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.