Fat tail of the day, oil edition

By Felix Salmon
May 5, 2011
crude oil is down 8.8% today. According to my colleague John Kemp, who knows everything, the standard deviation of oil prices, on a daily basis, is 1.64%. Which means that today's price movement is equal to 5.4 standard deviations.

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This is what a fat tail looks like: crude oil is down 8.8% today. According to my colleague John Kemp, who knows everything, the standard deviation of oil prices, on a daily basis, is 1.64%. Which means that today’s price movement is equal to 5.4 standard deviations.

In a normally-distributed world, 5-standard-deviation moves never happen. In this world, however, such moves can happen even when there’s no news at all. (Reuters, for what it’s worth, blames “concerns about economic growth and monetary tightening”, which is code for “we have no idea why this is happening, or whether there even is a reason”.)

I do think today’s price move should give pause to anybody who dismisses theories that high prices in oil or other commodities are the result of financial speculation. Clearly there’s no fundamental reason to explain this move: most likely the market was just very long oil, and does what it always does in such situations, which is to move in the direction which causes the greatest pain to the greatest number.

For most of us, these kind of intraday gyrations, rare though they are, are pretty much irrelevant. But they do inflict a toll on the economy, as companies feel the need to hedge such things. And all hedging operations involve some kind of profit for Wall Street.

All of which is to say that a financial-transactions tax looks particularly attractive on days like this. It would reduce speculation, and raise lots of money. What’s not to like?


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The chance of a 5.4 standard deviation move is 3.326629e-8.
There are approximately 25200 days in a century. That’s (1-3.326629e-8)^25200 chance of not seeing at least one move this large. That works out to 99.92% chance of it not happening once in a century. Not never happen, but close.

Posted by OneEyedMan | Report as abusive

That should be trading days in a century, not day in a century

Posted by OneEyedMan | Report as abusive

1) Market movements are not normally distributed. This has been known for a long time. We get 100 year floods every few years.

2) No one has described a plausible theory as to how speculation can affect oil or other commodity prices unless there is physical withholding of oil from the market, in the form of high inventories. Supply and demand. For example, http://krugman.blogs.nytimes.com/2009/07  /08/oil-speculation/

Posted by 3oosion | Report as abusive

I have daily data going back to January 1986 for oil prices that show the standard deviation of log changes as 2.58%.

Another interesting quirk of statistical time series is time varying volatility (GARCH). Since I don’t have Matlab handy to do the calculation, I just took the rolling 20 day standard deviation. Most recently, I got like 1.66%, which is consistent with what you have. So over the whole period, volatility was a lot more than it has been just recently.

Posted by jmh530 | Report as abusive

Might seem crass to even present it, but I guarantee that conspiracy nuts out there will think this is Obama’s doing through his army of Goldman Sachs cronies all to make George Soros a few extra bucks or buy votes.

I’m pretty impressed by silver dropping 30% in a week because of a minor tightening of capital requirements myself…

Posted by CDN_Rebel | Report as abusive

Blame the quants and their equations.

Posted by GRRR | Report as abusive

You are missing the mean in your std dev calculation. It was more than a 5.4 std dev movement.

This t-shirt should clear up your confusion.

http://rlv.zcache.com/standard_deviation _root_mean_square_of_values_tshirt-p2358 11735824455090trlf_400.jpg

Posted by david3 | Report as abusive

On a one day horizon, the mean of most financial securities is close enough to zero that it won’t matter much.

Posted by jmh530 | Report as abusive


I apologize that I only comment when I have a complaint because, honest, I enjoy reading your stuff!

But I second 3oosion above… Mandelbrot observed that financials don’t follow a normal/gaussian distribution. That was a few decades ago. I really don’t understand why otherwise sophisticated financial commentators forget this all the time.

And, really, going after speculators?

Posted by nedofbaker | Report as abusive

Does anyone know why retail gas prices are higher than 2008 levels when crude was ~115?

http://www.GasBuddy.com/gb_retail_price_ chart.aspx?city1=USA Average&city2=&city3=&crude=y&tme=48&uni ts=us

The graph is tough to pin down, but looking at the data point on 4/19, it seems as if gas was around $3.60 national average with crude trading around ~115.

Why the 8% increase in retail?

Posted by djiddish98 | Report as abusive

Chart link fail

http://www.gasbuddy.com/gb_retail_price_ chart.aspx?time=48

Just tick the crude box

Posted by djiddish98 | Report as abusive

Eliminate the mortgage deduction, raise the retirement age for Medicaid and social security and institute an effective transactions tax.

Posted by xyz70 | Report as abusive

I was commenting on this move myself. No rhyme or reason, no news, nothing changed. Except suddenly the trading price of oil dropped by ten dollars a barrel.

Posted by TFF | Report as abusive

The margin requirements were raised, and speculators push leverage to the limit. They had to cover and cover fast.

This is the definition of speculation and in our current overly financialized world it happens far often than Gaussian math can accomodate. The earlier comment about Mandelbrotian math being more accurate is correct.

Posted by Beezer | Report as abusive

easy, restrained and stylish

Posted by traducere romana daneza | Report as abusive