The Hotelling Theorem and the Future Price of Crude Oil by Dr. Brad Cornell

Despite the avalanche of reports and prognostications regarding the future of crude oil prices, there is virtually no mention of the starting point on which all scholarly research on the subject is based – the Hotelling theorem. Though the derivation can be daunting, the conclusion of the Hotelling theorem is straightforward. The theorem states that, irrespective of the current spot price, the price of crude oil should be expected to rise at the rate of interest (adjusted for risk). The intuition underlying the theorem is simple. If prices are not expected to rise at the rate of interest, then owners of reserves should pump more oil and invest the proceeds in financial assets. If prices are expected to rise faster than the interest rate, then it is rational to slow production and leave oil in the ground.

In Hotelling equilibrium, the spot price is set so that as prices rise at the interest rate reserves are drawn so as to maximize the present value of the stream of oil profits. Over the last 18 months, of course, prices have not risen but headed straight down. So what has gone wrong? Is the Hotelling theorem overly theoretical nonsense? In defense of the theorem, note that throughout the oil price collapse during the last 18 months the futures curve has always been upward sloping just as the theorem predicts. However, rather than following the curve upward, spot prices have been on a relentless decline from over $115 to under $30.

The Hotelling theorem points to three primary factors to potentially explain the spot price collapse. The first is new information about either the stock of reserves or the demand for oil by final consumers. The problem with this first factor is that during the last 18 months there has been little new news remotely sufficient to explain a 75% price drop. On the supply side the impact of fracking has been known for years and there have been no large unanticipated discoveries. On the demand side, the usage of crude has followed a predictable, slow upward trend despite the slowdown in China.

#### The second factor is speculation. Oil is not only a commodity, it is also a financial asset. Like other financial assets, its price responds to speculation and sentiment. Unfortunately, assessing the impact of this factor is next to impossible because motives for investment are not observable. Suffice it to say that a change in speculative sentiment probably has played a role in the drop, but it cannot explain the massive collapse.

hird, the Hotelling theorem depends on the long-run rational behavior of reserve owners to draw down their reserves so as maximize the present value of the future profit stream. However, actual owners of reserves seem to be responding to other forces such as maintaining the political status quo, punishing competitors, undertaking strategic initiatives and so forth. Given the relatively inelastic demand for oil, and the rising marginal cost of adding storage, pushing more oil into the spot market can have a dramatic impact on prices. Nonetheless, for whatever reason, reserve owners keep pumping when they should be leaving oil in the ground. It is this third factor which the Hotelling theorem suggests accounts for most of the dramatic price decline we have witnessed. The theorem also suggests the when bleeding will end. At some point, the spot price will be so low that the anticipated rate of future appreciation will be large enough to convince even the most skeptical reserve owners to leave more oil in the ground. At that point, the spot price will stop falling.

BRADFORD CORNELL

CALIFORNIA INSTITUTE OF TECHNOLOGY

PASADENA, CA 91125

626 564-2001

bcornell@hss.caltech.edu