How The Random Walk Become A Not So Random Climb, And How To Know When The Climb Is Ending

Tyler Durden's picture

Submitted by Jerry Bogart

A Less-Random Walk Climb and How Will We Know When The Game Changes?

Regular readers of ZH are all too familiar with the market-distorting impact of the various incarnations of QE on the equity markets.  One interesting way of looking at the result is a histogram of daily returns on the S&P 500.  First, the histogram for 1990 through March of 2009:

Now, the histogram for April 2009 thru 2010:

The most relevant observation is the lack of symmetry in the daily returns since April 2009.  In the prior decades, the bars immediately to the right and left of the mode (and on out the distribution) are nearly identical in size giving a VERY symmetrical distribution.  Since April 2009, each pair of bars as you work away from the mode show a clear skew toward the more positive return than the less positive counterpart.

Another observation is that the bin at each “tail” is fatter for the historical returns than for the last 21 months. 

Thus, the stock market has become a less-random climb from its previous random walk.

The ability of QE to achieve these results in spite of Dubai, Greece, Ireland, commodity price spikes and a reversal in 10 year Treasury rates has been remarkable.  That which cannot continue, will . . . until it does not.  How will we know we are approaching the point at which this phenomenon stops continuing?

1.    One could argue that the commodity price and 10 year Treasury increases over the last 60 days are signs that the distortion in equity returns will soon stop and we will see the return of more negative return beginning in January, especially if these trends continue.
2.    As noted in this post, Observations, the turning point may be when the market needs confirmation of the never-ending nature of QE .
3.    There may be an unexpected shock (Icelandic volcano, bankruptcy by major US municipality, terrorist attack, etc) which overcomes the market’s conditioning to “buy the dips” and reliance on the Bernanke put.
4.    Or, the march toward hyperinflation may simply continue unabated with a perpetual positive skew to equity returns that fail to keep up with the rate of currency destruction.

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hungrydweller's picture

The smaller data set will likely show less symmetrical tendency.  No real significance here.

ZeroPower's picture

Exactly. Youre looking at a more specific sample (time-wise) and hence you'll see more variation away from a normal distribution.

Akin to taking a sample of <30 and extrapolating that results are skewed away from the norm dist of a 100n sample.

A constructive suggestion for the author: look at 1991-2000 and then 2001-2010.

alpds's picture

I do agree with your points; however, the recent market intervention, is of unprecedented magnitude, has started with "green shoots" of 09 not in 2001 and there ain't much data thus far...

ZeroPower's picture

Yes the recent times are indeed interesting. This could be a good segue to work on something related to analyzing monthly index returns compared to how much POMO there is during that month overall, and/or the level of QE (or, indication of a beginning of QEx).

AllenX's picture

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Jadr's picture

Agreed, I'm a bit dissapointed with the strength of the thesis in the article. Essentially any sample in which one is has roughly 1/10th the datapoints is going to be a much rougher distribution (obviously depending on on the number of observations in each sample).

drbill's picture

Beat me to the punch. I believe it was Samuel Clemens, a.k.a. Mark Twain who said, "There are lies, damn lies, and then there are statistics."

UncleFester's picture

I think the Twain quote needs some modern updating:

"There are lies, damn lies, and then there is POMO."

Cursive's picture


Lulz.  Also said the following:

October is one of the peculiarly dangerous months to speculate in stocks in. The other are July, January, September, April, November, May, March, June, December, August, and February.

Variance Doc's picture

No, it is not the sample size; they are large enough.  The problem is the use of histograms.  Histograms are dependant on bin sizes, in this case a bin size of .41.  These are arbitrary.  If you change the bin size, you will get different results.

What *should* be used are kernel density estimators.  That will give a much clearer picture of what is going on (shape wise) with the return distribution.

All in all, meaningless results.

Nigh Eve's picture

Many thanks for offering this valuable suggestion (kernel density estimators). 

TonyV's picture

Sample size is one issue. The other is teh fact that the author is comparing the daily returns in a bull market gainst daily returns in a period when we had both bull and bear markets.

AllenX's picture

The economic system is not going to recover at the time many hope. Things appear good for the individuals earning money and they are the people stating the economic system will recover. In the event the economic system takes a dive you can find folks that experience some benefits. At times however it's not the people who really need a financial increase. Internet lending is growing a lot. Just do a little exploring to see the new types of loans accessible online. You will find bail bond loans on the market for citizens to acquire to pay for the bail agents, (See This really is just getting silly Watch the idiots who are instructing each person to waste money his or her savings to help keep the economic system running.

dwdollar's picture

It would be better to show each year from 1990 to 2009 separately to get a clearer picture.  Or wait for 20 years of QE.  I think we'll all have that opportunity.

Jace0228's picture

Anyone care to give a guess as to when?

plocequ1's picture

As soon as the almighty gets angry enough and shows his rath for  worshiping The golden calf. Until then, Dow 40,000

dark pools of soros's picture

bring this back next new year and it should balance out by then..  unless QE3

Tense INDIAN's picture

How to Know when climb possible way is by being a time traveller from the future......Whacko....just read this ....this is definitely POSSIBLE:

trav7777's picture

I guess he never looked into the historical record of his own incarceration in 2003, not that it'd have made any difference

Diogenes's picture

(sarkylert) L Ron Hubbard's ghost says he is a time traveller so what more do you want? (sarkylert off)

rickardswhite's picture

Can someone please explain to me why the 10 year yields have anything to do with the stock market in a QE environment??


Did they study this in Zimbabwae??? I wonder if they were saying their stock market must come down because interest rates were approaching 20%?!

TraderMark's picture

Great set of interviews with Roubini, Stiglitz, VW Reddy (the central banker of India that America wished it had), and Rajan (former IMF Chief economist who warned of our culsterf*** in 2005)

Oh regional Indian's picture

Actually, to all the posters saying sampling numbers are vastly different, spot-on.

A more interesting chart (same idea) will be to see a comparison of S&P 500 daily return vs. the Daily Return for each of Apple, Netflix and Amazon.

That will make this author's thesis scream out as to QE effect. If I had access to numbers I'd do it. Anyone?

So, it'll be rather easy to spot (the turning point that is) when you see those Charts start to look similar.

I'd really like to see that analysis. Can do the same in India for some of the Hot IT stocks and Real estate+Infrastructure. Same shit.


WTF2's picture

Random  and irrational markets means intuition will be the best guide.  Proofs and data points have limited use.  Five month bull move in equities coincided with a huge sell off in treasuries.  Market moved up way before the official QE2 and will correct well before the end of QE2.  Fed is rapidly running out of rabbits to pull from its hat, I would not want to hold my breath for QE3 as major institutional sell decisions have been posponed till early 2011. 

Sudden Debt's picture

Last week, for the first time ever, I actually sold EVERYTHING.

I went totally cash, which I will keep for at least 6 months.

I've got a pretty big silver stash and that will be making the money.

Everybody is just expecting the market to go up. Nobody is bearish?!

My guts tell me the wind will change.

Everyman's picture

I hope your gut is right.  The market (and the economy) needs a full reset because of the manipulation.  The outswell of anger against the financial criminals will be large and rough.   We need it none the less.  No money is going into the markets until the manipulation stops.  You are evedence of that.

ExploitTheMarket's picture

The extreme sentiment levels are enough to knock the market down a couple of % at this point, and I expect that to happen in January... I have a small short position in CAT, no big deal if it loses but I do think there will be better levels at which to get in on the long side and exploit the bubble again.

ZeroPower's picture

Did you sell out from your PMs as well (paper or otherwise)?

pomogranate's picture

on the contrary, I think everyone is expecting a correction.  the sentiment #s, put/call ratio, etc. have all been widely covered.  given that everyone is expecting this ... don't be surprised if it doesn't happen.  Or doesn't happen until people don't expect it anymore.


TexDenim's picture

If you take any bull market, you will see the same distortion.

bankonzhongguo's picture

Who bogarted my data?

AHpublius's picture

Your analysis is flawed.  You are comparing 19 years worth of data to 1.  A more appropriate analysis is to examine each year as a histogram and ask if any of those 19 individual years has any skew.  If each of the previous 19 years, examined year by year, has  no skew then you are on to something. 

Motorhead's picture

And, what, no 'manipulation' from 1990-March 1999?


f16hoser's picture

We have fucking idiots running Washington and the NY Fed. I accept the fact the dollar will fail shortly after the Euro. (Estonia, really? Couldn't wait 6 months?) I just hope we don't lose electricity for too long. I'm buying a generator soon. Propane generator that is. At least I'll have water and heat. My garden will be extra big this summer. I'm getting out of the dollar by as much as I can.....SILVER BABY, SILVER! Good luck to all of us. Side note: the Republicans are just as corrupt as the Democrats. Nothing will change.........If you Google Fascism you'll understand whats happening. I told my friend 2 years ago that there was a fine line between Fascism and American democracy.


nopat's picture

No difference of means test? No test of a null hypothesis? I mean, come on, two more fucking clicks and you're there. Any undergrad taking business stats knows this, nevermind making more meaningful and representative samples. Cute visual inspections are just lazy science, nice way to demonstrate confirmation bias to the rest of the class. If you think the equity side of every balance sheet on the S&P should have been taken to zero, the market says you're wrong. And even if the market's wrong, it can remain irrational far longer than you can remain liquid.

You might as well throw in a NWO/Reptilian conspiracy to your list, because the most blindingly obvious - that the market had just bottomed out and could go nowhere /but/ up - apparently escapes our author. No wonder our financial system is doomed if this is what passes for research.

RobotTrader's picture

Financials, retail, or cyclical stocks will crack first.

So far, neither have shown much weakness.

Watch CYC, it might be the first one to crack.

ranrun's picture

I acknowledge the need for data to make a convincing argument, but as the Fed continues to manipulate markets and the length of time its tools can make an impact are vanishing.  How else does one try to show this?

nopat's picture

So there have never been economic recoveries before in the past? Business cycles are now a unique phenomena of central planning? No other heavily-traded market indexes have gone through similar machinations, with varying degrees of intervention? There are no other ways to back into this by proxy by looking at other classes of assets?

That's the burden of every researcher, but at least make it look like the default assumption that you're entirely wrong was at least considered.

TruthInSunshine's picture

I genuinley believe the United States is in a strong and rapid clip of structrual economic and social re-aligment, and in the opposite direction and trend of what occurred after WWII.

After WWII, the U.S. (and Canada) possessed the best infrastructure of any developed nations, able to fabricate and manufacture goods for domestic consumption and export, and to foster a very wealthy service sector to feed off of the manufacturing one, as the formerly great powers in Europe were literally bombed into pieces, as were Japan, Korea (and then there was the Korean War) and China (to a lesser extent).

Germany, France Britain, Japan Italy, Spain, Korea - all had physical and/or political structures annihilated. 

That left the U.S. and U.S.S.R. to jockey for pole position, and the U.S. won.

Now, however, since roughly the late 60s, and as European and Asian nations built out their infrastructures and gained political stability, and as Asian nations took the lead to become the manufacturing hub of the world (first Japan, and lately, China, Korea, Taiwan and Singapore), the U.S. has grown weaker economically, as the global elite have sought to re-adjust (and possibly equalize?) living standards.

The game now is not how many USD or Chinese Yuan a worker makes: It will be how much purchasing power those fiat have, and where living standards will go.

So, to answer your question, at least in the context of 'The American Experiment,' bringing up the subject of 'economic recoveries' and 'business cycles' are irrelevant concepts.

We are marching in a long-term structural decline, now, and it has nothing to do with either of those concepts, which are now relics of a bygone time when we had, at least 'free-er,' even if nothing close to completely 'free,' markets.

nopat's picture

Nice soapbox you're standing on, but that wasn't what was being asked.  The question was how to demonstrate prolonged central-bank intervention as the key structural force behind market moves.  You do that by examining prior market behavior at different points in the economic cycle, by examining other markets that have different levels of central-bank activity, and by doing specific event-based analyses with regard to fiscal and monetary decisions. 

Right now we're saying a 1-year sample of the S&P almost doubling value is comparable to, in it's entirety: the invention of the world wide web, adoption of evidence-based management and information technology, three full-fledged wars in the Middle East plus one in the Balkans, the entire rise and fall of Silicon Valley, Home Depot, Starbucks, two real estate booms, the threat of the Japanese economy overtaking the US, the emergence of China as a threat to overtaking the US economy, the Asian crisis, 9/11, and countless other historical events.  Obviously economic cycles (both narrow and broad) become throbbingly important, what the fuck are you talking about?

TruthInSunshine's picture

Why are you comparing rising equity markets with economic activity?


That is what you said, or at the very least, strongly implied, no?

Here are your words:

"[A] 1-year sample of the S&P almost doubling value is comparable to, in it's entirety: the invention of the world wide web, adoption of evidence-based management and information technology, three full-fledged wars in the Middle East plus one in the Balkans, the entire rise and fall of Silicon Valley, Home Depot, Starbucks, two real estate booms, the threat of the Japanese economy overtaking the US, the emergence of China as a threat to overtaking the US economy, the Asian crisis, 9/11, and countless other historical events.  Obviously economic cycles (both narrow and broad) become throbbingly important.."

So, what the fuck is your point?

Do you not realize that the equity rally occurring so far is a result of monetary injection by central banks, arguably in a manner more rampant and direct never before done in the United States, and not because of any measurable 'economic cycle' effect?

Or do you not realize this?

And if you do, why are you even referencing 'economic cycles?'

Equity markets have been rising despite a lack of significant 'economic cycle' activity, and not because of it.

MiningJunkie's picture

Hail Zimbabwe! The Best Performing Stock Market on the planet over the past decade.

(Pssssss....that's a hint for the bears out there)...

In 2011, I shall only follow the chart of the Dow and S&P as measured against the CRB or gold/silver. To measure it in FRN's is meaningless.


jm's picture

Why not post the moment stats for the two time periods?

Kolmogorov-Smirnov normality test results would help out too.

watmann's picture

I recall when Enron was exposed I stated that we should wait until the US Governement does Enron even better. I asked the question as to who would make the arrests in Washington? We are and have been here. Our Government was set up with a system of checks and balances. there were three segments of the Government. As I recall from fifth grade the Federal reserve was not one of them as they have no check built into the system. Isnt it the job of the Supreme Court to declare the Fed uncinstitutional?

spinone's picture

An act of congress established the federal reserve, so yes, the Supreme Court could declare the act unconstitutional.  That would require a plaintiff with standing.  The best plaintiff I can imagine is the Treasury.

TooBearish's picture

Wow watmann - did you just wake up from a 30 year slumber /- the Supreme court gave up on the constitution after they found it was more fun to legislate social issues from the bench Re : Roe v Wade.

Keep waiting for them to declare the FED, the Patriot Act, Obamacare, etc unconstitutional - we'll see you at Dow 40,000

knukles's picture

Most interesting though, is that actual historical financial market return data do not display "normal" symmetrical distributions. 
Go figure. 

PD Quig's picture

Yow! I'm glad I remembered to Xerox my underwear!

Sorry, but haven't seen Zippy in quite a while.