This page has been archived and commenting is disabled.
Guest Post: Stop Chasing Tails: Some Long-Only Opening Lines in Portfolio Theory
Stop Chasing Tails: Some Long-Only Opening Lines in Portfolio Theory (pdf link)
Submitted by JM
»
- 6832 reads
- Printer-friendly version
- Send to friend
- advertisements -
Warrant issued for Wikileads founder for rape in Sweden:
http://www.9and10news.com/Category/Story/?id=248205&cID=3
and promptly cancelled....
http://www.bbc.co.uk/news/world-europe-11049316
it almost seems that the Government is trying to make Julian Assange and WikiLeaks the premiere site for truth....i smell a rat
Yeah, a little Sun Tzu maybe
This is a pretty silly article. The author simply sets up Ordinary Least Squares (OLS) as a straw man and concludes "...that all predictions fail...."
There is nothing wrong with using linear regression in a non-linear world; you as the user just have to realize its limitations. It's actually quite robust to non-Gaussian departures. If you want to capture the time dynamics of the probability distribution or non linearities, you switch to a Bayesian approach or nonlinear regression with non-Gaussian errors or both. Yes, the estimation becomes harder (possibly much harder), but that is price you have to pay. No free lunch and all.
It reminds me of students who take regression and think that they are at the end of statistical knowledge as a body. Well, ...
George Box once famously stated that all models are wrong, some are just useful. I would extend the notion to most articles are wrong and useless, just like this one.
There is nothing wrong with least squares when the p.d.f. is stationary. When it is constantly changing due to bayesian updating, there are problems.
There is nothing wrong with using OLS or vector autoregressions or any other stat tool. Just know that forecast errors diverge expontentially, and there ar elimitatison to any tool.
"When it is constantly changing due to bayesian updating, there are problems." This is not true in general. There are robust Bayesian methods for the prior. If the Bayesian approach is too hard to understand, you can always use robust classical methods (e.g. M-estimates) too (static or dynamic models). If people use amateur methods, they will get amateur results.
"Just know that forecast errors diverge exponentially” This is not necessarily true either. The forecasting error structure depends on the model used.
Be careful of hasty generalizations, for that is a sword you will repeatedly fall on.
I offered no hasty generalizations. In time all predictions will fail, regression or no. To rely on a mathematical tool as the end all be all is too hasty.
If they were foolproof, there would be people that can consistently beat the market without any inside information.
I agree, and would add an additional thought... The reality of betting on the tails is different than achieving the tails- one does not have to reach the tail for the tail to be priced in an option model. ie be long gamma before people need protection. So in my view, you dont have to have a correct prediction, only partially correct, if you are willing to take the convexity.
Variance Doc wrote:
(mostly) Agree. This article is slightly misleading, showing only symmetrical distributions. In trading or in economy the distributions are often SKEWED, or weird, and trader/investor has to use (at least as complicated as) as You already said so-called M-estimates.
http://en.wikipedia.org/wiki/Skewness
http://en.wikipedia.org/wiki/M-estimator
http://en.wikipedia.org/wiki/Robust_regression
jm wrote:
I dont like to dissapoint you, but in 50% of all cases this is wrong. The least squares method (by it's definition and by it's proof) works when you beleive that your model varies from the real process *very low* by the means of the squares of error. This is the case with mechanics-robot-natural errors (for example measurement errors), but this is not a case with human-generated activity, having a TARGET.
What does force you to think that traders or bank employees push the buttons on a keyboard RANDOMLY? Is it a random process? If not, you can not apply DIRECTLY statistical methods, developed for random events/processes.
I agree. I should have said more about the higher moments, but there were space issues, and the yawn factor.
I was thinking of jumps (or bifurcations if that is your poison) as they are often real model killers, and hard to accomodate. So practitioners sometimes assume stationarity and don't worry about them.
I may be wrong, but I get the feeling that people using quantitative methods are seeing this article as an attack. It isn't meant that way.
No, I think You are on a right way.
An attack? No, I think You simply run into conclusions too early.This article should be five times larger only to depict the main problems with robust statistics (classical statictics does not work for predictions in economy. At all).
In my opinion running robust statistics is a very slow and thin process, with re-checking the math definitions on every step.
Eventually one almost surely hits some outliers that will blow up a model. I'm not sure how that conclusion comes too early.
Five times larger is not suited for these posts.
Variance Doc wrote:
Hm-m-m. Partly agree: this article could be called "Plain and simple introduction into the problems of modern statistical methods' application to trading".
Conclusions of this article: yes, totally wrong.
Hm-m-m, what? If correlation is near -1.0 or +1.0 You get LINEAR DEPENDENCE between events, but if correlation shows NEAR ZERO, you get NOTHING. Correlation near zero does not say ANYTHING about dependence: it is not LINEAR, but at the same time can be very strong NON-LINEAR.
Regression methods rely on so-called "conditional expectation", means that You deal with the expected value - calculated (ha-ha) having in mind that the distribution is NORMAL. That is the GENERAL problem with the modern statistics theory: it implies there and here that the distribution is normal (or (Carl) Gauss-ian) *by default*, which is not always a case.
Be carefull: what is "quite"? On stock markets the 1.0% precision is good enough, while on retail-Forex with 1:100 leverage, or in airplaine's control you need a precision of 0.1%, which can not be provided by classic statistical approach.
But in general, agree with You.
This is a great and healthy discussion.
My statement of the use of linear regression in a heavy tail/nonlinear setting was qualified by the fact that the user has to be aware of the limitations - such as biased estimates and inefficency. Never-the-less, the point estimates are still consistant, hence my statement of robustness to non-Gaussian departures.
Would I use it in FX with a multi-million dollar book? NO, beacuse I know of the limitations. FX is too well understood. Would I use it for some quick and dirty estimates and predictions in a not very well understood market? You bet. Would I use it for initial starting values for advanced numerical methods? Yes, etc.
Cheers!
JM, I like you...never read a stupid comment from you, Sir.
That is very kind, but I confess I say stupid stuff all the time.
Ooh me too, it's on balance what counts, kinda like risk management is the key to successful trading
Yeah, the first sentence is pretty stupid-
“It appears that Kyle Bass doesn’t know how to be long stocks…”
Actually, his fund was long $56mm of Citigroup at one point this year and has since sold it. Also, he bought over 7% of HFF, Inc. (HF) at the end of 2009. It’s up over 20% YTD while the S&P is down 4%. JM, perhaps you can give us some of your utility picks or your portfolio composition since we can’t verify your equity holdings with SEC filings like we can with Kyle’s.
that merely refers to the ZH post earlier in the weak, it does not mean actually that Kyle Bass is a moron... but maybe too deep
I realize that it was said tongue-in-cheek. JM is criticizing a successful hedge fund manager for being bearish. I'd like to hear what stocks JM is bullish on right now so we can see how they do.
No offense meant. Just a teaser to the article because of the response he got a couple of days ago.
You say one should "buy underpriced tail-risk, and sell over-priced tail risk." Could you tell us what mispricings you currently see? Just looking for more substance and less theory.
I don't think the well-received SKS microfinance IPO is an accurately priced tail. Such tails are better captured over a broader index, avoiding concentration.
I don't think that a well-received JGB40 is properly pricing in tail risk. In an uncertain world, there is such a thing as too much term.
The world is mean-reverting to more historical volatility and risk premia IMHO.
I could swear that leptokurtotic distribution curve was giving me the middle finger.
Lets see, to summarize - market action has more events in the 'tails' than anticipated, the mean frequency is narrow and pronounced within +2/-2 standard deviation.
The only real takeaway is according to the Hurst exponent, past events do feed into forward price action, with the only real antipersistent mean-reverting behavior occuring in volatility-based instruments.*
Now time for a beer...
*Source - Edgar Peters, Capital Market Analysis of Price Cycles and Volatility
One could say that mean reversion only works after crashes. The stuff in between crashes is just noise.
That is the key to Warren Buffett's success.
Warren reinvests the insurance float (the free money), this is why he made so much. there are others with higher returns, but no float, so less money. And yes the permabulls that caught the mean reversion rally, what a sorry bunch...
Where are observations to support the theory?
If my memory serves correctly, Benoit Mandelbrodt looked at a very long price series, Cotton in USD, and found that this prices followed a specific distribution, not arbitrary ones like suggested in this article.
Moreover, sometimes predictions about the future are possible, take weather proverbs for example. Two out of three times they prove to be correct and beat any supercomputer prediction. A similar method for the stock market is Dow Theory properly applied. Robert Rhea states in his book “The Dow Theory” that the theory, if properly applied, works seven out of ten times.
That is way better then stating nobody really knows what is going to happen while throwing unproven distributions around.
Think of it this way. The economy is a machine made up of interacting people and the institutions they create to optimize their interactions. Call this type of machine a dynamical system.
The measurements of GDP, stock prices, bond yields are all just discrete samples from the continuously generated flows from the dynamical system.
All I'm saying is that as the dynamical system that you sample data points from changes wildly, your sampling distribution changes wildly. Assuming a constant distribution is barking up the wrong tree IMHO.
For the dynamical system to change wildly you need complex behavior from it. The analytical tools aren't there yet. Get ready.
A mathematician named Sheldon Newhouse proved there are dynamical systems with an infinite number of attrating sets. He then proved that there structures are dense in a pretty general class of function spaces. This means that as a stock price evolves in time, it is constantly tugged around in time, attracted by an infinite number of equilibrium points. It will look a lot like a random walk, but it is not a random walk. Seven time out of ten it will behave like a random walk until it doesn't. Then you're screwed, hopelessly because you surely levered you past successes.
The math isn't there to characterize these structures, but I think they are the reality.
Sheldon Newhouse. Respect.
The dynamical system is a bit too complex to be properly modeled. So, it looks like random.
Still some people were able to find patterns in that so called random. The claim goes so far that these patterns are tradable and differ in bull and bear markets. If orthodox financial theory fails to see that, I can not help orthodox finance.
Dow Theory might be too vague but there is a somewhat similar set of rules written down by someone with a great name in the real business - Jesse Livermore.
In his book “How to Trade in Stocks” he published a full set of rules to make the pattern in the seeming random visible. I read those rules as similar to Dow Theory but more sophisticated.
Applying these rules to stock or commodity price series shows distinct patterns that have predictive value. Moreover, that gives indications of major turning points or likely end of bull / bear markets. It does not predict tomorrow's prices but the trend of prices, what for investment purposes is sufficient.
That system is not fool-proof but supposed to work seven out of ten times and does not follow the random-walk-bullcrap.
Towards the distribution: Does the distribution itself change or do parameters in the distribution change?
While applying my trading system sourced from the above mentioned books I observed different market behavior during bull and bear markets. Apparently bear markets have a bigger random element then bull markets as traders now since a long time.
That is a good question, and I'm not certain of the answer.
Distribution itself changes = you know it is unknowable.
The parameters change = you can know it for a finite time before you're out in the cold again. The very act of using the information in a trade (in size) would cause the market to absorb your success and adapt so you couldn't deploy the trade effectively in a short time. Typing as a think.
You seem to have thought about it, and I'd like your thoughts.
To test and adapt those old trading rules I needed to check something like a distribution of prices.
Robert Rhea puts it as follows:
Determining the trend: – Successive rallies penetrating preceding high points, with ensuring declines terminating above preceding low points, offer a bullish indication.
Conversely, failure of the rallied to penetrate previous high points, with ensuing declines carrying below former low points, is bearish. Inferences so drawn are are useful in appraising secondary reactions and are of major importance in forecasting the resumption, continuation, or change in the primary trend. For the purpose of this discussion, a rally or decline is defined as one or more daily movements resulting in a net reversal of direction in exceeding three percent of the price of either average. Such movements have but little authority unless confirmed in direction by both averages, but the confirmation must not occur on the same day.
This is the original formulation of the”higher high followed by a higher low” and contains something highly unusual in finance but very common in science; in science terms that is an error margin.
Viewed as distribution, it is a rectangular distribution. A filter is applied in the sense that both price series must move in the same direction.
While back-testing those rules I observed that the error margin is bigger during bear markets then during bull markets. This would be the same distribution but different parameters.
Another observation was that sometimes the market moves orderly with rallies and reactions and at other times and much more seldom there are erratic moves in both directions. I noticed the difference while charting but at the time did not look for an explanation. To find this different pattern would require digging through a lot of numbers so I can not give an example right now..
Gunther-
(from control system/radar perspective). I've wondered whether the "crop circle" HFT thingie that we have seen is being used to characterize the current market and, since it is not stationary process(es), to characterize the rate of change of the process.
http://www.zerohedge.com/article/how-hft-quote-stuffing-caused-market-cr...
http://www.zerohedge.com/article/its-not-market-its-hft-crop-circle-crim...
http://www.zerohedge.com/article/algorithmic-crop-circles-redux-rise-sto...
Gotta watch them cliffs, though.
Do you see any relationships here?
Thanks,
- Ned
To characterize the current market is complex;
only the price action is still bullish in the big picture.
Price/volume is typical for a bear market; Dow/Gold is typical for a bear market too. Something similar to the flash crash happened few times at the end of down-moves:
11/13/29: DJI high 212, low 195; DJT high 134, low 127
10/5/31: DJI high 92, low 86; DJT high 49, low 45
10/6/31: DJI high 100, low 88; DJT high 52, low 46
If my memory serves correctly, Livermore called the the ancestor of HFT “painting the tape”
To sum it up, today's market looks like a bear market papered over with printing press money.
Anyone know of a good discussion on non-symmetric or non-continuous distributive solutions? How about some financial models using differential equations of probabilities using discrete distributions for solutions?
http://en.wikipedia.org/wiki/Distribution_%28mathematics%29
I think the best avenue to start is the subject of long range dependence. Some call this long memory processes. It will take you to ergodicity.
I've got some stuff on my scribd that may interest you:
http://www.scribd.com/lyapunov
To CONners:
Your link is about "generalized functions". (There is a "distrubution" wording mess in modern math).
Correct link about statistical distribution:
http://en.wikipedia.org/wiki/Probability_distribution
The best books/articles on this matter were published in 1930-196x in russian only and by very limited issues.
A friend of my has most of their portfolio in CEG a Utility provided. What is interesting is that it was trading around $87. Dollars until Buffet wanted to buy the Company. The stock fell to $15. a share. Eventually another company came in an bought 1/2 the nucular plants. Yet, since then the stock will not get out of the Basement. Currently trading for about $28 and change.
I would not invest in Energy stocks as if someone like Buffet wants to buy it the stock will go to the basement and stay there for years.
Waterfall-
I was visiting them in Rochester, didn't get much done that afternoon (mid-Sept '08). Crackberries going off, ashen faces, I got back to the hotel just as the market closed, missed a buy, then Buffett came in overnight, bent them over the table. Was it Buffett manipulating their positions in the energy trading (Constellation New Energy) arm? Never even mentioned-was a mini-Enron situation.
EdF came in and bought 1/2 of their nuclear division vs. Mid-America owning 1/2 of CEG. Penalty was like $1BB and return the $5BB a month later. That be a killing.
Stock not go up? Blame Baltimore in large measure.
FPL, EXC, SO would be OK imho. FPL throws a good dividend and the captive units in FL have guaranteed ROR.
NRG in cash flow difficulty with STP, not bad, but not scads of free cash flow. Examples:
http://online.barrons.com/article/SB124182248204002189.html
http://online.barrons.com/article/SB113719872212046602.html
- Ned
Wow. Can we split some hairs here?
Regurgitating info such as this is not exactly rocket science. Bass was talking about stocks in general, perhaps value and growth stocks. That he failed to highlight possible exceptions does not mean his entire message was wrong.
Next thing you know I'll be reading about swarming and game theory here. It's not that complex. Really.
Soon the big debt Godzilla will come calling with a bankrupt world that can't feed him anymore. And there will be those that argue whether is a Triassic or Jurassic beast.
"Soon the big debt Godzilla will come calling with a bankrupt world"...Can´t hear it anymore. You guys should better think about what bond investors will do if austerity measures in Europe and elsewhere kicks in and governments need much less refinancing "liquidity" ! I smell a gigantic cash overhang rushing into "THE" markets..;=)
If "THE markets" = equities. I'll take my chances.
Bonds are somewhat more expensive based on past history, but stocks are not cheap by any stretch of the imagination.
Look at the yield on SPOOs compared to IBOXX. No contest.
"Soon the big debt Godzilla will come calling with a bankrupt world"...Can´t hear it anymore. You guys should better think about what bond investors will do if austerity measures in Europe and elsewhere kicks in and governments need much less refinancing "liquidity" ! I smell a gigantic cash overhang rushing into "THE" markets..;=)
While the occurence of this article on ZH is very usefull (in general), this matter is too complicated for a too fast consideration. Look, why GS, JPM etc. use high-freq-trading? Because they know that they can hire *any* mathematician in the world (hm-m, except ... me), but modern math, modern statistical methods are so SEGMENTED, that those methods can predict nothing, especially in a crash conditions. Here I agree with the author of this article.
But this author's nice attempt is too narrow. It is really only "an introduction".
I am bearing an honour to be a first person, who used a word "autocorrelation" on MarketWatch.com site (in it's 13 years).
http://www.marketwatch.com/story/using-the-200-day-moving-average-2010-0...
You see? Other web-sites, even called "traders'" or "investors'" dont even mention such "sophisticated" words as "regression", "autocorrelation" or "probability distribution".
Small respect to JM for this attempt, respect to Variance Doc for the scientific comments, and big respect to ZH for the publishing an article on a serious matter.
I'm confused. I get "small respect" even though you agree with the conclusions re: methods.
Another dude gets "respect" simply because he used technical terminology even though he is dead wrong in his conclusions (as I understand them).
Seems messed up.
I suppose I should talk about hyperbolic attractors even though they have no place in finance to pass muster in some eyes.
Small respect? I think I get it. PDF? You might as well use the exponential-polynomial closure method.
Too, true robustification is achieved only outside the margins of traditional quadratic or conic approaches. What do have to offer out on this ragged edge?
Still lots of respect on this post, not a junker in sight, lolz....
Zero Hedge isn't the place for it. Just trying to write up an introduction to some issues.
Right on, many thanks.
O-o-o-PS, sorry, gentlemen, it was a misspelling. It means descending BIGGEST respect to ZH, smaller respect (plain, simple respect) to Variance Doc for his/her very important corrections, and further (smaller) respect to the author for his heroic attempt to disclose very complicated matter.
(smiling widely) Wanna try to suit me for offense?
(Creative persons, authors are so sensitive....)
Hey dude. I called you a "condescending douchelord" in my first run at this reply. Here's a more measured approach.
Your reply was extremely condescending, but I think the more prescient issue is the role of quantative practitioners in finance. I know that traders shit all over quants, and people develop defense mechanisms like smugness and an air of superiority.
But there is something important that quants have to say to a wider audience. We have to get out of the silo. I enjoy talking to clients and interacting in that way. You can't do that when you throw around an attitude.
Maybe you like the silo, or you are some academic that does... what you do. Some of us want something more.
I appreciate your stat KNOWLEDGE, but your ATTITUDE sucks.
I'm not even impressed with his stat knowledge....I think he's using Wiki....
Sorry but Kyle Bass makes much more sense than this article.
In short, too many people use statistical tools without knowing their limitations
because of that tail events are so much more likely to happen and this is
why I would put my money with Kyle than the author of this aritcle.
Kyle can step back apply common sense to verify if statistical analysis makes sense.
Very good article and very helpful commentary. Thank you JM and Co.
Please post more of this stuff.
Thanks for such a great post and the review, I am totally impressed! Keep stuff like this coming!...
cheap site hosting
windows web hosting
windows vps hosting
windows vps