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Friday, March 03, 2006

A Bet, Price Discovery, and the Peak Oil Predicament

Update 3/5/06: Added some verbage to make a couple of points clearer...

There's seems to be an ever increasing number of perplexed pundits pontificating about the purported peak oil predicament. For example, Russ Roberts at Cafe Hayek links to the following New York Times article excerpt:

[T]here will come a day when oil production "peaks," when demand overtakes supply (and never looks back), resulting in large and possibly catastrophic price increases that could make today's $60-a-barrel oil look like chump change.

In this post I will show why I think the peak oil problem isn't a crisis (or anything like a crisis), won't lead (by itself) to large and “catastrophic price increases” and doesn't warrant a lot of government intervention (which is the conclusion of the NY Times article). To do so, I will begin by describing an amusing bet by a couple of the Daily Duckie dudes, and use that scenario to illustrate the concept of price discovery mechanisms. Those mechanisms will lay the foundation for us to examine the concept of a cost-of-carry market, which will in turn be used to argue against any rapid and "catastrophic" changes in the price of oil due to the peak oil concept that has so many people so worried. I'm going to keep this all as non-technical as possible, but being a commodities future trader (though currently inactive), concepts that I consider to be obvious may not be, so ask questions in the comments and I'll be more than happy to answer them.

The bet is between Duck and Oroborous. Duck bets that oil will hit $100 per barrel by the end of this year (2006). For Duck's sake, I hope the bet is small, because he's not only betting against Oroborous, but he's also betting way, way against all of the money in the crude futures markets, and that is generally a very, very bad idea.

First, a few definitions are needed. In the world of commodities, the “spot market” refers to buying or selling (or at least pricing) the specific commodity right now. Entities that use the spot market are actual producers and consumers of the commodity.

A futures market is a market that enables buying and selling (and pricing) a commodity at a specific date in the future. For example, you can enter into a contract to buy or sell 1,000 barrels of Light Sweet Crude in July, 2006 via the New York Mercantile Exchange (NYMEX). Entities that utilize the futures markets include the producers and consumers of the commodity (known as hedgers), speculators, and arbitragers.

The hedger's goal is to lock in a price for the commodity that they want to buy or sell in the future. For example, if you're a corn farmer, it's important that you know you can sell the corn that you're about to plant for a profitable price after you harvest it. So you enter (sell) a contract before planting to deliver your corn after harvest at a profitable price. If the futures price is too low (i.e. doesn't enable you to make a profit), you don't bother planting and you don't sell the contract. If the price is adequately profitable, the futures contract enables you to get a loan from the bank to buy the seeds and other necessary equipment. So for the hedger, the futures market provides an insurance function.

The speculators provide that insurance. They do so by providing the liquidity that drives the market to the point that best balances the expected needs of buyers and sellers for that market on the delivery date (also called the expiration date). If the market were perfect with perfect predictive powers (e.g. godlike), the price of the futures contract would be driven by the speculators (and arbitragers) to what the spot market price of the commodity will be on the day the contract expires. The spot market price is the price that best balances the needs of buyers and sellers for that market at that given instant in time.

For example, let's say that in July, 2006 the spot price for oil ends up being $60.00 a barrel. If the market were perfect with perfect ability to predict the future, then the current price (and yesterday's price and tomorrow's price, etc.) of the July 2006 futures contract for oil would also be $60.00 barrel. But, market's cannot perfectly predict the future. They can only predict the future based on currently available (and historical) information. As new information regarding supply and demand becomes available, the price fluctuates, though it eventually converges on the the spot price as the contract nears the delivery date.

The speculators have a powerful incentive to be right. If a futures contract price is below what the spot market price will be when it's time for that contract's delivery, and the speculator buys that futures contract, he'll make a lot of money. If he sells, he'll lose a lot of money. Speculators that are able to analyze the data and consistently make the right decisions make a lot of money. Speculators who can't consistently make the right decisions lose money and generally drop out of the game pretty quickly. Thus, the speculators, on aggregate, tend to drive the price toward an optimal price point. This is what's known as the futures market price discovery mechanism. The market finds the best possible prediction of the price of that commodity for the specified future date. Note that this price discovery mechanism, via the speculators, takes all information about all current and future events (including an estimation of the probability of those events) into account. This includes information about the likelihood of war in Iran, unrest in Saudi Arabia, depletion of oil fields in Kuwait, etc.

Now back to Duck's bet. The futures prices for all of the remaining contracts for this year show a price between $60 and $70 per barrel. That means that the people who are willing to put big money on the line, in aggregate, expect oil to remain in that range for the rest of the year. Again, it's people putting big money on the line, who in aggregate, have taken all known information into account. And Duck has bet against them - to the tune of $35 dollars per barrel.

Well, not quite. Duck still has one small thing in his favor: volatility. In other words, even though the predicted price of oil for all months is less than $70, there is some probability that short term swings will happen to push the spot price of crude oil over $100 for at least one trade (in the spot market), in which case Duck wins the bet. It turns out we can roughly estimate that probability fairly easily.

First we assume that the distribution of price changes is a normal distribution. It turns out that the distribution of price changes is not quite normal, but it's close enough for a rough estimate. Next, we look at the monthly price changes for crude oil (in the spot market) and see that the standard deviation of those price changes is approximately $10. Next we know that the standard deviation for price movements over a different time frame for a normal distribution is the square root of the ratio of the time frames times the original standard deviation. There's roughly ten months left in the bet, so we can estimate the standard deviation over the time remaining in the bet to be the square root of 10 times $10, or approximately $32. That means that $100 per barrel of oil is a bit more than one standard deviation higher in price than all of the current futures prices for all of the months remaining in the bet. Using standard normal distribution statistical tables, we can conclude that Duck has an approximately 85 percent chance of losing the bet at this point (or a 15 percent chance of winning). This is still not quite accurate, since the above analysis includes only those possibilities that end over $100 per barrel and not those that go over $100 and then end below $100 per barrel at the end of the year, but it's good enough for a rough estimate in this case.

Let's check our calculations by looking at the price of call options on $100 oil for the remaining futures contracts. The price of the calls for each of the remaining months is only pennies, so our estimate of Duck having a 15 percent chance of winning is generous (and my guess is that I've overestimated the monthly standard deviation, which I did by eye, not spreadsheet). If the bet between them is big enough (which I somehow doubt), Oroborous could actually lock in profit by buying a call for each of the contracts between now and January 2007. There's no way for Duck to lock in profit.

But it's not over until the fat lady takes an oil bath (not a pretty sight), so Duck still has a chance.

We now need to explore an important constraint on the difference in the price between any two points in time for a given (non-perishable) commodity.

Let's say that due to expected changes in supply and demand that next month you expect crude oil to be $80 per barrel. Since you can currently by a barrel of oil for less than $70, it would make sense to buy oil and store it and then sell it next month for a profit. Indeed, as long as the spot price is far enough below the price you expect next month, you would keep buying and storing all the oil you could. How much is far enough below? This question introduces the cost-of-carry model of an asset:

F = S + C – R

where F is the price of the commodity in the future, S is the spot price, C is the cost of carrying the asset for the time you're going to hold the asset, and R is any return you might get on the asset while you're holding it (which is zero for crude oil but non-zero for some financial instruments). The cost of carrying the asset includes storage and financing costs.

What's important here is that people will continue to buy in the spot market as long as F > S + C – R, because it's basically free money. This isn't even a speculation, rather it's a type of arbitrage. This drives the spot price up and alleviates current gluts and potential future shortages while reducing overall volatility.

You actually see carry cost markets in real life when there is a glut of the commodity (at least relative to the expected future supply). When this happens, the commodity generally has a much lower than average price and relatively low volatility. Each futures contract is priced over the previous contract by nearly exactly the amount it costs to carry the commodity for the length of time between the two contract expiration dates.

The important point is that the expected future price of a commodity can never be very much above the current spot market price plus the carrying cost for that commodity. If it is, people will buy in the spot market and store the commodity. Because of this, the current spot market price already takes into account expected future shortages, if any.

Because there is the upper bound on the price of oil in the future relative to the current price, it is unlikely that at some arbitrary point in the future huge spikes in the price of oil will occur simply because of long term expected changes in supply and demand. There are many things that can cause large changes in price (e.g. middle east wars, though even this sort of thing is already reflected in the spot and future prices), but the peak oil model of dwindling supplies is not one of them. The peak oil concept will not bring civilization as we know it crashing down. The F = S + C – R relationship guarantees that the sort of supply/demand price dislocation predicted by the peak oil alarmists will be relatively steady and smooth, giving the world economy many years, or even decades, to adapt.

Crude oil futures trade quite far out. The latest available contract is for delivery in December of 2012. That's almost seven years from now. Yesterday's settle price for that contract was $65.10. Yesterday's spot price was about $63. The big money says that in seven years the price of crude is going to be more or less the same as it is now.

Don't believe it? Think that the peak oil model will make the price far higher by then? Then do a type of trade called a spread: buy the December 2012 contract and sell a nearer term contract. Short term price fluctuations cancel each other out since you'd be on both sides of the market and you'll profit handsomely on the spread if you're right about the effects of the peak oil model. Your action would cause the December 2012 contract to rise relative to the near term contracts, and if you're right, you would be adding good information to the market and benefiting everybody. Indeed, the cost-of-carry model limit for December 2012 is probably somewhere around $100 per barrel. If $100 was the price for that contract, I'd take the peak oil alarmists much more seriously (though I'd bet we could easily adapt to $100 per barrel oil over the course of 7 years since it's only about a $5 per year increase in price). But right now, clearly, the peak oil alarmists are hugely outnumbered in the market by money that says they're wrong, making it difficult for me to give their opinion much weight.

Technological innovation is accelerating. Seven years is a long time. And even after that, our favorite equation (F = S + C – R) guarantees slow long term increases in price (short term volatility can still be huge, but has nothing to do with the peak oil model).

Thus I conclude that the peak oil model is not a good reason for governments to get involved in energy technology development at the current time.


Howard said...

not sure, I think this is the fifth or sixth time we were going to run out of oil...

if we have a great need to squander lots of money then let's get the government involved in a grand plan for alternatives

shout out to the late Julian Simon!

Bret said...

Yeah, yeah, you'd think that hearing the same prediction over and over and watching it be wrong every time would give people some skepticism by now, but I suppose it is a valid point that being wrong repeatedly in the past doesn't guarantee that they're wrong this time (or next time, or the time after, ...).

I wanted to clearly explain the pricing mechanism that shows why they can never, ever be right. Not then, not now, not in one-thousand years.

The most rapidly that oil prices can increase due to dwindling supplies because of "peak oil" is roughly the carry cost rate. That's it. As long as government doesn't interfer in the market. And the carry cost rate for oil is maybe around 10 percent. A ten percent per year increase would gently nudge us towards new energy approaches without the government ever getting involved.

Oroborous said...

Thermal depolymerization (more detailed here, less detailed here)pretty much ensures that oil prices can't go over $ 100/bbl during the 21st century, except for short periods, as you mentioned.

Further, due to the increased efficiency with which the American economy uses oil, we now are much more productive per barrel than we were just decades ago.
Thus, oil prices would have to rise to $ 180/bbl, in current dollars, to have the same effect on America that the 70s' "oil shocks" did.

$ 100/bbl oil would be irritating, but not crippling. (For America, that is - China would have BIG problems).

One quibble; when you write:

Note that this price discovery mechanism, via the speculators, takes all information about all current and future events into account. This includes information about the likelihood of war in Iran, unrest in Saudi Arabia, depletion of oil fields in Kuwait, etc.
There are many things that can cause large changes in price (e.g. middle east wars, though even this sort of thing is already reflected in the spot and future prices)...

The current pricing of futures doesn't really take into account those things happening, just a consensus estimate of their probability of happening.

For instance, if speculators thought that there would almost definitely be an embargo against Iran this year, then those $ 100 futures would be getting a lot more play.

Which is why I disagree with your conclusion that the government shouldn't be spending money on alt-energy projects and research.

Just as producers and consumers hedge against future price volatility, finding that it's worth leaving some money on the table in order to lock in a known cost or return, so too would it be worth paying more for energy, as a nation, in return for having an uninterruptible domestic supply of energy.

While that might seem foolish when the sun's shining, come the rains it'd seem like genius, and it takes time to construct facilities, implement production, and build a distribution infrastructure. Best to start now.

Bret said...

Oroborous wrote: "The current pricing of futures doesn't really take into account those things happening, just a consensus estimate of their probability of happening."

I agree. But I did use the word "likelihood" in the first sentence of mine that you quoted. Nonetheless, somebody else made a similar comment, so there's a significant "probability" that I'll update the wording later to make it more clear.

Oroborous wrote: "Which is why I disagree with your conclusion that the government shouldn't be spending money on alt-energy projects and research."

I don't think you've portrayed my conclusion quite accurately. I simply concluded that "peak oil" is not a good reason for government to do anything. I didn't say that the government shouldn't be involved if there are other good reasons.

Nonetheless, I guess I'm just more of a risk taker than you. I don't want the government to lock in losses at my expense. I'd rather be confronted with the high prices should things go farther south. The price point doesn't count on the sun shining. I think it's more like a drizzle - it could get worse but it could get better.

Duck said...

The bet is for a book, so I'm not deep in the hole on this one. And I believe that Oroborous gave me 2 for 1 odds.

Yes, I think that the only chance I have for winning the bet is for a short term spike. I'd be happy to lose this bet, but here are the factors in my favor:

1. Hurricane season will be back this summer. If it is anything like last summer, look out!

2. The recent attempt to bomb the oil facility in Saudi Arabia shows that Al Quaeda is targeting oil as a way to disrupt world markets.

3. Iran. Nuff said.

4. Venezuela. Nuff said.

5. Worldwide production of light, sweet crude has peaked. Most refineries are set up to refine light, sweet crude, not heavy, sour crude. Refiners have not invested, for the most part, in building new facilities or converting old facilities to accept the increasing volume of heavy and sour crudes. Thus the supply of light sweet crude relative to demand will begin to shrink, putting upward pressure on the price. And the bet is based on the NYMEX price for light sweet crude.

Beyond that, it was just a wild guess on my part. I had won a bet with Orrin Judd in 2004 that oil would hit $50 by the end of the year, which Oroborous had also pooh-poohed, (but didn't pony up any dough), so I felt lucky.

Oroborous said...

Yes, 2 - 1.


I agree that "peak oil" is rubbish.
Not only is it not a cause for alarm, it won't happen in the 21st century due to supply constrictions - although I expect that slackening demand for oil throughout the latter half of the century will result in less oil being produced in 2100 than 2000.

Hey Skipper said...


That is by far and away the best synopsis on this subject I have ever read. Thanks for clueing me in on some words and concepts I have frequently read, but never understood.

Something else that suggests peak oil is, if not a total fallacy, is at least way into the future is fuel cells in automobiles.

Internal combustion engines work at about 15% thermodynamic efficiency.

Fuel cells (once whichever group of clever people qualifying as "they" figure out how to use things like methane or ethanol as a hydrogen source without clogging the fuel cells ion transfer membrane) will easily double that.

Combining price-point substitution with a doubling of thermodynamic efficiency looks like a fair bet to significantly reduce the demand for oil.

Bret said...

Hey Skipper,
Thanks for the complement. I wrote this synopsis specifically because I tired of economists talking about market mechanisms and not seeming to realize that relatively few people understand how those mechanisms work, especially long term price discovery mechanisms like the ones I've described.

It's funny that my two areas of expertise are robotics and commodities futures trading, yet I almost never write anything about either. I guess it's more fun to write about things I know very little about. Why is that?

Hey Skipper said...


I'm not sure why that is, but it must be the same reason I like to write about nearly everything.