Question about Bionic Turtle's 2009 FRM Program
07 Jan 2009
Jan
23
Contango, backwardation & expected future price
by David Harper, CFA, FRM, CIPM
FRM |
Steve Campbell asks,
Can a normal market be in backwardation and can a inverted market be in contango? And, does Contango and Backwardation only relate to expected futures prices not the fact that it is simply above or below the spot price? And if the a futures price is equal to the expected futures price then doesn't this leave many arbitrage opportunities as the price may not fully reflect carrying costs? Thanks for your help. Regards,Steve
Thanks for the question, Steve. Hopefully, the technical definitions help clarify:
Backwardation and contango speak to the slope of the observed futures curve.
- Contango = futures price > spot price.
- Backwardation (i.e., inverted curve) = futures price < spot price.
"Normal backwardation" and "normal contango" are, I would argue, theoretical. They refer to instead to a relationship that is directly unobservable: the relationship between the spot price and the expected future spot price.
- Normal contango = futures price > expected future spot price.
- Normal backwardation = futures price < expected future spot price.
The meanings are often confused. As you suggest a physical commodity typically has a carrying cost. Take corn futures, for example. Here is a plot I used in last year's FRM lesson on the cost of carry (caveat: it's an old futures curve); corn futures here are in "contango" (futures price > spot price), as we'd expect. So, this is a normal situation but it doesn't not help to say it's "normal contango" (it could be normal contango, it could be normal backwardation, we actually do not know. What we know is that's it's contango!):
Now assume we could magically infer the expected future spot price (assuming we could win the argument against folks who would say to us, "the future price is the best estimator of the expected future spot price!"). You can see that, it could fall above or below the future price, such that: while the curve is in contango, it's theoretically possible to be in either "normal contango" or "normal backwardation."
This whole business of normal contango and normal backwardation might seem sort of academic. It concerns the theory that futures ought to generally be in normal backwardation (again: regardless of the "slope" of the curve). The theory is that speculators buy futures and hedgers sell them. If that's true, why would a speculator buy a futures contract unless he/she expected to profit (i.e., unless he/she perceived normal backwardation). In short, normal backwardation is consistent with the idea of a risk premium for the buyer. I say it's sort of academic because normal contango/backwardation isn't known at the trade, it's proven or disproved over time. Simple contango or backwardation are observed.
On the other hand, traders are obviously concerned with the relationship between future prices and expected future spot prices. Profits are made this way. As contracts tend toward maturity, the futures price converges toward the spot (i.e., the basis converges toward zero); so if you purchase (go long) a futures correctly assuming normal backwardation, you'll profit. Futures prices are, in part, adjusting to the market's consensus view of the expected future spot price.
Carrying cost offset by convenience yield (or dividends, in the case of financial commodities)
On the point of carrying costs, for a physical commodity, the cost of carry model is something like this:
Where (r) is the a riskless rate, (u) is storage cost, and (y) is convenience yield.
In English, we'd expected the future price to be a function of the spot price plus the net cost of carry. Specifically, higher for the financing cost (r), higher for storage cost (u), but lower for any convenience yield (y). The latter is the quantifiable benefit of owning the asset; you can think of it an offset to storage costs. Finally, the convenience yield is the analog to dividends for a financial commodity, as both are benefits to the owner (and opportunity costs to the long forward holder)
Okay, that's a long way to answer your questions (sorry!). But hopefully that's sets the context to suggest the following:
Can a normal market be in backwardation and can a inverted market be in contango?
If "normal" refers to upward-sloping, then technically speaking: normal = contango. But also, a contango market can be in either normal backwardation or normal contango. Arguable, to take a long position in the futures contract is to reflect your view that the market is is normal backwardation; to short is to reflect a view that the market is in normal contango.
Does contango and backwardation only relate to expected futures prices not the fact that it is simply above or below the spot price?
"Normal backwardation" and "normal contango" refer to expected future spot prices.
And if the a futures price is equal to the expected futures price then doesn't this leave many arbitrage opportunities as the price may not fully reflect carrying costs?
I define arbitrage as a simultaneously risk-less and profitable trade. I don't think any of the above implies for true arbitrage. A flat future curve may merely be impounding the benefit the convenience yield. Sometimes trades seem like arbitrage because the risks of the trade are not getting explicitly factored into the equation.
Metallgesellshaft is an example of why it's not arbitrage
For example, among the FRM case studies is Metallgesellshaft. They were, for a while, successfully employing a stack-and-roll hedge strategy against an oil futures market that historically showed backwardation. As below, backwardation is when the futures price of oil is lower than the spot price:
How can the oil forward be cheaper? Because of the convenience yield, which offsets the cost of carry. Now, if you imagine the curve holding up in perpetuity, you can see why Metallgesellshaft was able to profitably execute its stack: they would enter long into a "cheap" futures and then, at a future point near to maturity, they would offset ("roll over") for a profit. That's if the spot price is steady (or increases) because over time the futures price will converge toward the spot.
This cannot be called arbitrage, as history proved. It was merely correct speculation that the backwardation would continue. Until is was incorrect. When the curve switched to contango, the rollovers were losses. The losses created a funding liquidity crisis-problem that ultimately led to a $1.5 billion loss (1993 dollars).
(I think it's also fair to say they were assuming normal backwardation in addition to perpetual backwardation. But the real point of Metallgesellshaft story is basis risk. The basis is the difference between the futures price and the spot price. What ultimately profit or hurts the trader or hedger is unexpected change in the basis. In this case, there was an unexpected weakening of the basis).
I hope that's helpful and interesting...
Comments
Beautiful explanation!
Finally I understood “Normal” Contango / Backwardation
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