Contango, backwardation, and all that good stuff

From some of the comments that have appeared both here and on some other blogs about my post
Oil futures and the
future of oil
, it seems that some readers might appreciate a technical background
discussion of the way in which carrying costs and convenience yield influence the relation
between spot prices and futures prices. So if that describes you, by all means read on.

It’s easiest to see through the fog here if we first consider what the equilibrium outcome
would be if all market participants were risk neutral, that is, if they don’t care about the
risks they assume as long as on average they come out with a profit, and further initially
assume that there are no transactions costs from entering or liquidating a position. For
concreteness, let’s talk about the relation between what’s going on at the present (June) and
what people think is going to happen in the future (December). The three magnitudes we’re going
to be interested in are the June spot price, the June price of a December futures contract, and
the December spot price. The first two of these numbers we know right now in June; the third
value we won’t find out until six months from now.

There are two separate equilibrium relations between these three numbers that will result
from arbitrage by two separate possible trading strategies. The first is a relation between the
June spot price and the expectation traders form in June about what the December spot price will
be. The trading strategy that will force there to be a relation between these two magnitudes is
one of borrowing money in order to take physical delivery of the oil today (which requires
buying it at the June spot price) and selling it six months from now at the then-prevailing
December spot price, using the proceeds to pay off the loan.

One’s first thought might be that the nature of this relation would be that, in equilibrium,
the expectation of the December spot price that traders form in June would have to equal the
June spot price plus the interest cost per barrel. If the expected December spot price were greater than
this number, then arbitrageurs could make an expected profit by taking physical delivery of a
greater volume of oil today (which actions would drive up the June spot price), intending to
sell a greater quantity of oil in December (driving down the expected December spot price).
Such arbitrage would continue until the stated relation held.

There are two reasons why this initial guess is too simplistic. The first arises from
storage costs. If in fact you tried to take physical delivery of oil today and hold it for 6
months, your costs could substantially exceed your interest borrowing costs. If there are
significant costs from the physical act of maintaining storage facilities, the equilibrium would
be one in which the June expectation of the December spot price is substantially above the June
spot price. This calculation arising out of the physical storage costs will be responsible for
producing the phenomenon referred to as “contango”, for which we’ll give a formal definition
shortly.

A second reason why the prediction that the expected December spot equals the June spot plus
interest could fail to hold is that there may be a reward to you from delivering the oil to your
customers in December that exceeds the actual December sales price. This could be the case if
you are fighting for market share, and if you don’t have oil to sell to your regular customers in
December, you’ll lose them forever, or if you have other aspects of an ongoing business
operation that make it costly for you to make changes in the volume of sales over time. Such
factors are referred to as a “convenience yield” from holding oil, which could cause the
expected December spot price to be below the June spot price. This will form the basis for the
phenomenon known as “backwardation,” for which again we’ll momentarily give the complete
definition.

So, given the possible presence of both storage costs and convenience yield, in equilibrium
it would be possible to see the expected December spot price either above or below the June spot
price. If we use the expression “cost of carry” to refer to interest cost plus storage cost
minus convenience yield, we could characterize this outcome as requiring that the expected
December spot price equals the June spot price plus the cost of carry.

Now let’s turn to the second equilibrium relation we talked about, this time a relation
between the June price of the December futures contract and the expectation that traders form in
June about what the December spot price is going to be. Here the arbitrage strategy is one of
buying a December futures contract today (committing the buyer to take physical delivery of the
oil in December), and planning on selling the oil when it gets delivered on the December spot
market. If the December futures price is less than the expected December spot price, there’s an
expected profit to be made from this transaction, because you’ll be buying the oil in December
for less than you’ll be turning around and selling it right back. As traders try to engage in
this strategy, more people are buying December futures contracts in June (driving the price of
the contract up) and are planning to sell oil on the spot market in December (driving the
expected December spot price down). In equilibrium, the expected December spot price would be
forced to equal the price of the futures contract that you could buy in June.

Now, because investors are free to contemplate either of these arbitrage strategies, both
the relations we discussed will have to hold in equilibrium. As a result of arbitrage strategy
1 (traders take physical delivery of oil and hold it), the expected December spot will equal the
June spot price plus cost of carry, and as a result of the arbitrage strategy 2 (traders buy
futures contracts that are closed out by offsetting sales on the December spot market), the
expected December spot must also equal the June price of the December futures contract.

Notice that if you put those two together, you come up with a third relation that’s implied
by the first two, namely, that the June price of a December futures contract should equal the
June spot price plus the cost of carry. The expressions “contango” and “backwardation”
mentioned above actually apply to this third relation. If cost of carry is dominated by storage
costs, the December futures price will be above the June spot price, and we refer to such a
condition as “contango”, whereas when the cost of carry is dominated by convenience yield, the
December futures price will be below the June spot price, and this is the situation that the
term “backwardation” is used to describe. If you like (and many texts and expositors of these
ideas do just this), you can jump directly to this third relation by considering what seems to
be yet a third arbitrage strategy, namely, buy the oil today taking physical delivery on the
June spot market, and lock in your profit by also selling it off for delivery in December using
the December futures contract to do so. I say this seems to be a third arbitrage strategy,
because in fact it’s nothing more than a simultaneous execution of the first two. You could
imagine executing this third strategy in two steps, first buying oil on the spot market and
physically storing it until December in order to sell it off at December’s spot price (which was
arbitrage strategy 1 discussed above), and second selling a December futures contract in June,
planning to buy oil on December’s spot market to fulfill the contract (the reverse side of
arbitrage strategy 2 described above). Of course, if you executed both these strategies
together, you’d be both buying and selling the same quantity of oil on December’s spot market,
and those two trades would cancel out, in which case you have in effect exactly implemented
arbitrage strategy 3. So strategy 3 is just a combination of simultaneously executing
strategies 1 and 2.

I know that it’s a little confusing to describe strategy 3 this way, which is why texts that
are trying to explain contango and backwardation usually do it by discussing strategy 3 directly
rather than the sum of strategy 1 and 2. But analyzing it the way I have done here clarifies a
key point that is often missed in this literature, which is that the relation between the
expected December spot price and the June price of a December futures contract has nothing to do
with storage cost or convenience yield, because you can arbitrage a discrepancy between the
expected December spot price and the futures price without ever having to store the oil
physically for any length of time or miss selling a drop to a single customer. Anybody can
participate in this arbitrage, over and above whatever you’re already storing or not storing in
June or selling or not selling in December. Whenever the December spot price that you’re
expecting as of June exceeds the June price of a December futures contract, there’s an expected
profit to be made from buying that futures contract.

So, with that as background, let me now repeat the point of my earlier post. The peak oil
hypothesis holds that global production of petroleum is soon going to start declining every year
rather than increase each year as it’s done in the past. That scenario implies that oil prices
will be rising rapidly in the future. The 2011 futures contract that you could buy today is at
a price that is in fact below the price of a 2006 futures contract (backwardation). So, if you
believe in peak oil, you should buy that 2011 futures contract. But you should also take into
account, in evaluating the plausibility of the peak oil hypothesis, that there seem to be a lot
of people who disagree with you and are prepared to wager substantial sums against you.

And now let me get into some further details and qualifications for those whose eyes have
yet to glaze over. The above calculations ignored the fact that futures contracts have margin requirements, which are cash you have to put up front as proof that you can fulfill the commitment you’ve undertaken with the contract. If the market moves against you (e.g., the oil price went down when you were on the buying side of a futures contract), you’ll need to put in even more cash. So you may need cash on hand
to ride this through, and the interest rate or opportunity cost on that cash is also going to
enter into your calculations. But this has nothing to do with either the convenience yield or
the cost associated with physical storage. Furthermore, if you think that the possibility is
really pretty remote that oil prices could fall for more than three years before they begin the
big climb up, you could always hedge this margin-call risk by simultaneously selling a 3-year
futures contract when you buy the 6-year contract.

Second, the above discussion abstracted from aversion to risk that both you and the market
might have. Market participants in large numbers might be using futures contracts to hedge
against risks in either the petroleum industry or the economy at large. While that’s a
possibility, I just don’t see any scenario in which the market as a whole believes in the peak
oil scenario, that is, believes that oil prices are about to go through the roof, but still
wants to be promising to deliver oil in the future at low prices in order to insure themselves
against some sort of risk. The story just doesn’t make sense– markets can’t be interpreting
the current situation from the perspective of peak oil.

Third, one can ask, how close does the December futures price usually turn out to be in
terms of predicting the December spot price? The answer is, not all that close. Markets often
make big mistakes one way or the other. Joseph Haubrich, Patrick Higgins, and Janet Miller, in
a study put out by the
Federal Reserve Bank of Cleveland last December
, concluded that the oil futures market is
systematically making mistakes in predicting spot prices. By contrast, a <a
href=”http://www.ssc.wisc.edu/~mchinn/w11033.pdf”> working paper put out by the National Bureau
of Economic Research this January by Menzie Chinn, Michael LeBlanc, and Olivier Coibion
concluded that the market does a decent but by no means perfect job given that oil prices are
inherently quite difficult to forecast. In any case, nobody is suggesting that markets know for
sure that the peak oil hypothesis is wrong. But I nevertheless am compelled to draw the
conclusion that the moves we’ve seen in oil prices this past year are not consistent with the
claim that markets have suddenly decided that peak oil is upon us. And, I still say that if you
think peak oil already is here, there’s some big money to be made.

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15 thoughts on “Contango, backwardation, and all that good stuff

  1. Big Gav

    Thanks for this interesting commentary – those of us in the peak oil world always appreciate some intelligent economic analysis of the oil markets.
    Its also refreshing to see an economist who analyses the market and relates it to the peak oil idea, rather than simply dismissing the idea out of hand and saying that market forces always solve resource scarcity issues (ala Michael Lynch).

  2. The Glittering Eye

    Catching my eye: morning A through Z

    Here’s what’s caught my eye this morning: David MacDuff of A Step at a Time, scholar and professional translator. Reminisces about his second trip to the Soviet Union in the late 60’s. That was when, following the Soviet invasion of…

  3. Hal

    “One’s first thought might be that the nature of this relation would be that, in equilibrium, the expectation of the December spot price that traders form in June would have to equal the June spot price plus the interest cost per barrel. If the expected December spot price were greater than this number, then arbitrageurs could make an expected profit by taking physical delivery of a greater volume of oil today (which actions would drive up the June spot price), intending to sell a greater quantity of oil in December (driving down the expected December spot price). Such arbitrage would continue until the stated relation held.”
    I don’t understand the reasoning here, because this logic only seems to show that the December spot price should be LESS THAN OR EQUAL TO the June spot price plus interest. You show why the December spot price should not be greater than that, but it does not follow from this argument why it should turn out to be equal. If oil were a seasonal commodity (as many are) then there might well be an expectation that the price will be lower at some point in the future.
    I also don’t understand the discussion of convenience yield. I thought that storage and interest costs put a limit on how much future expected prices (and hence futures contract prices) could exceed spot prices. Future prices can be higher than spot prices by only so much, otherwise your first arbitrage strategy works. However I did not think there were any forces that would prevent future prices from being considerably lower than spot prices. Is there such a factor?

  4. JDH

    Going back to that simplest first case with no storage costs and no convenience yield, let’s consider Hal’s question. What happens if the expected December spot is less than the June spot plus interest? Then anybody who’s currently storing oil should sell it now and invest the proceeds so as to earn that interest rate on the cash rather than trying to get a capital appreciation from the oil. You’d get a higher return on your money by selling the oil now rather than storing it. If there’s no convenience yield, then any time there is a positive amount of oil being stored somewhere with the expected December spot below the June spot, somebody is missing out on an opportunity for expected profit.
    Of course, as inventories get lower and lower, that convenience yield starts to become more and more important– you can’t run any business on zero inventories. So, we often are in a situation where the expected December spot is below the June spot plus interest. But whenever you see that, the reason that people are holding inventories is the convenience yield, not to make a capital gain on the storage.
    And, to the extent that everybody’s trying to flood the June spot market by selling off the oil they stored, and nobody has stored anything to have to sell to those folks in December, that tends to lower the June spot price and raise the December spot price, undoing the hypothetical.
    In equilibrium, the expected December spot has to equal the June spot plus cost of carry.

  5. Financial Rounds

    Contango, Anyone?

    James Hamilton is a very well respected economics professor at the University of California-San Diego. He wrote a classic econometrics text on Time-Series Analysis ever done. Now it turns out that he also has a blog, titled Econbrowser.

  6. jpf

    Peak Oil, as I understood it, means that there will be more depleation of known reserves than there will be new discoveries.
    That doesn’t necessarily mean that oil prices have to go up in the near to medium or even long term.
    A prolonged recession could lower the oil price even though the known reserves are shrinking.
    So – it’s possible to both believe in this definition of Peak Oil AND still believe that oil prices will not sky rocket (when adjusted for inflation)
    jpf

  7. JDH

    Peak oil refers to the idea that global petroleum production will start to be lower each year rather than higher as existing reservoirs are depleted. A falling price of oil would mean that, as this happens, the oil is becoming less valuable to consumers and less costly to produce. I think you’d have a very difficult time working out the details of a scenario in which peak oil would lead to a prediction of falling oil prices.

  8. disinterested party

    The oil-price bubble

    It doesn’t seem like two months ago that I wrote this: In many ways today’s oil market reminds me of the dot-com insanity, what with analysts like Goldman Sachs’ Arjun Murti channeling Henry Blodget, predicting $105-a-barrel “super spikes,” a…

  9. Guansu

    Hello, Professor, do you mind if you give some comments on the copper markets recently and the concept of “super spike”? Thanks a lot.

  10. Guansu

    I agree with Hal. Firstly, the seasonal adjustment should be considered in the arbitrage one. Secondly, storage cost provides contango cap while the convenience yield could just offer a meaning relation between both prices rather than a certain quantitative frame.
    What is more, since the storage cost and convenience yields make sense for the real industries, this kind of argument conflicts sort of with the pure financial arbitrage tradings.
    Could you give me a hint, professor? Thanks.

  11. Guansu

    I am an analyst in China focusing on arbitrage and spread trading between London Metal Exchange and Shanghai Futures Exchange. Therefore would professor and any friends talk about the historical low level of inventory and high level of cash-3’s premium, and the historical price on copper market recently? There is some kind of guess around the market that the copper market is temporarily controled by some corporation (maybe Glencore)or investment funds for short corner. Any opinions? Thanks.

  12. disinterested party

    The oil-price bubble

    It doesn’t seem like two months ago that I wrote this: In many ways today’s oil market reminds me of the dot-com insanity, what with analysts like Goldman Sachs’ Arjun Murti channeling Henry Blodget, predicting $105-a-barrel “super spikes,” a…

  13. Andrew

    I guess one reason why the convenience yield will exceed the cost of carry for commodities like oil and gas is that you’re holding the oil/gas not against one future time but a whole series. As you get closer to the term date for the futures contract the risk of supply distruption decline and the convenience yield on that contract declines. Does this explain why oil and gas futures contracts tend to increase towards their expiry?
    Also how does hedging through correlated commodities play into this? And what does it tell us if the futures contracts for two related commodities diverge the futhur out you go, e.g. NYMEX WTI and natural gas?

  14. Matt

    I am interested in long-term prediction by futures markets of peak oil as a major economic or cultural problem.
    The reports cited appear to be quite convincing that the futures prices are not very predictive and therefore we ought not take comfort by the fact that long term oil futures don’t have a huge “peak-oil” induced upward slope.
    In 2001, how far was the long-term futures market prediction of 2006 oil prices away from truth?
    On the other hand, a 1998 Scientific American article entitled “The end of cheap oil” appears to have predicted the squeeze quite accurately based on physical constraints and industry experience, saying that it would start between 2005-2010.
    If there is no information in the futures, was there information in the options? Do the premiums of long term oil options now reflect an anomalous situation?
    Another potential conclusion is that we should stop listening to markets and start listening to geologists.

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