Oil Price Bubble?

For the past several years, there have been many who have suggested that oil prices may be rising in an unsustainable bubble. To be sure, there has been an upward bias in this market as reserve production capacity appears to have dwindled since around 2004. Major exporters such as Saudi Arabia have had production declines at a time when global demand has picked up with China and India enjoying rapid economic growth. The question of whether global oil supplies have peaked has enjoyed vigorous debate as prices have seen a dramatic rise over the past eight years.

The Oil Drum examined the question of whether oil prices were in a bubble back in 2006. Using Didier Sornette's approach of looking for faster than exponential growth in the time series of oil prices, this analysis by Stuart Staniford concluded that oil at the time did not exhibit the characteristics of past stock market or housing bubbles. He found that the logarithm (to base 2) of oil prices followed roughly a straight line:

"I have taken the start of the price rise as November 15th 2001 which is when prices bottomed out after the tech crash and the events of 9/11. To that price rise I fit both a linear trend, and a quadratic. To the extent the price was curving up in a bubblicious manner, we would expect the quadratic to depart markedly from the straight line. It elects not to do so - the two are very close. Thus we see that although there is considerable volatility in the price (and the pattern of that is worth further analysis in the future) the price rise is very much exponential in nature. So I take this as further evidence that we do not have a self-reinforcing bubble.

At least not yet."

So what has happened in the past two years since Stuart Staniford's analysis? Oil prices have continued to rise and recently has topped $128. On a log scale (base 2) this corresponds to 7. Is this just continuation of the exponential rise since 2001 or is there now more evidence of a faster than exponential rise which would suggest an oil price bubble that could be approaching a breaking point?

To look at this question, Figure 1 simply extends Staniford's analysis to the present time. The data is West Texas Intermediate from the same source, EIA. During the past two years the data shows first a correction in prices and then an accelerated rise to present levels. The past two years data represent a faster rate of rise than the prior period covered by Staniford's data. However, the linear fit to the log chart suggests that on average these may be random fluctuations in an overall exponential growth pattern versus the faster than exponential growth associated with a price bubble. The quadratic fit also doesn't deviate much from the linear fit over the period dating back to 2001.



Figure 1. Log (base 2) of West Texas Intermediate spot price in nominal US dollars together with linear and quadratic fits to the data. On this scale, 4 is $16, 5 is $32, and 6 is $64.

The next step is to extend the period of time covered by the exponential growth back to 1999 (approximately two years). This provides for the period that includes an initial price rise before the 2001 low. As shown in Figure 2 by including this period the exponential rate of rise is on average slower, leading to a much sharper contrast in the price action of the past two years. In other words, the linear fit to the entire time series has a lower overall slope and the sharp rise in prices the past two years is much greater than the overall exponential rise. The quadratic fit also deviates remarkably from the linear fit, again suggesting that there could be a possible faster than exponential price rise or bubble in the works.



Figure 2. West Texas crude spot prices from May 1999 to present.

Finally, we look for the possibility of an Log Periodic Power Law (LPPL) signature using Sornette's approach. The methodology to do so is based on fitting a somewhat complex LPPL function to the historical time series. This function has a faster than exponential characteristic and an oscillation that increases in frequency as the system approaches a singularity or critical breaking point. Unlike the linear or polynomial fits to historical time series, the LPPL method requires a guess as when the critical point will occur and fits the function back from this critical date.

Figure 3 presents one possible fit (not necessarily the best possible fit) of an LPPL signature to the oil price time series. It assumes a critical point at July 11, 2008. This is not a prediction of a crash on this particular date; rather it is used to illustrate the fact that there is a possible bubble with an LPPL signature. If the market continues its faster than exponential rise beyond this date, it would presumably be possible to revise the model to a new future critical date. Hence this methodology may be useful to indicate that the conditions for a bubble exist, though it may not provide a precise date for when the bubble might break.



Figure 3. Oil prices do exhibit the Log Periodic Power Law (LPPL) signature of a possible price bubble.