note that 'normal backwardation' is not quite the same as 'backwardation.' (source: Futures, Options, and Swaps by Robert Kolb and James Overdahl). Backwardation is the same as 'inverted.' Backwardation is simply when futures prices are lower than spot prices.

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