According to Pimco’s global strategic adviser Richard Clarida and CEO Mohamed El-Erian, the new normal is not normal, and that has profound implications for investors. Some of the conclusions may sound a tad self-serving, in that Pimco is a bond shop, and fat tails implies more risk (or more accurately, higher odds of more extreme outcomes) which in turn makes more volatile asset classes like equities look less appealing relative to stodgy old fixed income instruments.

But the implications are even more far reaching that the authors suggest. Normal, or bell curve, distributions have long understated market risk, as mathematician Beniot Mandelbrot discovered in 1962. Yet the overwhelming majority of financial models use normal distributions because they are computationally convenient. So the edifice of risk management, which was problematic even in the best of times (as the blowup of hedge fund LTCM during the Great Moderation attests) is likely to show even more serious flaws in the coming years.

From the Financial Times:

It seems that, wherever we look, the snapshot for “consensus expectations” has shifted: from traditional bell-shaped curves – with a high likelihood mean and thin tails (indicating most economists have similar expectations) – to a much flatter distribution of outcomes with fatter tails (where opinion is divided and expectations vary considerably)….

What is less appreciated is the extent to which this changing shape of distributions affects conventional wisdom in the investment world, together with the rules of thumb that many investors have come to rely on.

We can think of five implications, some of which are already evident while others will only be obvious over time.

First, investing based on “mean reversion” will be less compelling. Even though flatter distributions with fatter tails have means, the constituency for mean reversion investing will shrink as those means will be much less often realised in practice. A world where the realised return rarely equals the expected valuation creates a bigger demand for liquid, default-free assets; it also lowers the demand for more volatile asset classes such as equities. These shifts are already taking place.

Second, frequent “risk on/risk off” fluctuations in investors’ sentiment are here to stay. Investors, based on 25 years of rules of thumb that “worked” during the great moderation, thought they knew more about the distribution of risk than they in fact did. This led to overconfidence during the bubble. The crisis reminded investors that these rules of thumb are less useful, if not dangerous.

With declining confidence in a reliable set of investing rules, markets have become more susceptible to overreactions to daily news and, are, therefore, more volatile. Just think of the number of triple-digit days in the Dow….

Third, tail hedging will become more important. An understandable consequence of the crisis is less trust in diversification as the sole mitigator for portfolio risk. We are already seeing increased investor interest in tail hedging, though the phenomenon is still limited to a small set of investors.

Fourth, historical benchmarks and correlations will be challenged. In this new “unusually uncertain” world, many investors will need to fundamentally rethink the design of benchmarks and the role of asset class correlations in implementing their investment strategies. The investment industry is yet to give sufficient attention to this.

Finally, less credit will be available to sustain leverage and high valuations. Even apart from the inevitable response to regulatory actions aimed at derisking banks, a world of flatter and fatter distributions will reduce available supply of leverage to finance trades and balance sheet expansion.

This is not just because extreme bad scenarios “melt down” positions but rarely “melt up”. Even with a balance among good and bad scenarios, the provider of leverage does not benefit from the fatter good tail, but faces greater likelihood of loss with the fatter bad tail.

Investors had 25 years to get comfortable with the great moderation. Its end poses challenges that extend well beyond policy circles as it fundamentally undermines the rules of thumb that served so many investors for so long. The sooner this is recognised, the better.

bob goodwinAlthough I agree with most of the conclusions in the article, I see a tendency to conflate volatility with fat tails. They are wholy different beasts.

High volatility means a high standard deviation (flatter distribution). Even “Mean Reversion” is a term of art for excess volatility that will spring back. The costs of high volatility are all of the points made in the article. Volatility is bad for everyone except traders who like to make mean reversion trades.

Long tail risk occurs when an unusual (but still bell shaped distribution) of snow falls, and this causes an avalanche. At the bottom of the hill you have a catastrophe that is well beyond the probabilistic models.

fat tail risk is relevant for macro economic discussions because one of the causes of fat tail risk is the concentration of bets made due to hedging (which largely relies on bell curves). The collapse of these bets has systematic causes and effects.

I also disagree with your assessment that people use bell curves because they are convenient. It is simply impossible to judge extremely rare events, so there is no viable alternative than to use standard statistical tools with great care.

Yves SmithPost authorWith all due respect, you need to read more on statistics and the development of financial economics. My remark about computational convenience is not an “assessment”; it’s a well known fact with a robust historical record to support it.

Mandelbrot’s findings were rejected precisely because non-normal distributions (or as Mandelbrot liked to call them, “wild”) range from computationally daunting to uncomputatble. From ECONNED:

And probability assumptions were central to the emerging field of financial economics. It was taken as a given that securities prices moved in a random fashion; that was the core of the EMH, and the later theories built on that. But what sort of randomness?That question is not trivial. There are many types of randomness. All the models in the financial economics edifice assume a normal distribution. But not only is a normal distribution the most tractable form of randomness from a mathematical standpoint, it is also the least prone to wild extremes.

By contrast, there are types of random behavior that can be characterized mathematically, yet the resulting distributions

elude the explicit mathematical formulation that economists traditionally aim for.The Lévy distribution family is an in-between case. Lévy distributions have a property called “stability,” which characterizes any distribution that will look roughly the same whether you take a thousand samples or a million.

Another property of Lévy distributions is “alpha.” Alphas can range from zero to two. The lower the alpha, the wilder the distribution.

One limit case, when alpha is two, is the economists’ best friend, the Gaussian distribution, which is familiar and easy to manipulate directly in formulas. But when alpha is any value less than two, the required mathematics becomes much more difficult, and the prospect of coming up with the sort of “proofs” that economists prefer becomes remote.29

However, these supposedly exotic distributions are for the most part deemed irrelevant to working statisticians. In classic drunk under the street light fashion, they stick to what is “tractable” or fits well with their tool kit, no matter how important the more difficult phenomena might prove to be. Yet again and again as we look at the crisis, we will see that the preference for computational convenience helped pave the road to disaster.Your assertion re fat tail risk being due to hedging is also incorrect. Mandelbrot first found fat tails in cotton data going back 100 years (this as of the early 1960s) when statistical based hedging was non-existent. He found similar patterns in every other market in which he could find a decent sized data sample.

The chapter discusses how economists presented with Mandelbrot’s findings, that trading markets did not conform with normal distributions, rejected using approaches that would provide a better fit with the data precisely because they were too hard.

marc fleuryyeah, gaussian or normal distribution is predominant not because there is a conspiracy of dunces but because the statistical definitions featuring them solve analytically.

Yves I think you meant “analytical” and not “computational”. Computationally you can explore whatever with things like matlab. When there was no computer around (30 years ago? 1980) it was handy to have exact analytical solutions, it meant research on them could happen on paper and pen… and so it did. As simple as that. Do not suspect malice where convenience would do.

Levy distributions have fatter tails and do lend themselves to analytical progress. Also, levy functions are available in most software packages. Making them expedient from a computational standpoint.

But the main point remains, that widespread use of normal functions for whatever reason led to a dramatic underpricing of risk.

ScottAThanks for this insight, Yves.

As a sometime mathematician and computer programmer (with particular interest in areas such as complexity in the mathematical sense, and complex event processing in the programming sense), who nonetheless has for some reason never really been able to stay awake through most economics or quant texts, I am appalled, but in the end not terribly surprised, that most economists and quants have been so lazy that they went and based the entire quadrillion-dollar notional edifice of the world’s economy on such a major unproven assumption: the supposed good “fit” between their untested, obviously oversimplified, idealized Gaussian distributions and the much more complex real-world behavior of markets and people.

It seems that any layman could have seen that there is not necessarily any good “fit” between something truly random such as the simple act of rolling fair dice – versus the vastly more complex (economic, historical, psychological, etc.) interactions, feedbacks, correlations etc. involved in people and markets and money.

I remember being very excited about Mandelbrot in the 80s when I heard about his work on fractals.

In those pre-internet days, it wasn’t so easy getting information about cutting-edge discoveries. I remember personally visiting the offices of Springer Verlag back then, in or near the Flatiron Building in Manhattan, so that I could pay 50 bucks or so for a beautifully color-illustrated coffee-table edition of Benoit Mandelbrot’s research on fractals.

I was also intrigued to read at the time, in another book on fractals (can’t recall the author – it was a squarish, smallish format – I have it somewhere) that Mandelbrot himself had been regarded as something of an oddity or maverick within the mathematics community itself for many years – merely because he had the audacity to be much more interdisciplinary than many of his specialized, pigeonholed colleagues, and because he was interested in measuring and modeling less platonic and more real-world issues – such as the “length” of the coast of California (at various “scales”), or the turbulence of a wisp of smoke.

Too messy for most mathematicians to deal with – just like the reality of fat tails has been too messy for many economists and quants to deal with. It’s a pity that their lackadaisicalness about picking the right models has helped contribute to the biggest financial disaster in history.

As you say, this is the kind of stuff we might expect from a drunk looking under a lamp post for his keys – but not from our leading economists and quants, who are now seen to be driving the economy off a cliff with their ridiculous (and possibly self-serving) oversimplifications.

It was interesting to find out, much later, that Nassim Taleb had based some of his research into the notion of “black swans” on this other discovery by Mandelbrot which again was too real-world for many mathematicians and economists to come to terms with: the inapplicability of random or Gaussian distributions to many natural phenomena.

Of course, this wouldn’t be the first time in the history where something seemed to be true on a small scale or for a small batch of observations, but later turned out to be false on a larger scale or with more observations.

There are several other situations we’re all familiar with: locally the Earth appears flat, although globally it’s round; and Einstein showed that certain behaviors that appear one way locally can appear quite different under more extreme conditions: the hard-to-observe ability of gravity to affect the path of light (which we were eventually able to confirm empirically during a solar eclipse when light from a star near the lunar disc gets deflected, or by observing that light can’t escape from a black hole), or the “slowing” of time which can supposedly be undergone by an object moving at a velocity which is a significant fraction of the speed of light.

Just as the helio-centrism of Copernicus replaced the geo-centrism of Ptolemy, and Magellan’s round-the-world voyage disproved the flat-earthers, and Einstein’s relativity was found to be more accurate than Newtonian mechanics, we are evidently witnessing a similar paradigm shift in the world of mathematical modeling of real-world phenomena such as market behavior: learning that Gaussian distributions need to be replaced with some other, more fat-tailed model(s), such as the ones proposed by Mandelbrot and Taleb.

I would love to find out more on the mathematics (if any) that really *does* apply to modeling market behaviors. There are actually some ultra-high-performance columnar (vector-based) database computer languages out there now which may be quite capable of handling the additional computational complexity surprisingly efficiently, if we’d roll up our sleeves and do the necessary work.

The old saying, “Garbage In, Garbage Out,” still applies. We shouldn’t just throw up our hands and use the wrong models simply because they’re “easier”!

ScottARereading Yves’ post, I see mention was made of “Levy distributions” in Econned.

This sounds interesting and I will be reading up on it.

ScottAThis excerpt from Wikipedia about “Levy distributions” shows some interesting applications:

Applications

The Lévy distribution is of interest to the financial modeling community due to its empirical similarity to the returns of securities.

It is claimed that fruit flies follow a form of the distribution to find food (Lévy flight).[1]

The frequency of geomagnetic reversals appears to follow a Lévy distribution

The time of hitting a single point (different from the starting point 0) by the Brownian motion has the Lévy distribution.

The length of the path followed by a photon in a turbid medium follows the Lévy distribution. [2]

The Lévy distribution has been used post 1987 crash by the Options Clearing Corporation for setting margin requirements because its parameters are more robust to extreme events than those of a normal distribution, and thus extreme events do not suddenly increase margin requirements which may worsen a crisis.[3]

The statistics of solar flares are described by a non-Gaussian distribution. The solar flare statistics were shown to be describable by a Lévy distribution and it was assumed that intermittent solar flares perturb the intrinsic fluctuations in Earth’s average temperature. The end result of this perturbation is that the statistics of the temperature anomalies inherit the statistical structure that was evident in the intermittency of the solar flare data. [4]

http://en.wikipedia.org/wiki/L%C3%A9vy_distribution

Thank you so much for pointing this out Yves in your book ECONNED.

Between your reporting on Magnetar’s heavy involvement in CDOs and now your discussion of Levy distributions, I’m starting to see that ECONNED isn’t merely yet another chronicle of the great recession. Magnetar was a really important story you broke, and Levy distributions may turn out to be very important as well in order to bring some sanity to our models.

Raging DebateMandelbrot’s work on fractals and including real-time data alongside historical variables leads to a paradigm shift of management, from pyramid shape to circular.

Each fractal doesn’t just represent a physical variable of data, each also represents a train of thought. The final formation of combined fractals is circular shaped. What it means simply is that information (which is power)flows throughout the circular construct versus the current top-down pyramid version where information does not. That is what Zuckerman’s Facebook is so excited about with their new insignia and what it means. Zuckerman will have to be careful as when you plant wheat, the weeds grow up alongside it.

The pyramid paradigm is why there is a constant debate about the roles of the elites vs. the masses.

Mandelbrot or other thinkers like him require a Quantum computer to complete the circular paradigm to create the tech tools or what I call and Actionable Plan Engine.

As for fractals representing particular trains of thought, I will leave the group with one of my own called the Pyramid of Thought and how to apply it toward wealth generation if you so choose and a couple of footnotes:

“I think of thought as a pyramid. At the top of the thought pyramid is Concepts such as Truth, Freedom, Equality, Peace, Justice, Love. Below the Concepts are Issues such as Freedom of Speech, Foreign and Economic Policy. At the bottom of the pyramid are Details. Many, many details about the Issues.

Now try something. Draw this out. To the right of Concepts on your pyramid (outside of it), put ‘Adults’. Next to the Issues put ‘Adolescents’. Next to Detail put ‘Infants’. The Adults will understand all three levels of the pyramid, the Adolescents will understand Issues and Details, but rarely Concepts. Infants understand Details and some Issues never Concepts.

An individual’s title is not important. What is important is what you can get done with another individual. Practice identifying whether an individual is an Adult, Adolescent or Infant. You’ll become expert at it and your mind will adopt the practice on it’s own.

Religions that focus on do’s and dont’s fall into the Issues and Details camp.

All religions on earth have Concepts baked into their teachings which erode into time to just Issues and Details. A culture is a reflection of there religion or simply substitute Value System.

Restoration of a culture can occur with restoring Conceptual level thinking at it’s foundation.

There is a startling similarity of mathematical ability tied into cultures that built pyramids, statistical forecasting (prophecy) and a belief in an after-world, beings of light, be it angelic or some other mythical substitutions for light and darkness, alpha or omega, good or evil.

Civilizations and all organization devolve over time, focusing on Issues and Details, creating broad divisions within a culture making them prone to invasion or collapse/revolutions. Mankind is a record player with a chunk missing, creating cyclical behavior leading to it’s own demise. The reason for this is the Pyramid of management or how our thoughts are organized surrounding this paradigm.

The loss of Conceptual level thinking creates the loss of wisdom. Wisdom is the ability for the mind to simultaneously crunch large volumes of bits of intelligence. Without this ability, a culture becomes more animalistic and can no longer see the forest through the trees of endless Issues and Details.

bob goodwinperhaps we are saying the same thing.

“computationally daunting to uncomputatble” is only different from “impossible” in theory, not practice. If there is wide spread usage of Mandelbrot (which I have read and written software models for, but I lack the skills to put it to any practical use) in the financial world for modeling trades I would be surprised. But you would clearly know better than I do.

I know that in my humble world, I must use gaussian evidence coupled with common sense discussion of unknowable risk. My use of statistics has rarely involved trades.

Clearly gaussian denial has been a huge problem for traders and economies. But so has underwriting denial, and bubble denial. I just wanted to defend the hammer as a valuable but imperfect tool.

rickOne of the reasons, I think, for the predominant use of the Gaussian in many fields (not just finance) is the Central Limit Theorem that says – roughly – that if, starting from an unknown distribution, you apply a repeated averaging process then the resulting sequence of “new” distributions will, under some simple assumptions, converge to the Gaussian.

To put it another way: in the limit all is Gaussian so you get a kind of second order justifcation for using it.

The trouble with this, and the statistical elephant that was brushed under the carpet in search of fake profit, is that (many ? most?) fat-tailed distributions don’t satify the key assumption of the CLT which is that the original distribution has finite variance.

Since the CLT is a standard part of any mathematical curriculum the quant world (indeed the whole mathematical economic world) knew damned well that the key assumption on which their Ziggurat of equations was based was flawed right from the beginning. Mandelbrot’s results are just empirical evidence of an area where CLT breaks down.

Exclusive use of the Gaussian was not, IMV, merely because it was convenient and analytically/computationally tractable. It was a deliberate, culpable, deception on the part of the quant community to conceal the existence of the “mad distributions in the attic”

OldSkepticI did a paper back in 2004 on this very fact. Showing that VAR calculations using gaussian distributions dramatically understated risk, sometime by several orders of magnitude (powers of 10).

Result: Nothing, not a single person contacted me afterwords (even though I worked out and demostrated a crude, but workable solution). Over a few beers some of the younger analysts confided that they agreed with me, but as everyone used the standard equations they had to.

How this unmitgated rubbish became so dominante escapes me. Number 1 rule, if you have assumption dependent equations, test the data to see if they actually follow the assumptions?

Take for example Scholes-Black. Lovely set of equations … took me just an hour to disprove a fundemental assumption they use (normality) … using just a spreadsheet with some real data, the other key assumption (independence) would have only taken another hour or so if I could have been bothered (if 1 key assumption is blown, then the equation is rubbish, you don’t need to go any further).

Must have been the (psuedo) Nobel prize that baffled everyone.

DownSouthOldSkeptic said: “How this unmitgated rubbish became so dominante escapes me.”

I’ve often wondered that myself.

Some of it I believe is cultural. Somehow Americans have managed to convince themselves that they can create and live in a risk-free world. The Mexican poet Octavio Paz in

El Libertino de la Soledadspoke of this phenomenon with regards to death and old age.Americans deal with death and old age (which of course are not risks, but certainties) by denying them. Old people are shuffled off into assisted care and nursing homes where they are out of sight and out of mind. And whereas Mexican culture celebrates the dead, such as in the popular

Dia de los Muertos(Day of the Dead) celebrations, in the United States the dead are quickly buried and forgotten, the quicker the better.But much of it was because downplaying risk served the interests of powerful economic players. Take social security for instance. Social Security is all about providing economic security in the event of one of those fat tail events. So in order to eliminate social security, and hand all those trillions of dollars in retirement funds over to Wall Street, it was necessary to convince people that those fat tail risks didn’t exist—-“you’re retirement security is perfectly safe in stocks and bonds.”

While I’m sure there was plenty of self-delusion going on in academia and Wall Street, much of it was more malicious in that it was a deliberate attempt to generate pseudoscience to justify greed and self-interest. It was the polar opposite of searching for veridical truth, much less serving the general good.

NOTaREALmericanInteresting comment. So much is “decided” before we think.

Re: much of it was more malicious in that it was a deliberate attempt to generate pseudoscience

There’s also the simple effect of “religion”. When something is repeated enough it’s very difficult for most people to question “known facts”. It even happens in areas like corporate IT (which you’d think wouldn’t have much in the way of “beliefs”). In this case there’s nothing malicious (exactly, not counting the consulting companies) but the end-result is the same: stupid ideas continue forever.

marc fleurywell, normal distribution were just widespread in use because they were expedient analytically and there was research to support them.

Clearly normal distributions are a platonic ideal.

Conscience of a ConservativeI draw a distinction between dispersion in the opinion of policy makers and the presence of fat tailed risk in the market place. Previously the market expectations discounted the tail risk, now everyone is more aware of it. The problem with our policy makers is too much “group think” and one reason why just about everyone is convinced we are set for deflation. I would welcome a little more debate.

OldskepticYves, there are other approaches than difficult to use ‘exotic’ distributions. You can ‘brute force’ it, provided you have sufficient data.

Basically a Markov chain type calc with sufficient real data to sample from that will encapsulate all real probabilities.

For my example (very, very crude) I used Australian stockmarket daily results back to 1970. With a bit of analysis you can work out how much history you actually need and the granularity.

Then its reasonably simple conceptionally, though computationally difficult. Though with sufficient research you can reduce the computational overhead with clever (and non gaussian) sampling techniques. I worked out some possibilities with a friend (who’s a much better mathematician than I am) and we could have reduced my (8 hour runs) to half an hour or so … on a 2004 PC.

If you don’t have a sufficient history, then the ‘exotic’ distributions come into play, though from a computational point of view I’d still probably go with the sampling approach, based on generated data from a potential distribution equation (you can of course compare different ones with this approach to determine tail sensitivities and even create ‘blended’ sample spaces).

But of course this requires research, ability and judgement.

The ‘standard’ equations offered a wonderful illusion .. the perfect solution out of the box. Just crank the handle and get a result … whee and we all get rich.

The real world is much, much, much messier.

Anyone wnts to get flavour for non-liner modelling, goto Godard Space Institute and download some of their climate models. Orders of magnitude more complex (and clever) then any financial model in existance … plus they actually test them against known past history (wow gosh, radical).

If anyone had done that with Scholes Black they might just have got a booby prize instead of a psuedo Nobel .. and we would have all been much better off.

ScottAOldSkeptic – In my off-and-on tinkering with math and computers over the years (specifically areas including complexity, ultra-high-performance columnar databases), I’ve come across some concepts and tools which may be useful for these “computationally difficult” situations you describe.

I would be interested to discuss with you, possibly via email, some of the mathematical and processing issues you encountered in those areas. I think it would be very worthwhile to have an efficient implementation for some of the more “non-standard” or “exotic” distributions.

It seems ridiculous to use a Gaussian or Black-Scholes models if they don’t fit reality. If the real models are more complex, bring the math on – there *are* a few quite expressive and surprisingly efficient vector-processing languages out there that can handle this sort of thing.

If you would like, please contact me at:

s t e f a n x (at) u s a (dot) c o m

OldSkepticI should add that in all my experience in many industries over many years … normal (ie gaussien) distributions are unusual.

Inventory control, optimal cpaital equip replacement, any form of insurance, anything that involves a queue, et all .. all non normal. In fact if I find a normal dist in data I immediately double check it because it is so unusual.

Outside a few real examples (most at quantum or molecular levels) and some human contructed and constrained situations (ie some gambling games), the ‘normal’ distribution doesn’t exist. Heavily skewed distributions (of both kinds, some we can fit a formula to (ie gamma), many not) are the real ‘normal’.

The real staistical experts in heavily skewed distributions are not in acedemic stats, or (obviously) economics or finance. Rather engineering or, especially recently, medical statistics .. basically those who deal with the real world.

Bates” medical statistics .. basically those who deal with the real world.”

…and, insurance companies actuarial tables. Death and taxes have always been a sure thing.

ScottAThank you for sharing these very important observations about how most distributions in the real-world are not Gaussian, OldSkeptic.

I would be curious to hear more about whether, in your experience, there have been any mathematical models which did seem to be useful.

As I mentioned in another reply to you elsewhere, I do like to dabble in computers and math, and there are some interesting ultra-high-performance vector-processing (columnar) database languages I’ve played with.

If, as you say, one of the obstacles to using more realistic models is simply their complexity (and consequent slowness of the computations), then it might be worthwhile to try implementing more realistic models in some of these more high-performance languages. Speed-ups of one or two orders of magnitude can be possible in many cases.

If we could show that a computation that formerly took 8 hours could now be done in, say, 8 minutes, then this might encourage adoption of the more realistic albeit more computationally complex models.

I can’t really summon the motivation to slog through implementing stuff like Black-Scholes now that people like Taleb have shown that it’s simply not applicable.

If there are better models out there which we’re not using much simply because they’re too “computationally complex”, then I say: Bring ’em on!

I’ve been playing with some blazingly fast columnar database languages capable of handling very complex equations and very large datasets, and I’d love to apply them to something that’s actually realistic and useful.

As I mentioned in another reply to you, feel free to contact me at

s t e f a n x (at) u s a (dot) c o m

if you have any slow models you want to see if I can help you speed up!

ScottAPerhaps on an even more realistic “real-world” note, given recent revelations by Nanex, it may turn out that the distributions with the best fit to model our markets may turn out to be neither Gaussian, nor Levy, nor Mandelbrot… in view of the fact that up to 70% of transactions are now due to High Frequency Trading, whose graphs display the following interesting but not even remotely bell-curved shapes:

http://www.nanex.net/20100506/FlashCrashAnalysis_Part4-1.html

Is there any point in using any models when “special liquidity providers” are able to flood the market in this fashion in pursuit of their own objectives?

Parvaneh FerhadThe problem which Mandelbrot pointed out, is that economic events as well as natural events might be better described by power laws and not by distributions that require random variables (random events).

If he is right, and I think he is, than the entire math being used in finance is wrong. The flaw my lie in the assumption that you are dealing with random events – that have no relation to the event(s) before and after it – when in reality events do very much rely on the events preceding it, i.e. the initial conditions.

The incovenient truth for the fiance sector is, however, as was correctly pointed out here, that power laws can be very difficult or even impossible to treat, and, even worse are not always useful in making predcitions, unless you know the exact initial conditions – something which in the real world is often impossible to know.

ScottATo Parvaneh Ferhad:

I agree. It seems ridiculous that quants would take as their basic assumption the notion that markets take a totally random walk.

Although markets seem to us to rise and fall arbitrarily or randomly, that obviously doesn’t give us any right to use something like a roll of fair dice to model markets.

Of course, it may have been convenient for quants to have some source of randomness to work with in order to run some tests, and it may have been convenient for them to use the simplest distributions available (Gaussian) – but how on Earth did they ever think that gave them the right to base the entire edifice of our planet’s economy (whose uppermost reaches – the derivatives – may now total nearly a quadrillion notional dollars) on their convenient little computational simplification?

“The entire math being used in finance is wrong.” Indeed. And now we’re seeing the disastrous results of their little oversimplification.

liberalI don’t see how the housing bubble was a tail event. After around 2004, it was a near certainty. Going further back, real estate bubbles occur pretty often

BatesI find it amazing and amusing how Pimco can point fingers at other asset classes and discuss the high risk of venturing into those ‘other’ markets without mentioning eqities HF Trading…or how the unknowns of future government intervention via fiscal policy/regulation or interest rate change via the Fed can destroy portfolios of institutions or individuals instantly. Pimco approaches the discussion of risk as if the only risk is a piece of ‘normal’ bad/good news affecting markets, and fails to mention that every government in the world is issuing treasury debt like flapjacks. We can see flapjacks, what we cannot see or know is if treasuries/central banks are secretly monetizing debt. But we can know that when China (and others) backed off buying Treasury issues GB started buying a LOT more of them…doubling their Treasury holdings in less than 6 months. How can GB accomplish that when they have annouced an austerity plan that calls for a 40% reduction of expenditures?

“Pimco is a bond shop, and fat tails implies more risk (or more accurately, higher odds of more extreme outcomes) which in turn makes more volatile asset classes like equities look less appealing relative to stodgy old fixed income instruments.”

Bonds are a safe haven? No doubt at times they are. But, ask those holding Greek bonds, Spanish bonds, PIIG debt, munis issued by various US state, county, and municipalities if they feel the debt they are holding is safe…and forget the lipstick applied by ratings agencies.

“With declining confidence in a reliable set of investing rules, markets have become more susceptible to overreactions to daily news and, are, therefore, more volatile. Just think of the number of triple-digit days in the Dow….”

The Dow is totally disconnected from ‘daily news’ and reality. HF Trading rules in US equities markets and now the markets are as likely to rise on bad news as on good news and vice-versa. Tell me the market has priced in the news…I will laugh. If you want to play in equities and make money expect to shell out ~$30million for state of the art equipment and a staff that knows how to use the stuff. For this investment in equipment and personnel expect ~$100,000+ profit per day. Of course the equipment will need frequent upgrade or replacement to stay a millisecond ahead of the competition. Work out the equipment ammortization for yourself. This is the ‘new economy’ of the US…it is a business model. Notice that it has absolutely nothing to do with the Main St economy…with but one exception…if the HFTrading blows up and threatens to destroy the world financial system the Main St economy will be called on (again) to pony up the bucks to bail the gamblers out…socialized losses!

“Finally, less credit will be available to sustain leverage and high valuations. Even apart from the inevitable response to regulatory actions aimed at derisking banks, a world of flatter and fatter distributions will reduce available supply of leverage to finance trades and balance sheet expansion.”

Let’s see…6 banks reported good earnings. The other ~960 reported break even or losses. ‘Less credit will be available to sustain leverage and high valuations’…unless you are one of the 6 that are the ‘chosen’…the TBTF with connections in high places.

“Investors had 25 years to get comfortable with the great moderation.”

Total baloney. Investors had 25 years to become accustomed to the biggest credit expansion the world has seen. Now many soverigns have a little problem…The amount of tax revenues required to service their accumulated borrowing/debt is becoming a huge drag on their GDPs. This is accompanied by bad demographics of aging populations that are drawing down savings, retirement funds, and retirees are spending less (except on med care). In addition globalized wage arbitrage will insure that the US will not have the tax revenues going forward to sustain the credit expansion in the US. There is no way the US pays off accumulated public debt without monetization or default. If interest rates on treasury issues rise significantly it’s lights out. Ben and pals can jawbone all they want about raising rates…talk is cheap on the street.

Pimco’s discussion of risk is merely a distraction from much bigger problems that most soverigns and individuals face…and, of course they are talking their book. This one might fly on a bobble head tv outlet on a day when the Dow is up 200+ into the close.

RichFamFat tails, black swans… Is there a chance that once we expect them the white swans become more unexpected? Or not. But if there’s one place where the chance a fat tail is building its where PIMCO operates – rates. But expect lower rates first because its not a bubble until everyone has been sucked in – think sub 2% 10yr notes. The size of the PIMCO total return fund might be a way to track the suck.

marc fleuryClearly pimco is talking its own product up. That in a world of uncertain returns (increased vol) many people will seek the predictability of bonds.

The one thing I would point out, as a real money investor, is that bonds pay very little right now. For monetary reasons, the price of money, which supports the bonds structure, is close to zero. So yeah, it is predictably crap.

In a world of volatility, sell lemons… when there is vol, I trade vol…

sunny“..frequent “risk on/risk off” fluctuations in investors’ sentiment are here to stay..”

we are already witnessing ‘maniac/depression’ behavior in the markets, almost every other day, may be accentuated HF trading!

It is like daily war between perception (spin) vs Reality (fundamentals). Without hedging one cannot participate as a trader or even for a investor fairly long time horizon.

Roger BigoddA bit of history: the Black-Scholes formula created the modern options market. There had been options for a long time, but the prices were set by intuition, which is to say guess. Humans are not good at integrating the area under a probability distribution curve. Because the market-makers recognized their incompetence, the spreads were huge which repelled customers. After B-S, the trading floors were quickly populated by a small army of traders with Hewlett-Packard calculators programmed for the formula. It was an enormous ego boost to academic economists. Even better, the derivation started with the diffusion equation from physics.

To be fair, it’s probably the only example of a multibillion dollar industry created by a single intellectual insight in a few years. The insights of the great physicists took decades for practical benefits.

But early on, the market makers noticed that the formula tended to underprice out-of-the money options. This is the phenomenon of the fat tail, but I’m not sure if they used the term. So they added a little fudge factor to the extreme options. I don’t think it made the difference between profit and loss. The guys in the its weren’t going broke by not using it. But on the high volume the market makers were dealing with it was worth the trouble to make the modification.

This was well known. I recall seeing it in a popular book on options at least 20 years ago.

The intellectual issue isn’t recognizing that the distributions are fat-tailed. It’s coming up with a better distribution. By definition, the events are rare, so it’s difficult to get enough data to decide between different distributions.

There’s a continuum of malperformance here. Some of the participants were ignorant of the fat tail problem. Some knew about it but threw up their hands under the pressure of getting out the daily VAR statement. And there were guys who knew the situation but figured that writing cheap insurance on a 100-year flood (that was really a 10-year flood) was something they get away with.

I don’t remember how much coverage this gets in Econned, but the bigger impact of the Gaussian assumption was on Modern Portfolio Theory. In the introductory version, the standard deviations are a key input. There are many variations in the real world, but it’s used in managing trillions in assets and contributes to the prestige of academic economics.

SkippyIn reality we are talking time travel forward, based on past events and so called probability.

Fun as a hobby or academic pursuit but sucks as a metric for planing our must be lived out lives.

Skippy…how much death and diminishment must this world suffer before we stop arguing over today’s valuations as compared to the pasts and what the future ones will be, and call it making bread.

Parvaneh FerhadThis reminds me of the Infinite Improbablity Drive:

http://www.urbandictionary.com/define.php?term=Infinite%20Improbability%20Drive

SkippyI have my towel, do you.

bob47 is the inflation adjusted 42.

SkippyOhhh…not the infected number 47….SCIFI addicts incoming…run!

OlsSkepticScotA,

Useful long tail distributions (not for investments though, mostly in insurance and physcial processes, etc) that I’ve used are:

Gamma, Weibul, Paretto (bit of a sod to use), occasionally log normal, various power series.

Software mostly APL, still the best for vector/matrix/ragged matrix manipulation.

Watch out for the ‘ugly’, as I call it, the Cauchy (shudder). Plus distributions of ratios are always problematic, as they depend on the numerator and denominator distributions, always better to deal with num/den sperarately, especially when forecasting.

When in doubt (actually probably even when not in doubt) test the distribution first before any manipulation. I’ve seen people come real croppers (such as in GLM usage) assuming distributions in the data that are not the case. In one case putting in the correct dist REVERSED the original results.

derpolaristWhat about liquidity of options? As Nicholas Dunbar has illustrated in his book “Inventing Money” the key problem, particulary with LTCM, actually was that once an event happend which was expected to be totally improbable and led to an immediate decline in demand and hence prize for some financial products, the stop-loss limits and similar mechanism initiated a vicious circle driving up supply and shrinking demand further and further. That finally led to illiquid products which had no real prize at all and caused massive loss.

OldSkepticRick made a great point about the CLT. Plus even with distributions that it applies to, you may need a lot of data to trend towards the gaussian. The more skewed it is the more data needed to meet the condition.

I’ve seen some people come a real cropper with GLM’s with a lot of variables (therefore cell sizes are small).

OS: “checked the underlying distribution?”, IA*: “oh but the CLT will save me”. OS:”how many data points in each cell”. IA:”oh”.

The annoying thing is that you can do a lot with empirical distributions and things like transformations. Plus there are some clever techniques to segment funny distributions, approximating each part with something more tractable, them combining the results.

Sheer lazyness IMHO. Imagine if medical statisticians had taken the approach of finance quants (med stats is full of extremly skewed distributions), we’d all be dying from incorrect results from badly analysed clinical trials.

True story: did some consulting work for a certain rating agency. To get around the heavily skewed dist they simply cut off the tail so they could use a GLM!!! Yet survival analysis could easily have been applied and would have worked fine as we later proved.

*IA = inexperienced analyst, or the entire quant finance industry.