Econbrowser

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 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.