"The End of the World as We Know It?"

In a TheStreet.com($) story with the above headline (hat tip reader MIchael), Doug Kass noted that the price increase in the Financial Select Sector SPDR was 13%, an 11 standard deviation event.

According to Kass, the odds of an eleven standard deviation event is equivalent to the world ending – between three and four times.

We noted in an earlier post:

Reader Juan provided this quote from presentation by Frank Veneroso last year to the World Bank:

[O]ne may ask, is it a bubble? Two years ago the noted money manager Jeremy Grantham posed this question in an interesting way. He presented a chart of the real inflation adjusted oil price going back to 1875.

He then noted: “Over the years we have asked over 2000 professionals for an exception to our claim that every asset class move of 2 sigmas away from trend had broken, and not one of the 2000 has ever offered an exception! This should be scarier than the fact that GMO has tried so hard to find one and failed. But we always have said that intellectually you can imagine a paradigm shift in an asset class price, even if we have been unable to document one yet in history. …

Financial stocks are not an asset class, so they may tolerate larger moves before exhibiting mean reversion. But no matter how you look at it, 11 standard deviations is a pretty big move.

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  1. Anonymous

    I’m just a residential landlord type guy who loves this site and generally can understand. However, this one needs explaning to me.

    Can someone put this in plain english for me?

    Oil is so far above historical norms that it is bound to crash???
    Oil is so far above historical norms that it won’t come back down???

    and what the heck is a standard deviation?

    Thank you,

  2. Anonymous

    it is just some kinda statistic tool to extract information. Just wanna let u know, a normal distribution model (which i believe most of the investment house and banks use) only cover 3 standard deviation, so if it is about 11 SD, it is similar to everyone using car insurance crash their cars in same moment…which mean the insurance company goes broke

  3. Mitch

    Ack! Stock prices are not gaussian! Their actual distribution has significant skewness (toward the upside) and kurtosis (fat tails).

    Point being, the probability of that SPDR movement is way, way higher than Kass calculates.

  4. anewc2

    According to Kass, the odds of an eleven standard deviation event is equivalent to the world ending – between three and four times.

    If we assume that the underlying distribution is Gaussian. But since the result is impossible, this is just another data point for the falsity of this assumption. WHEN WILL THESE MORONS … ahem. When will people start to see this?

    Anonymous: the standard deviation is a measurement how how much the price changes in a typical day. (I think we’re talking about daily changes here — I don’t have the $ for the link to the source.) To change 11 times that amount in a single day (or whatever) is a huge change. But the 1 in a gazillion calculation that results from that is a sign that whoever says it doesn’t know much about probability and statistics. A good rule of thumb is to keep your wallet far away from anyone who uses the term “standard deviation.”

  5. Anonymous

    Mitch is right that it’s not 11 standard deviations … probably more like 4 or 5, with a suitable “fat tails” adjustment for non-normally distributed market moves. But it’s a big pop.

    And illustrating the principle that volatility is bidirectional, we now have a sharp afterhours selloff, after Merrill Lynch, Google and Microsoft all crapped the bed with their earnings reports, and got slammed for 7% apiece.

    Nevertheless, a near 30% pop in the BKX bank index in two days is not mere noise. It doesn’t quality as a “new bull market blastoff” (A/D ratios are too low), but it may well be a “bear market rally” blastoff. Me long (for now).

  6. malabar

    11 std deviations or not. Financials have been whacked over the past 6 months.

    This bounce does nothing compared to the Mar-May bounce. Note that all that has happened this time is that Paulson and Bernanke have asked Congress for a blank check and all the politicos have said they will not allow FNM & FRE to fail. No banks balance sheet has changed, the fundamentals of the housing market has not changed.

    Indymac is not the only one going under. Before we are done many more banks will bite the dust!

    Many of those that are getting to the short side of financials party as usual are coming rather late and they will get burned. The market will always take the hide of those that don't know what they are doing and follow the emotion of the moment. For those short WM or DSL or WB or FNM or FRE from when they were $60 this melt-up did nothing. They are still sitting on heavy profits.

  7. Anonymous

    “what the heck is a standard deviation?”

    A standard deviation is a measure of how far away from average something is. The bigger the standard deviation, the more unlikely the event.

    A person who is more than one standard deviation more intelligent than average is considered borderline gifted. A person who is three standard deviations more intelligent than average is entering the genius range.

    Albert Einstein was probably 7 or 7 and a half standard deviations above average.

    So an eleven standard deviation event is MUCH MUCH less likely than running into someone as smart as Albert Einstein at the local Starbucks.


  8. Anonymous

    Cox’s little move is going to push us closer to a crash. The desperation is getting more and more Banana Republic like and at some point it is going to have just the opposite of the desired effect.

  9. Michael McKinlay

    The phenomena is systemic, not individual …

    We are moving into a systemic crisis not a crisis of individuals … though it surely does effect individuals.

    And these latest moves look to be, as previously mentioned a classic short covering with the market setting up for another “Bear Trap” somewhere down the line.

  10. Lune

    I agree with Tom Lindmark. This is simply the result of the SEC cracking down on short sellers. It’s only an 11-SD event if you believe it was random movement, which it’s not (and even then, only if you believe stock prices fall under a normal distribution, which they don’t).

    Slighty OT: Why do people keep bashing the shorts? I’d like to see an equally vigorous prosecution of the people who keep leaking bogus financial info to CNBC in the early afternoon just before markets close. That is much more of a clear SEC violation, but since it went to artificially inflating a stock, I guess it’s okay…

  11. Yves Smith

    We’ve discussed Gaussian distributions, skewness, and kurtosis before……but even with the much greater propensity to fat tails that idealized distributions suggest, Jeremy Grantham’s observation is an interesting one.

    My favorite statistical blooper came last year:

    On August 12, in a post titled, “The Subprime Meltdown Hits Quant Hedge Funds,” DeLong summed up the quant attitude:

    “‘Our strategy is fine. We were just hit by a sixteen-standard-deviation event.””Then it didn’t happen: the universe isn’t old enough for even one sixteen-standard-deviation event to have ever happened.

    “Tails are fat.”

    The next day, from an article in the Financial Times, “Goldman pays the price of being big”:

    ‘”We were seeing things that were 25-standard deviation moves, several days in a row,” said David Viniar, Goldman’s chief financial officer. ‘There have been issues in some of the other quantitative spaces. But nothing like what we saw last week.'”

    And investors trust these guys with their money….

  12. mock turtle

    i’m kinda sorta with the landlord guy at the top.

    i have an understanding of the bell curve and sigma events etc.

    but what i dont get is as follows

    does the article argue that oil markets… OR… financial SPDRs are behaving outrageously? or both?

    AND is the article saying oil has multi sigma-ed up and will return to earth…

    or financials have multisigma-ed down and will get back up?

    what’s the bottom line?

  13. Anonymous


    a) Everybody’s forgetting about using the square root of time


    b) Doug Kass is having a bit of fun

  14. Anonymous

    I thought a standard deviation was a straight person in frisco that didn’t use crisco.

  15. S

    The move to halt naked shorts on the “19” special companies has everthing to do with it. The proposed legislation to give a balnk check to the Treasury is nothing more than un american. This congrss has a 12% approval rating and it is handing out taxpayer money all in an effort to save people like Dick Fuld. A telling referendum that everything is a systemic risk these days. Bunning has it absolutely right, these people are the systemic risk. Ironic to hear the SEC, absent during the decade long pump monkey routine, now the house of ethics. This entire bank stock rally was orchestrated beginning with Wells Fargo, who will be rewarded like JP MOrgan with a “merger.” Note that the Treasury is being given the power to buy FHLB debt as well. Not mtoo much discussion of this $800B plus dumping ground for the banks. Roubini mentioned it, but there has been a mention since Countrywide drew down $60B. If ever there was a microcosm of the new “ethic,” this is it.

  16. Anonymous

    So how about this for a conspiracy theory? The Govt. and the Fed orchestrated the mother of all short squeezes in order to prop up Financial stocks (like Merrill, Fannie Mae, Freddie Mac, Citigroup, et. al) so that they can offer additional stock to the public next week at much higher prices!? Better than having the tax payer ultimately fund the recapitalization of these companies don’t you think? This may/should prove to be the mother lode of all security litigation battles over the next few years. The arrogance of Paulson/Bernanke and Christopher Cox to think they can pull this charade off is absolutely amazing. Desperate times call for desperate measures.

  17. Yves Smith

    I assume Kass got his eleven deviation factoid from someone else and was making fun of that sort of statement.

    But the more serious point per the second point is that really extreme moves, at least in asset classes, tend to revert. Since these financial stocks aren’t an asset class, that observation may apply to them. However, this sort of move was still pretty extreme. As the comments about short covering attest, there is reason to think that it won’t hold at that level.

    But we’ll find out in due course, regardless.

  18. Anonymous

    For what its worth, Einstein’s IQ was estimated to be about 160, which makes him smarter than 1 in 11,500 people on the street. I don’t think that I would call that a seven sigma brain.

  19. Observer

    I predict Benoit Mandelbrot will soon be regarded as the genius of finance mathematics that he actually has been for 40 years already.

    Note the year of this review, by the way. Not yesterday but 10 years ago. plus ça change … indeed.



    Last Year in Mandelbrot

    Fractals and Scaling in Finance by Benoit B. Mandelbrot Reviewed by Nigel Goldenfeld
    Physics Today, October 1998

    Department of Physics
    University of Illinois at Urbana-Champaign
    1110 W. Green St.
    IL 61801

    On October 19, 1987 the Dow-Jones Industrial Average, the widely-followed proxy for the US stock market, declined by 23%, a move that some observers noted was a 20 standard deviation event. This drop, which was almost twice as large as the famous stock market crash of 1929, is not an isolated incident, but one of a number of large drawdowns and bear markets this century alone, the most recent of which, the October 1997 crash, was only a “modest” 8% drop. Faced with these statistics, most of us would probably be prepared to agree that price changes are not Gaussian or examples of random walk behavior. However, events such as the 1987 crash, World War 1 and the crash of 1929 are extreme and properly regarded as outliers. What about business as usual?

    The answer, of course, depends on who you ask. On one hand, the well-regarded semi-popular book on finance, “A Random Walk Down Wall Street” (W.W. Norton, New York, 6th edition 1996) by Burton Malkiel, takes its title and its theme from the notion that stock price changes follow a Brownian motion. Virtually every textbook on advanced finance takes the Brownian motion description as its starting point, and the celebrated Black-Scholes formula for option prices is based upon this description.

    And on the other hand, there is Benoit Mandelbrot. No reader of this journal can be unaware of the enormous impact made by Mandelbrot’s earlier book “The Fractal Geometry of Nature” (Freeman, New York, 1982), which has introduced many to the notions of fractal dimensions, scaling and self-similarity, and which spawned a host of coffee-table imitations. What is perhaps less well-known, however, is that some of Mandelbrot’s earliest forays into fractals involved a detailed analysis of the time series for cotton prices in New York. Mandelbrot’s shocking conclusion, published in 1963, was that the time series was in no way Gaussian: in fact, he argued that the departures from normality could be accounted for by using distribution functions with infinite variance, which are termed L-stable. Mandelbrot examined the convergence in sample number of the variance of the logarithm of the daily price changes and found erratic variation rather than convergence. Subsequently, his student Eugene Fama (who has himself enjoyed a distinguished career in finance) examined the time series for the thirty stocks in the Dow-Jones Industrial Average, finding no exceptions to the long-tailed nature of the distributions observed.

    The implications of these and subsequent findings are profound, yet it is fair to say that the work was practically ignored by economists and practitioners of finance. Even today, the problem of “fat tails” is swept under the rug by the vast majority of financial risk managers, even though the phenomenon is sufficiently widespread and well-recognized as to have earned its whimsical name. Mandelbrot’s heirs are primarily physicists entering the field of finance, who recognize the fundamental importance of fat tails and are able to elaborate and extend Mandelbrot’s suggestive results. This is something of an ironic development, as Mandelbrot takes pains to emphasise, and reflects the close intellectual relationship between finance and physics. The discovery of Brownian motion, usually attributed to Einstein’s famous 1905 paper, was in fact anticipated by Louis Bachelier five years earlier in his Ph.D dissertation on finance “Theorie de la speculation”, which remained largely ignored by economists until the 1950’s and 60’s. Elements of Mandelbrot’s work in the early 1960’s, which superseded Bachelier’s analysis just as it was becoming widely accepted, arguably anticipate some of the concepts of scaling and renormalization which were a focal point of physics during the 1970’s. The concepts of fractional Brownian motion and multifractals which are still frontier topics of research in physics and academic finance (as practiced by physicists) were introduced by Mandelbrot in the late 1960’s and 1970’s. And most recently, legions of physicists have found gainful employment on Wall Street as “quants”, performing intricate calculations of price and risk of derivative securities, using sophisticated detailed models whose underlying premises remain those of Bachelier—Brownian motion (more accurately logBrownian motion).

  20. Anonymous

    “Anonymous Anonymous said…

    I thought a standard deviation was a straight person in frisco that didn’t use crisco.”


  21. Richard Kline

    Mandelbrot’s study on cotton prices is actually a fairly approachable piece of work for those who have a taste for order distributions in timeseries. Check it out, sez Joe Bob.

    And the bank stock bounce, at eleven standard deviations, not so much, but it’s still fundmentally nonesense, and don’t bet a nickle that it’ll stick, neither. What it does indicated to me, though, is that the public authorities will stop at nothing to keep equity prices from quitting. And that’s not only irrational but likely to inflict substantial collateral damage on the real economy in due course. . . . Sold to the system, and paralyzed in the headlights, they clutch their carpetbags full o’ bonds to their bosoms and cry, “Stop, thief!” At whom, precisely?

  22. anewc2

    In my earlier message, my reference to the standard deviation was linked to a book on sexual deviation. The same thing will probably happen here.

    I just want everyone to know that was not my doing, and I find it a little creepy, and not just in the sexual sense. I never liked or trusted Amazon, and now I have another reason. Now Blogger too. Damn.

  23. anewc2

    For those who wonder what it all means, here is my take. Statistics is not designed to tell you what it all means. Statistics describes the numbers you see. If you really believe that price changes are random in the coin-flipping sense, then no, you would not expect to see mean reversion. Each new day starts a new reality, and the past is forgotten.

    My own view is that price changes are not random in this sense, that there is a underlying fundamental reality that prices will always reflect, one way or another (and that maybe this is why they have fat tails). Then yes, you would expect mean reversion because that mean is anchored in reality.

    And in the case of the financials, I do expect it, and more, with a vengeance. These things tend to overshoot. (The statistics can estimate how much, but don’t ask me: I haven’t researched it.) But if you want to know what it means, read the papers and the blogs with large doses of salt on hand, and come up with your own conclusions. Read the history books too, especially about “buy when blood is running in the streets”. We’re not there yet.

    I’m no expert — note that “experts” are dropping like flies — but at least my explanation is not being sold to you. (Except by friggin’ Amazon. Jeez.)

  24. JB

    Lune and others are right… non-random, material events will obviously change returns and looking at them as ‘standard deviation’ is silly.

    If taxes on earnings suddenly skyrocketed to 90%, would the corresponding decrease in stock price be considered a 15-sigma event?

  25. Juan

    mock turtle,

    Veneroso’s 2007 presentation to the World Bank had to do with commodities in general and in particular, metals.

    Bottom line:

    I make the case that, in real terms, we have had an unprecedented commodity bubble in this decade. This bubble has occurred because of unprecedented investment and speculation in commodities, largely by way of derivatives. The far more important engine of this bubble has been leveraged speculation by hedge funds. Over the last two years prices have climbed even though the microeconomic fundamentals of commodities have deteriorated. There lies ahead a bursting of this commodity bubble. It is now being triggered by deteriorating fundamentals and it will be exacerbated by eventual investor revulsion which will reverse the extraordinary fund flows that have created this bubble.
    (Frank Veneroso, 2007)

    His complete argument can be downloaded at: http://www.venerosoassociates.net/

    I will only add that the notional value of OTC commodity derivatives held by U.S. and foreign banks, which one of his charts indicates to have risen from $1 trillion at end 2004 to $5 trillion at end 2005 has, according to the BIS, increased to $9 trillion (Dec 2007).

    Along with Frank, I certainly do not believe the New Era commodity supercycle theme provided by so many commentators.

    Bottom line 2: ongoing financial crisis will deflate this bubble.

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