Tuesday, October 13, 2009

Six Month Sigmas

Today, I put my quant hat on (a small one, to be sure) and go trawling in stockmarket data, specifically the historical performance of S&P 500 over six months. The reason I chose six months for my yardstick is because shares bottomed out in March 2009, i.e. six months ago.
  • First, the raw performance data going back to 1871 in chart form (click to enlarge).
From -40% to +40% In Six Months
Data: Robert Schiller/Yale

One immediate observation is that the market has just swung from one near record (-40%) to another (+40%) between March and September 2009. Since 1871, only the Great Depression era exhibited greater swings in share prices.
  • How unusual is such an event, from a statistical standpoint? Let's look at the next chart, a familiar distribution histogram (click to enlarge). The median 6-month performance is +3.1% (the mean is 2.7%) and the standard deviation around it (known as sigma, denoted by the Greek letter "σ") is 12.2%.
Back in March we were in -3σ territory and at the end of September at +3σ. A three-sigma event has, by definition, only a 0.27% chance of occurrence (i.e. 99.73% of the data are inside the -3 to +3 sigma band) if the data are normally distributed (which they are not, in the case of share prices). The swing from one extreme occurrence to the next has been very, very fast.

How often does S&P 500 move from -40% to +40% within six months, i.e. how frequent are such sharply positive V-type reversals? We can identify only two previous occurrences, and they both happened between May 1932 and September 1933 (see chart below, click to enlarge).

Extreme V-Type Reversals Only Happened Before In 1932-33

How can we explain what has happened in the last six months? What is the market anticipating?

This extraordinarily rare performance indicates speculators' bets that Mr. Bernanke's massive monetarist experiment will succeed. To wit, that his enormous bailout of the financial system will prevent the credit crisis from mutating into a virulent economic crisis.

How accurate is the speculators' analysis? Well... let's just say that they're largely talking their own book. People who now call the shots in the Fed, Treasury and White House are confirmed monetarists from the Milton Friedman - Alan Greenspan school of thought, itself harking as far back as Irving Fisher, the infamous "permanent high plateau" economist who lost a fortune in the stockmarket after the 1929 Crash because he simply couldn't believe the Fed would be so conservative.

By reverse analogy, could it be that the economy will continue weakening despite the Fed's largesse? That's what I think, because today's fundamental economic problem is not a lack of adequate liquidity (and the Fed can only affect that), but a lack of enough earned income to properly service the enormous debt that households have assumed. In other words, it's a solvency problem, and it necessarily affects personal consumption expenditures, the very heart of the economy (70% of GDP).

Look at the chart below, tracking household debt as a percentage of total compensation of employees, which I use as a proxy for earned income (click to enlarge). In just the few years after 2000 it zoomed from 113% to 180%. That's a serious challenge to solvency, no matter how low the Fed keeps rates.

Sudden Debt

I am not going to attempt a conclusion, today. Instead, since I still have my quant hat on, I am left wondering what are the statistical chances of the Fed succeeding in overcoming a massive debt-to-income imbalance with just monetary tools.

I don't know the answer- and can't know - because the data sample is tiny: just one occurrence, and it's still going on.


  1. The Fed/Govt can affect solvency: Just print money, give them to people with debt and that is it! Case solved. It is easy!

    My larger point is: you can get hyperinflation through political (misguided) intervention.

  2. If the US hyperinflates..

    a) It immediately loses the benefits of Dollar Hegemony.
    b) It collapses within an astonishingly short time, just like the USSR.
    c) It may spark WWIII (China and the oil exporters won't like it at all to see their dollars holdings reduced to shite).

    Hyperinflation IS NOT A REALISTIC OPTION. And neither is merely high inflation, a la 1980s.


  3. You might feel more sympathetic to Irving Fisher if you read his "Debt Deflation Theory of Great Depressions". It is the playbook for how excess debt, stagnant wages and industrial/financial overcapacity inevitably lead to deflationary depression.

    Fisher learned from his mistakes. Many trusting the Fed to do the right thing today will learn the same lessons in years to come.

  4. London Banker, I miss your old blog. Do you have a new one?

  5. Hellasious, the govt can pay off the debts, without hyperinflation. While paying off debt with accounting credits, they can simultaneously raise reserve requirements to "mop up the excess liquidity."

    Printing paper causes hyperinflation, paying off debt with credit does not.

  6. Hi LB, good to hear from you.

    Both Friedman and Bernanke became convinced of Fisher's views on the Great Depression. The latter is now putting them to the test in a big way.

    It's almost ironic, isn't it? Could the poor guy end up being wrong twice - once in person and the other from the grave?


  7. "You might feel more sympathetic to Irving Fisher if you read his "Debt Deflation Theory of Great Depressions". "

    I read the paper and do not feel at all sympathetic towards that idiot.

    After correctly describing the collapse in debt and all the fraud/delusion associated with it, what did Fisher prescribe in his 'seminal' paper? 'Print money and create inflation so that deflation does not happen'.

  8. You are assuming that hyperinflation is an "option" that our leaders can "choose".

    I am suggesting that our world leaders in the west are so attached (as in blind and sold) to the ideology of "growth", debt and bringing forward demand that they may cause hyper(inflation) unwillingly. Especially by the lack of trust that using the printing press might engender (surely not by increased consumption of the over-indebted and under-payed masses - that is deflationary).

    Not sayin' that I am an inflationista, just weighting arguments.

  9. Using the normal distribution for such relative changes doesn't make any sense. At most one should apply the lognormal distribution to the price ratios. (Or a normal distribution to their logarithms.)

    As you said, the normal distribution doesn't apply to stock market data, so counting sigmas doesn't tell us anything. Did you calculate the percentiles of the historic data that these extrema represent?

    That piece of information is independent of the actual distribution. As there are only a handful of these extreme events, the sample percentiles are very rough estimates of true frequency, though.

  10. Is there any way of determining how much of this is insider's selling to the general public mutual funds who's fund managers will take a 1-2% commission regardless of what happens?

    And London Banker, this reader misses your blog very much as well, it was a rare gem. A warm hello if it is you.

  11. @London Banker:

    Let me also say "hello." It's nice to hear from you again. And don't be such a stranger. We need to hear your expertise in these matters from time to time.

  12. In my humble opinion, Antal Fekete has as compelling an answer as anyone regarding how this is going to play out.

    Tiago, you make a very salient point in your second response.

    BTW, Thai, the dead links have been revived.

  13. Some semantic points on your post, Hell.
    I think that I have said before ( a rose by any other name...) that... "forgiving" debt for example (REALLY, what nice vocabulary, "forgiving" suggests that a SIN has been committed, and it induces a particular hegemonic relationship between the "forgiver" and the "forgivee") is NOT THE SAME THING as raising salaries and putting legitimate money in people's pockets. Debt maintains people as underlings. Salary DOESN'T (at least, not to the same extent, I think.).
    This is... a political and ideological issue.
    And I love the graph.
    Does it "describe" or "define" what FAITH in the stock market looks like ?

  14. And Hell, just curious (being kalifractalicious and all), any sense of how many standard deviations this would be in a standard Cauchy or Lorenz distribution?

  15. The truly breathtaking thing about a lot of the comments is the lack of understanding of power and its influences on people and therefore policy.

    Why would the government (specifically the controlling interests behind the curtain)socialize the losses of the financial institutions and privatize individual losses? Because they want to maintain power for themselves--no conflict of interest on having Paulson and Geithner as Treasury secretaries? Please.

    Why is it a safe bet the same government will not severely degrade the currency? The same forces that control policy control the lion's share of the currency, and its against their self-interest to collapse the currency.

    Why will the brunt of this be felt by the people with the least effect on causing this disaster? Because people with power found the ultimate rube--the average uninformed American taxpayer--that can be distracted with BS about Acorns and fascist communist leanings of the President.

    Are you this naive to not understand the force of power in this tragedy?

  16. Marcus, your observations have some serious flaws.

    1.) The maintenance of power that you assume has been achieved via the transfer of losses from private institutions to the public will not be maintained into perpetuity. What has transpired to date ultimately paves the way for the collapse of government itself.

    What's more, as government attempts more and more measures to save itself, its very legitimacy will erode to the point where any governance it attempts will be of a hollow sort. Onerous laws will be passed, and oppressive taxes employed, but equally, such measures will have a toothless aspect, and as such will increasingly be successfully defied by many.

    2.) The dollar is being managed, as I write, out of existence. This has been the case at least since the beginning of the decade. For obvious reasons, TPTB would like what is a terminal case to continue being an orderly one, but the very big problem for those who seek such an outcome is that, going forward, they will have less and less leverage over the process of ushering the dollar into oblivion.

    3.) Your last assertion is probably correct, but then who wouldn't assume that elites, in general, would suffer less than those over whom they govern.

  17. Edwardo,

    Re point number:

    1. So the result of this is anarchy not a blaming of the old and a changing of the guard? We'll see, my bet is against anarchy.

    2.So along with a lack of government we are going back to biting each others currency to validate authenticity? Or barter system?

    3. I don't considerer Obama an "elite", he's influenced and controlled by the elite, but just like Congress--wooden puppets in the play--not the controllers.

  18. Some of you appear to believe that the powers that be are conspiring against you. You should be so lucky.
    They aren't conspiring against you, they're just nuts.

    The US dollar hegemony (but not the US nation) will collapse much faster than the USSR. Got that right. All those CIA 'agents of influence' are going to be very, very, angry at the former US establishment when the dollar hyperinflates.
    The 'dare not fly' list is going to include a lot of people that used to be able to fly all over the world. No longer. Not going through any airport where some guy running security once had a bank account full of dollars in a Swiss bank full of Tbills.
    The former US establishment types could wind up extradited to a Cuban prison and I'm not talking about Guantanamo.
    The third (and a lot of first and second) world elites are going to be furious and in some cases are going to be in position to do something about it.


  19. Anarchy is a very misunderstood term as it pertains to politics. It is not a synonym for general mayhem in any event. I hope that the U.S. citizenry finds the fortitude to remake government, but I have serious doubts that we have it in us. Does that mean we simply devolve into "anarchy" as per the lay definition? I doubt it, but the outcome remains to be seen.

    Prospectively, the dollar will continue to exist in one form or another, but competition amongst national currencies will continue just as competition exists and persists between nations themselves. The greenback was first (some might say first among equals) but that is ending, and in future, just as water does, it will seek its own level. That spot is likely to be closer to the mud flats than in and around its former redoubts at higher elevations. As for barter, there may be periods where more of that occurs than not as befitting a nation that more and more appears to be oscillating between first and third world status.

  20. > Milton Friedman - Alan Greenspan school of thought, itself harking as far back as Irving Fisher, the infamous "permanent high plateau" economist who lost a fortune in the stockmarket after the 1929 Crash because he simply couldn't believe the Fed would be so conservative.

    I think you describe many things wrongly here:
    - There is a Friedman school but no Greenspan school. While Greespan never renounced Friedman, he didn't follow his advice, as Volcker had done it before, to a certain extent.
    - Fisher is not the intellectual forefather of monetarism, especially not with his 1929 optimism.
    - Fisher's losses were not based in his belief that the Fed would bail out investors but in his expectation in 1929 that the economy was healthy indeed and could grow more.
    - After his large losses, Fisher began look for causes of the crash(as others have written already), and his debt/deflation model is still the base for deflationistas.