Arnold Kling  

My Model of the Oil Market: Option Value

Spotted on the Gas Pump at the... My Question for James Hamilton...

Near the end of a "tiny theoretical paper," Paul Krugman writes,

the actual data we have on crude oil don’t show the signatures of a market driven by speculative demand. Inventory data don’t show a big accumulation; and the market has mostly been in backwardation, not contango.

Backwardation means that futures prices are below spot prices. Contango means the opposite. See this post from four years ago.

My model of the oil market treats inventories and oil in the ground as the same. I don't care whether it is sitting in a storage tank or sitting under the Saudi sand--it's all part of the stock of oil. To look for shifts between under-sand oil and in-tank oil as evidence one way or the other on speculation does not strike me as compelling.

To a first approximation, there is just one price of oil, and it has to equate demand and supply for all time. If that price is too low, then at the consumption rates consistent with that price we will run out of oil. The holders of oil will have foregone large future profits and sold too much oil today. If the price of oil is too high, then producers will keep too much oil in the ground, the price will eventually fall, and they will have foregone large current profits.

To a next approximation, there is a path of future prices of oil. As long as extraction costs are not decreasing and the interest rate is positive, that path ought to embody a gradual increase in the price of oil. That increase will be higher the higher the nominal interest rate (so it should be rather low now). This is called the Hotelling principle.

If oil prices are expected to decrease (backwardation), then you want to extract the oil now, sell it, and put the proceeds into interest-bearing assets. With backwardation, all stocks of oil, whether in storage tankers or under the Saudi sands, should head toward zero.

The preceding paragraph implies that we should never see backwardation in commmodity markets. However, we do see it (Keynes used the phrase "normal backwardation.")

Economists explain backwardation using the term "convenience yield," which is something of a fudge factor. People don't sell their stocks of a commodity when there is backwardation, hence they must get some utility from holding the stock, so let's call this "convenience yield."

Perhaps a more plausible story would be option value. If you retain your oil even when there is backwardation, you have the option of selling it later. On average, it looks like you will forego profits by selling it later, but with volatile prices there is the chance that you will get to sell it at a much higher price. If you sell the oil now, you do not have such an option. When oil prices are volatile, the option value is high, so you keep your stock of oil even if the futures price is below the spot price. For this story to work, there has to be an asymmetry in possible oil prices. That is, you have to believe that there is a floor, but not a ceiling. I suspect that the floor has to be rather high in order to matter--zero probably will not do.

In short, my model of the oil market is this:

1. Speculators determine "the" price of oil by placing bets in the futures markets that reflect expectations for the entire future path of demand, discovery of new oil reserves, development of alternative energy, etc. There is no such thing as a "signature" for when future-oriented speculation is determining the price. Future-oriented speculation always determines the price--high, low, or in between.

2. The relationship between spot and futures prices should be based on the Hotelling principle, which would imply that futures prices would be above spot prices, with the differential approximating the rate of interest. If the spot price were too low relative the futures price, producers would extract little oil, if any. If the spot price were too high relative to the futures price, producers would use up their oil too quickly.

3. If there is a floor on oil prices without a ceiling, then keeping oil in the ground potentially has option value. With volatile oil prices, there is an additional incentive to leave oil in the ground. For a given level of futures prices, the option value causes spot prices to be higher than what the Hotelling principle would predict.

UPDATE: One commenter and one emailer have pointed out that there are substantial adjustment costs in oil production, so that oil in the ground and oil inventories are not the same. You cannot suddenly extract from a given field at a higher rate without risking having the formation collapse. You cannot "cap" an oil well without having to re-drill it later.

I can see how this would affect short-run dynamics. The flow supply of oil would be less responsive to the differential between futures and spot prices than if production changes were frictionless. This in turn would mean that we could see more "slack" in the futures-spot relationship (wider movements between contango and backwardation).

However, it does not change my view that overall the price of oil is determined by speculation that incorporates expectations of future supply and demand. And since this is always the case, I cannot imagine what "symptoms" would show that today we are seeing speculation but yesterday we were not.

COMMENTS (11 to date)
aaron writes:

Very nice. Sounds like my model if I had words for it.

eric writes:

I thought that 'standard theory' has a risk premium for the difference between the futures and 'expected spot' rate. Assume the expected spot rate is the current spot rate. You have demand for hedging from consumers (eg, Boeing hedges its aluminum demand) and from producers (eg, Exxon its oil). They wish to transfer their risk to speculators via futures contracts. Alternatively, these players have 'real options' which can be as a buyer or seller. Thus, the net demand for hedging, in any one commodity, could be long or short futures, and so could produce contango or backwardization. Thus, the data are consistent with this theory, which is nonfalsifiable, so it's rather unsatisfying.

Also, note that Gold is always in contango, while the other commodities usually fluctuate from contango to backwardization.

HM writes:

In addition, the cost of storage can also affect the hoteling principal. There are plenty of speculators, but few hedge funds or investors are going to be running down to Texas to take delivery of 1,000 barrels of oil. Think of the contango that we had a few years ago. The differential between the next month contract and the contract expiring a few days was indicating that the risk free rate was ~20%. This is a clear case where speculators got ahead of themselves and drove up the price of the future and the future only.

Rich writes:

I think that one of your modelling assumptions is mostly false in the real world. Inventory in the ground is significantly different from other types of inventory. So, for example, if a country that would normally produces 2mm barrels/day decides not to produce any oil this year, it will not be able to produce 4mm barrels/day next year. Or, to extend your framework, the option value of oil held in inventory is significantly higher than the option value of oil in the ground, because it can be pulled out of inventory when there is a price spike (as one would expect given marginal storage costs).

Also, separating speculative in-ground hoarding from the supply function seems quite fraught when a significant part of the supply comes from a cartel with not very many members.

What does seem to occur though, is that to the extent producers are able to increase their supply, government budgets increase as oil prices increase with a reasonable lag, and then when prices come down some producers who have to meet budget constraints actually have a negatively sloping supply curve, thus leading to great volatility in prices.

shayne writes:

I concur with Arnold's model on this, but it still can be difficult to understand without understanding the underlying drivers of demand and demand estimation. I referenced an article by Andrew McKillop for an econ paper I was writing last year that was quite enlightening:

The data and prices in the article are somewhat dated, but the basic indicators remain unaffected and are probably more relevant now.

1.) Although the U.S. is the largest single petroleum consumer, it represents less than 25% of global petroleum demand. That U.S. percentage of global demand is declining and has been in fairly steady decline since 1970 when U.S. consumption was approximately 31% of global consumption.

2.) Historically, it has not been the largest economies/demanders that influence either spot or futures prices. It is the fastest growing economies - and their rate of growth - that exert the greatest influence on price.

The implications are that the U.S. economy/consumer is no longer the "tail that wags the dog" in terms of petroleum pricing, although many analysts and pundits still approach the problem with that mindset. In the contemporary past, the U.S. economic growth rates were as high or higher than any other significant economy on the planet and consequently exerted the greatest influence on pricing via growth-driven demand fluctuation. But that was due primarily to more robust economic growth rate, rather than absolute economic size. That is no longer the case.

Currently, the emerging economies' (primarily India and China) extraordinary growth rates, not their absolute size, will influence spot and futures petroleum demand and pricing. Even a 10% reduction in U.S. petroleum demand - either via conservation or ethanol use, etc. - would produce less than a 2.5% reduction in global demand, as a static figure. And that 2.5% is approximately the forecast increase for global demand this year. In short, any demand reduction in the U.S. will be rapidly absorbed by the rapidly growing BRIC economies with little, if any, demand-driven global petroleum price reduction. The rapidly growing economies are demonstrating they are willing and able to pay the price for high growth rates. I suspect the speculators (globally) know that

Peter writes:

A couple points:

Some wells can be turned on and off with relatively little damage to the formation. But more importantly, oil production from existing wells declines. If you don't keep spending capital, production goes down. There are always incremental wells being brought on line to maintain production flat. These wells can simply be deferred.

Secondly, while there may not be a significant difference economically between "inventory in the ground" and "inventory in a tank", it would seem to matter quite a bit those whose primary pursuit is not the economics but identifying the proper scapegoat.

Ruthless speculators overcome by Sudden Greed Syndrome have the ability to fill up tanks above the ground. They do not have the power to leave oil under the ground in OPEC countries. Which, of course, OPEC counties - who happen to be members of a worldwide cartel whose stated purpose is to manipulate supply to achieve higher oil prices - can do.

aaron writes:

Rich, you're definitely right about the higher value of the option on pumped and stored stocks, but the problem is that increasing pumping capacity drives down the price. The speculating is most likely being done on the assumption that pumping capacity will not increase. Current backwardization implies that speculator believe demand will fall slightly or production will incrase slighly, but apparently they don't expect much change.

Of course, unless people have found a way to borrow on the current value of the oil, it would be irrational to not pump oil because it will drive down the price. Knowing that to get the money you'll have to pump the oil and bring down the price, it just doesn't make sense. But bubbles don't happen because people behave rationally.

Mike writes:

I am not an oil industry person so I did not know oil wells could not be over pumped or shut-off without expecting damage to be done to the well. If the emailer in Arnold's update is reading this I would ask that he share any other things we non-oil industry people ought to know as this oil situation looks to be a big debate topic as the political season ripens further.

One idea I always had was to have government contract with drillers to find oil and then cap the well to be held in reserve to put oil onto the market when the market is in under-supply but this would suggest capping a well wouldn't work. Can the pump rate be cranked down to a minimum of say 10% of its optimum in lieu of capping a well?

BottyGuy writes:

How does oil storage in the ground work? Oil Production and been relatively steady for the last two years.

If I buy an oil contract, I expect the oil to be delivered when it expires don't I? In which case I need to store it. Can I ask the originator of the contract to just hold it in the ground for later? (I don't think so)

So unless the speculators are oil producing countries with excess oil production and are not originating contracts I don't see how there is storage in the ground. Plus it doesn't look like there has been any capacity taken off line, ala Enron and California Electrical Market.

Was there a big oil strike I'm not aware of?

mic writes:

I do not see how a floor>0 produces option value in forward or spot price. Forward price is a linear operator. So if cash has no option value and an asset has no option value, a portfolio of cash+asset has not option value either. But this portfolio is floored at cash.

With non-stochastic or non-correlated with asset interest rates asset forwards do not have convexity adjustments.

Martin writes:

I agree with Rich some of the supply curves are all over the place. For many producers whom have a need for a certain amount of cash their production volumes could actually vary in inverse proportion to the spot price. Thus high price = less volume which is the opposite of what most economists would predict. And since this cash is needed on a regular basis to meet budget requirements backwardation/contango doesn't really come into it.

I also remain to be convinced that producers do actually profit maximise. Exploration and production costs are significant and so once found producers simply suck the oil out as fast as possible to get a rapid and certain payback before nationalisation or tax hike.

Longer term of course there is a cycle of sorts but now heavily obscured by the release of billions of people from the shackles of socialism and communism to join the ranks of the insatiable consumer.

Comments for this entry have been closed
Return to top