Understanding all the talk about "tails"

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beardsworth
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Understanding all the talk about "tails"

Post by beardsworth »

Have searched the Bogleheads Wiki but came up with little. Have gone to Wikipedia, but the explanation there is so filled with jargon and equations––and not just limited to financial situations––that I immediately went into a haze. And then used the forum's general search feature, but that just brought up a lot of threads already using this terminology as if everyone who would ever read the thread already understood the language.

So . . .

From time to time there is talk on various forum threads about "tails." Fat tails, right tails, left tails, tail risk, etc.

Would appreciate explanation:

1. What do these mean, i.e., the definitions of the things themselves? (I was always lousy at statistics, so the closer the explanation to plain everyday English, the more likely I won't go into a haze. :roll: )

And

(2) Aside from mere definitions, what is this concept's significance––its usefulness––for thinking about an investment portfolio?

Just trying to understand the tales of the tails. :)

Thanks in advance to all who reply.

Marc
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Post by sscritic »

The long tail was used to describe music sales. A physical record store can only hold so many records. The owner therefore stocks only the hits, thinking that is where the profit is. Those records, while accounting for most of the sales, represent only a small fraction of all the records extant. An internet record store can list almost all the existing records, and while most of their sales will be of the most popular records, some will come from the much longer list of not-so-popular records. If you line up the records from most popular to least popular on a graph (with sales on the vertical axis), you will see a very long tail off to the right. Those are the records and sales that wouldn't exist in a physical store.

The original article from 2004:
http://www.wired.com/wired/archive/12.10/tail.html

wikipedia:
http://en.wikipedia.org/wiki/Long_Tail
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Post by Random Walker »

Fat tails refers to a deviation from the normal distribution of the classic bell curve. It means that real extreme events like financial crises occur much more frequently than one would predict with simple normal bell curve statistics.
The man who first described these fat tails in the stock market said that unusual events that statistics would predict occur something like once every 7000 years actually occur more like once every 3-4 years in the stock market. This is all because the stock market is very human, not unemotional math or molecules flying around in some sort of statistical equilibrium. Hope that helps a bit.

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The tale of the tails

Post by bobcat2 »

A left tail event is a very bad outcome. :cry: A right tail event is a very good outcome. :D Fat tails mean that really good and really bad outcomes occur more frequently than would be the case if the outcomes were from a normal distribution.

Typically an investment strategy that uses only diversification to manage risk contains both a left tail of possible very bad outcomes, but also a right tail of possible very good outcomes.

If you add hedging and insuring risk transfer techniques to your investment strategy to manage risk, either in addition or in lieu of diversification, you can more tightly control left tail risk (really bad outcomes), but at the cost of foregoing right tail outcomes (really good outcomes).

BobK
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Post by peter71 »

Hi Marc,

It's instructive to know that Nicholas Nassim Taleb, a big popularizer of these concepts, made most of his personal fortune with an options bet in October 1987 (when the market dropped over 20% in one day).

Drops like Black Monday constitute "extreme left tail" events, and the market is indeed non-normal on a daily basis. The concept thus matters a ton to highly-leveraged traders.

On even an annual basis, on the other hand, the tails of past market returns are quite normal. It's of course possible that stocks will drop 100% or gain 10000% this year, but no one's as yet seen annual stock returns much outside of what the normal curve would predict (and thus IMO the concept isn't that important for Bogleheads).

All best,
Pete
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Post by Bongleur »

And "barbell" asset allocation ???
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Post by peter71 »

Bongleur wrote:And "barbell" asset allocation ???
Though Taleb promotes both you don't need to believe in fat tails to have a barbell asset allocation, which typically means that, much as 80% of a barbell's length is the unnoticed bar, 80% or so of your AA is very safe stuff. Typically the other 20% is very risky stuff, as Taleb and others have correctly observed that once you're into stocks the differences in risk between "blue chips" and more speculative stocks are probably exaggerated.

All best,
Pete
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Re: The tale of the tails

Post by rustymutt »

bobcat2 wrote:A left tail event is a very bad outcome. :cry: A right tail event is a very good outcome. :D Fat tails mean that really good and really bad outcomes occur more frequently than would be the case if the outcomes were from a normal distribution.

Typically an investment strategy that uses only diversification to manage risk contains both a left tail of possible very bad outcomes, but also a right tail of possible very good outcomes.

If you add hedging and insuring risk transfer techniques to your investment strategy to manage risk, either in addition or in lieu of diversification, you can more tightly control left tail risk (really bad outcomes), but at the cost of foregoing right tail outcomes (really good outcomes).

BobK
Do most financial advisers use hedging for their clients? Your explanation of tails made me think that perhaps they do. To this I might add this would explain why they want us all to buy and hold. For in doing so we shore up their hedges. What's your opinion on this?
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Post by bobcat2 »

rustymutt asks.
Do most financial advisers use hedging for their clients?
No.
If they did they would be advising their clients to hedge longevity and inflation risk in retirement by planning to annuitize at retirement and during retirement with inflation-indexed life annuities. Likewise the advice for paying for a child's college education would be to invest in pre-paid tuition plans to hedge college costs instead of relying on diversification thru investing in 529 plans.

If many of financial advisers are predominately advising these courses of action, it's certainly news to me. For one thing these courses of action beg the question, "Why do I need a financial adviser?" :wink:

BobK
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Post by bobcat2 »

Bongleur wrote:And "barbell" asset allocation ???
Investors that rely only on diversification to manage risk sometimes try to control left tail risk with uncommon diversification strategies such as so-called barbell strategies. They are attempting to control left tail risk but keep right tail opportunity. But no matter what diversification strategy is employed, it will not be able to control left tail risk as well as hedging and insuring against the risk. Sadly, the laws of economics cannot be repealed, and there is no free lunch that can tightly control left tail risk without foregoing right tail opportunity. :cry:

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Post by nisiprius »

Introductory statistics courses (which is about my level of understanding) convey a very useful corpus of practical knowledge, much of which was developed in the early half of the 1900s and deals with things that follow the "normal distribution," also known as the Gaussian distribution or "the" bell-shaped curve.

The reason why it is so useful and powerful is that quite a lot of real things in the real world follow the normal distribution. A mathematical theorem, the "Central Limit Theorem," shows that under the right assumptions, if something you are measuring is the sum of a bunch of independent random variables, then regardless of what the distribution of each random variable is, their sum tends to follow the normal distribution.

So, for example, if you are shooting an arrow at a target, and there are many different factors that contribute to an error in aim--your hand shaking, the wind, the arrow not being perfectly straight, etc.--and those errors are pretty much additive (the wind just adds its effect to your shaking hand)--then you know that the arrow's error will be close to the normal distribution.

There are slews of statistical tests based on the assumption of normality, and they are used in quality control, in engineering, in medical trials, and so forth and they work.

Unfortunately, there are also many areas in which the assumption of normality is grossly wrong, sometimes because you aren't really dealing with a sum of many random variables, but most often because they aren't really independent.

"Fat tails" refers to a bell-shaped curve which looks "normal," but those tails--the parts that look like they're close to zero--are much farther from zero than they should be if they were normal. Calculations based on the assumption of normality say that the thickness of those tails is one gazillionth and the chances of ever seeing something ten "sigmas" from the mean are one in a gazillion. Yet in reality those tails, instead of being a gazillionth thick, are really the thickness of a hair, and the chances of that "ten-sigma" event, instead happening once in a trillion years, are more like once a decade.

The classic example is the collapse of Long-Term Capital Management, which occurred as a result of what one of its founders foolishly called a "ten-sigma event," the implication being that was an event calculated to be so impossibly rare that nobody could have foreseen it and the managers of LTCM should be blamed for it.
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Post by Joe S. »

Understanding skewness, kurtosis, and fat tails is hard without some pictures. Here are some pictures and discusstion which may help explain visually what these things mean:


http://investor.financialcounsel.com/Ar ... rtosis.pdf
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Post by baw703916 »

One other point has to do with the "random walk" hypothesis (the title of Malkiel's book, A Random Walk Down Wall Street). I have the book, and it has a lot of good stuff in it, but I really wish it had a different title.

A random walk, in statistics, refers to some repeated process in which each result is statistically independent of the previous one. Flipping a coin 100 times in a row is a good example--the coin is going to land on whichever side based on the position, velocity, and spin when it left your hand, not on how it landed on the previous flip. This assumption isn't as good in investing. For one thing, many people's decision to buy or sell does depend on what the market did the previous day--there's a lot of people staring at charts out there!

A random walk, except for a few special cases, always leads mathematically, to a normal distribution. So the fact that financial markets don't follow a normal distribution proves that they do not follow the assumptions of a random walk.

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Post by LadyGeek »

For clarification, Normal is synonymous with Gaussian distribution.

Is a normal distribution used due to the central limit theorem? (Conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed (Rice 1995).)

I see Student-T distributions used in economics, not so much in engineering.
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Post by baw703916 »

LadyGeek wrote: Is a normal distribution used due to the central limit theorem?
As one of my professors pointed out when I was in grad school, "Gaussian Integrals can always be solved."

I suspect that modeling using normal distributions has more to do with mathematical convenience than realism. :wink:

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Post by peter71 »

The central limit theorem is frequently invoked, but realism also depends on what your research question is:

QUESTION 1: What are the chances that highly-levered LTCM-type strategies blow up?

ANSWER: higher than the normal curve would lead you to think.

QUESTION 2: What are the chances than I'll have a more than 3 sigma loss in an entire calendar year of holding the entire S&P?

ANSWER: about what the normal curve would lead you to think.

(Worst calendar year loss in 140 years = 44.2% in 1931, which is within three sigma of the mean return of 10.6 given sigma = 18.9.)

http://www.moneychimp.com/articles/rand ... orizon.htm

All best,
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Post by VictoriaF »

peter71 wrote:Hi Marc,

It's instructive to know that Nicholas Nassim Taleb, a big popularizer of these concepts, made most of his personal fortune with an options bet in October 1987 (when the market dropped over 20% in one day).

Drops like Black Monday constitute "extreme left tail" events, and the market is indeed non-normal on a daily basis. The concept thus matters a ton to highly-leveraged traders.

On even an annual basis, on the other hand, the tails of past market returns are quite normal. It's of course possible that stocks will drop 100% or gain 10000% this year, but no one's as yet seen annual stock returns much outside of what the normal curve would predict (and thus IMO the concept isn't that important for Bogleheads).

All best,
Pete
Nassim Nicholas Taleb distinguishes White Swans, Gray Swans, and Black Swans.
- White Swans are manifestations of the normal randomness.
- Gray Swans are subject to power laws and are characterized by fat tails.
- Black Swans are the things that happen completely unpredictably, out of the blue. (Blue turning into Black? ;-) )

The distinction is always in the tails. Envision a bell, a physical bell, say, the Liberty Bell.

Image

You will notice that most of the "stuff" is in the middle, and it sharply comes to the end at the ends ("tails"). That's the White Swan model.

Now imagine the Liberty Bell stretched across the United States, with the tails getting more and more narrow but never coming down to zero. That's the Gray Swan model.

By the way, Taleb says that even if Gray Swans can be modeled they are still tricky. He feeds some power function into a random number generator using some value "a" of the exponent (power). The generator then generates a lot of data. When Taleb analyzes the data that came out of the generator and tries to estimate the value of "a" based on the data alone, it is always off. The estimated value of "a" underestimates the amount of randomness. In other words, when the experimenter does not know the generating function he tends to underestimate the tails.

Black Swans are an entirely different animal. They just jump out at you. For example -- it's a visual example, not a rule for spotting Black Swans -- you may have a thin or a fat tail, and then all of a sudden you may see a spike in the tail. Out of the blue...

Victoria
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Post by peter71 »

Hi Victoria,

I probably have the lowest stock allocation of anyone participating in this discussion (currently 6.5%) and in large part because I genuinely fear genuine "black swans" (which I believe I'm shielded from via the lags in the TIAA Real Estate Account).

But sigma in past data is one thing, observed skewness and kurtosis in past data are another thing, and never yet observed surprises bearing no resemblance to past data are another.

My sense is that this forum often underrates the importance of sigma and black swans and overrates the importance of left tail risk properly defined.

Put another way, while it would have been really smart for LTCM to plan for a ten-sigma left tail event even based on what we know about history (which I know Taleb hates, and I somewhat agree with him but that's a different issue) history tells us that a 6 or more sigma annual loss in the S&P is literally impossible because 10.6 - 18.9(6) = a 102.8% loss.

Or, at least, that's what left tail risk means to me . . . if others are literally rather than figuratively incorporating the possibility of a 10-sigma annual loss on the S&P into their planning I'm interested in hearing how they go about that . . .

All best,
Pete
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Post by VictoriaF »

Hi Pete,

I am not disagreeing with you. True, we cannot have a 102% drop in S&P 500. But I would like to provide another Taleb's argument, i.e., that the rate of unpredictable events ("Black Swans") is accelerating. Black Swans do not live in the physical nature.(*) The Black Swan habitat is the information domain.

And in the information domain we have the magnifying effects of the information spread, automated trades, and social networking to name a few. How many sigmas did we have during the "flash crash" in May 2010?

Again, with a single-digit allocation you should not worry about equities at all. (You may have to worry about other things that are outside this discussion.) My equity allocation is much greater, and I am a Taleb disciple. :)

Have a great Sunday,

Victoria


(*) Black Swans capitalized are events that comply with Taleb's definition of Black Swans. These are not small-case black swans that live in Australia.
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Post by Random Walker »

Just finished reading "When Genius Failed". I posted a quote from the epilogue on my thread regarding the book. I think the difference between risk and uncertainty goes a long way towards defining fat tails.

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Post by baw703916 »

peter71 wrote:Hi Victoria,

I probably have the lowest stock allocation of anyone participating in this discussion (currently 6.5%) and in large part because I genuinely fear genuine "black swans" (which I believe I'm shielded from via the lags in the TIAA Real Estate Account).

But sigma in past data is one thing, observed skewness and kurtosis in past data are another thing, and never yet observed surprises bearing no resemblance to past data are another.

My sense is that this forum often underrates the importance of sigma and black swans and overrates the importance of left tail risk properly defined.

Put another way, while it would have been really smart for LTCM to plan for a ten-sigma left tail event even based on what we know about history (which I know Taleb hates, and I somewhat agree with him but that's a different issue) history tells us that a 6 or more sigma annual loss in the S&P is literally impossible because 10.6 - 18.9(6) = a 102.8% loss.

Or, at least, that's what left tail risk means to me . . . if others are literally rather than figuratively incorporating the possibility of a 10-sigma annual loss on the S&P into their planning I'm interested in hearing how they go about that . . .

All best,
Pete
For large movements, it usually works better to plot the x-axis on a logarithmic scale. So, a 99% drop would be twice as bad as a 90% drop. But then a drop to zero value is infinite on a logarithmic scale.

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Post by baw703916 »

VictoriaF wrote:
peter71 wrote:Hi Marc,

It's instructive to know that Nicholas Nassim Taleb, a big popularizer of these concepts, made most of his personal fortune with an options bet in October 1987 (when the market dropped over 20% in one day).

Drops like Black Monday constitute "extreme left tail" events, and the market is indeed non-normal on a daily basis. The concept thus matters a ton to highly-leveraged traders.

On even an annual basis, on the other hand, the tails of past market returns are quite normal. It's of course possible that stocks will drop 100% or gain 10000% this year, but no one's as yet seen annual stock returns much outside of what the normal curve would predict (and thus IMO the concept isn't that important for Bogleheads).

All best,
Pete
Nassim Nicholas Taleb distinguishes White Swans, Gray Swans, and Black Swans.
- White Swans are manifestations of the normal randomness.
- Gray Swans are subject to power laws and are characterized by fat tails.
- Black Swans are the things that happen completely unpredictably, out of the blue. (Blue turning into Black? ;-) )

The distinction is always in the tails. Envision a bell, a physical bell, say, the Liberty Bell.

Image

You will notice that most of the "stuff" is in the middle, and it sharply comes to the end at the ends ("tails"). That's the White Swan model.

Now imagine the Liberty Bell stretched across the United States, with the tails getting more and more narrow but never coming down to zero. That's the Gray Swan model.

By the way, Taleb says that even if Gray Swans can be modeled they are still tricky. He feeds some power function into a random number generator using some value "a" of the exponent (power). The generator then generates a lot of data. When Taleb analyzes the data that came out of the generator and tries to estimate the value of "a" based on the data alone, it is always off. The estimated value of "a" underestimates the amount of randomness. In other words, when the experimenter does not know the generating function he tends to underestimate the tails.

Black Swans are an entirely different animal. They just jump out at you. For example -- it's a visual example, not a rule for spotting Black Swans -- you may have a thin or a fat tail, and then all of a sudden you may see a spike in the tail. Out of the blue...

Victoria
Hi Victoria,

In keeping with your visual representation, the Liberty Bell cracking would be a "black swan" event. :wink:

Brad
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Post by VictoriaF »

baw703916 wrote:Hi Victoria,

In keeping with your visual representation, the Liberty Bell cracking would be a "black swan" event. :wink:

Brad
Hi Brad,

You are right! :idea:

The crack is a gap in the distribution in the midst of the highly-expected region. In Taleb's words, "expected things not happening are Black Swans, too."

Victoria
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Post by grabiner »

peter71 wrote:Put another way, while it would have been really smart for LTCM to plan for a ten-sigma left tail event even based on what we know about history (which I know Taleb hates, and I somewhat agree with him but that's a different issue) history tells us that a 6 or more sigma annual loss in the S&P is literally impossible because 10.6 - 18.9(6) = a 102.8% loss.
The proper distribution for a normal model would be a log-normal distribution. If you aren't familiar with logarithms, think of sigma as multiplied by the return rather than added to it. Thus, if an average one-year return is 100 becoming 110, and one sigma above is 132, which is 6/5 as much, then one sigma below is 91.67, which is 5/6 as much. Two sigma below is 5/6 as much as one sigma below, which is 76.39, a 24% loss. Three sigma below is 5/6 as much as two sigma below, which is 63.65, a 36% loss (about the loss in real-dollar terms in both 1931 in 2008).

The reason for the log-normal distribution is that changes are relative to other changes. The probability that the market drops by 20% in the second half of the year is relatively independent of what happened in the first half of the year, but it is a larger point loss if the first half of the year was a bull market.
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Post by peter71 »

Hi David,

We can certainly pick other distributions that will reduce sigma and thereby increase the probability of an n-sigma event, but I don't think we can simultaneously critique Gaussian dummies for using the normal curve and talk about what sigma would be if they didn't use it.

As per my earlier post, I'm simply taking this site's historical estimate of the standard deviation of returns as 18.9% per annum.

http://www.moneychimp.com/articles/rand ... orizon.htm

I've certainly seen people argue that a lognormal distribution is the "true" distribution, and, for that matter, that the distribution should be seen as "undefined," but my point is simply that plain old vanilla standard deviation in association with the normal curve already makes annual losses of close to 50% look perfectly "normal" in the ordinary language sense . . . put another way, my view is that the second moment tells us most of what we need to know about annual S&P returns . . .bringing in the 3rd and 4th moments doesn't really add much.

All best,
Pete
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Post by hsv_climber »

VictoriaF wrote: I am not disagreeing with you. True, we cannot have a 102% drop in S&P 500. But I would like to provide another Taleb's argument, i.e., that the rate of unpredictable events ("Black Swans") is accelerating. Black Swans do not live in the physical nature.(*) The Black Swan habitat is the information domain.

And in the information domain we have the magnifying effects of the information spread, automated trades, and social networking to name a few. How many sigmas did we have during the "flash crash" in May 2010?
And what if Taleb is wrong?
Where is the proof that Black Swans are accelerating? Flash Crash of 2010? Ok, how about 1987 one day 23% drop then? Where is the acceleration?

What you show as input (i.e. information, social networks, etc.) does not necessarily lead to the conclusion of the output (Black Swans).
In fact, it could be quite the opposite. Availability of more information can lead to the reduction of the Black Swans, since it might limit the space for them to hide.
And if you are really convinced that unpredictable events are accelerating, please create a table that will demonstrate that number of such events have significantly increased over the last 5-10-20 years in comparison to the previous century or two.

Otherwise, you might sound like a religious fanatic, who claims that God exists only because he/she believes in the existence of God.
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Post by gatorking »

peter71 wrote: a 6 or more sigma annual loss in the S&P is literally impossible because 10.6 - 18.9(6) = a 102.8% loss.
Annual sigma numbers are completely meaningless because they ignore the geometric nature of returns.
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Post by peter71 »

gatorking wrote:
peter71 wrote: a 6 or more sigma annual loss in the S&P is literally impossible because 10.6 - 18.9(6) = a 102.8% loss.
Annual sigma numbers are completely meaningless because they ignore the geometric nature of returns.
They're actually quite meaningful, but let's just take it as a given that you're right. Will the Gaussian dummy who prepares for two consecutive 3 sigma annual losses underestimate or overestimate the possibility of severe losses?
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Post by VictoriaF »

hsv_climber wrote:
VictoriaF wrote: I am not disagreeing with you. True, we cannot have a 102% drop in S&P 500. But I would like to provide another Taleb's argument, i.e., that the rate of unpredictable events ("Black Swans") is accelerating. Black Swans do not live in the physical nature.(*) The Black Swan habitat is the information domain.

And in the information domain we have the magnifying effects of the information spread, automated trades, and social networking to name a few. How many sigmas did we have during the "flash crash" in May 2010?
And what if Taleb is wrong?
Where is the proof that Black Swans are accelerating? Flash Crash of 2010? Ok, how about 1987 one day 23% drop then? Where is the acceleration?

What you show as input (i.e. information, social networks, etc.) does not necessarily lead to the conclusion of the output (Black Swans).
In fact, it could be quite the opposite. Availability of more information can lead to the reduction of the Black Swans, since it might limit the space for them to hide.
And if you are really convinced that unpredictable events are accelerating, please create a table that will demonstrate that number of such events have significantly increased over the last 5-10-20 years in comparison to the previous century or two.

Otherwise, you might sound like a religious fanatic, who claims that God exists only because he/she believes in the existence of God.
This is an unreasonable request for the reasons as follows:
1. I quoted Taleb; you are requesting a proof from me.
2. You request a proof in a specific form you have defined.
3. If I don't comply with the request as stated, I risk qualifying as a religious fanatic.

I find this insulting and refuse to respond.

Victoria
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Post by hsv_climber »

peter71 wrote: Will the Gaussian dummy who prepares for two consecutive 3 sigma annual losses underestimate or overestimate the possibility of severe losses?
He makes the correct assumption that government will bail him out in case of truly severe losses.
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Post by hsv_climber »

VictoriaF wrote: This is an unreasonable request for the reasons as follows:
1. I quoted Taleb; you are requesting a proof from me.
2. You request a proof in a specific form you have defined.
3. If I don't comply with the request as stated, I risk qualifying as a religious fanatic.

I find this insulting and refuse to respond.

Victoria
Sorry if my post sounded rude. I did not mean it. Please feel free to provide the proof in any form.

You are not quoting Taleb. You are interpreting and maybe worshipping him. You know pretty well what quoting is. Taleb's book was published before 2010 flash crash :wink:. How can you quote Taleb's "Black Swan" when you are talking about a 2010 event?
But once you start interpreting, you have to start providing your own proofs.
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Post by VictoriaF »

hsv_climber wrote:
VictoriaF wrote: This is an unreasonable request for the reasons as follows:
1. I quoted Taleb; you are requesting a proof from me.
2. You request a proof in a specific form you have defined.
3. If I don't comply with the request as stated, I risk qualifying as a religious fanatic.

I find this insulting and refuse to respond.

Victoria
Sorry if my post sounded rude. I did not mean it. Please feel free to provide the proof in any form.

You are not quoting Taleb. You are interpreting and maybe worshipping him. You know pretty well what quoting is. Taleb's book was published before 2010 flash crash :wink:. How can you quote Taleb's "Black Swan" when you are talking about a 2010 event?
But once you start interpreting, you have to start providing your own proofs.
Here are relevant quotes (the italics are mine):
Nassim Nicholas Taleb on p.xviii [i]The Black Swan[/i] wrote:A small number of Black Swans explain almost everything in our world, from the success of ideas and religions, to the dynamics of historical events, to elements of our own personal lives. Ever since we left the Pleistocene, some ten millennia ago, the effect of these Black Swans has been increasing. It started accelerating during the industrial revolution, as the world started getting more complicated, while ordinary events, the ones we study and discuss and try to predict from reading the newspapers, have become increasingly inconsequential.
Nassim Nicholas Taleb on p.33 [i]The Black Swan[/i] wrote:So while weight, height, and calorie consumption are from Mediocristan, wealth is not. Almost all social matters are from Extremistan. Another way to say it is that social quantities are informational, not physical: you cannot touch them. Money in a bank account is something important, but certainly not physical. As such it can take any value without necessitating the expenditure of energy. It is just a number!
For me, this logically makes sense. The concept of Black Swans is philosophical in nature and cannot be measured as such. I am not aware of any specific definitions of Black Swans, e.g., financial domain-specific Black Swans. Perhaps, there are some statistics that show how often certain measures fall outside three standard deviations. But I don't know what these measures are and how legitimate they are, and I doubt there is a general agreement that these measures identify Black Swans.

I mentioned the Flash Crash as an example of where the calculus of standard deviations did not work. Whether it was a Black Swan is a matter of a philosophical interpretation. I provided this example, because:

1. I agree with Taleb that Black Swans are more likely to be found in information domains, because actions in these domains are more scalable, i.e., same effort produces orders of magnitude differences in impacts.

2. I agree with Taleb that Black Swans strive on complexity.

3. Flash Crash is a recent example of how the increasing complexity of trading coupled with the magnifying effects of information technologies have produced an outlier event.

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Post by Value_Investor »

How can Taleb make the statement that black swan events are accelerating? Does he have a total of all black swan events in 1900 and compared those to say, 2000?

Of course not. He's falling into a trap that he himself complains about. That is the nature of people trying to give too much credit to themselves versus the role of luck. In addition to that, he's also assuming perfect knowledge of the past (i.e. he knows of all the black swan events and can accurately show their relative rate of change).

The argument for increased complexity causing more black swans in as impossible to prove as the existance of god.

An anecdotal example. In 1910 if a person was stabbed to death in South Dakota, the occurance was not known to those in New York. Today, that same occurance is known to more people due to social media, traditional media, etc. That something is more widely known doesn't mean it's more prevalent. It simply means that it's more known. The actual occurance of stabbings in North Dakota could very well be lower today than in 1910.

If a tree falls in the woods and no one is there to hear it, does it make a sound?
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Post by Value_Investor »

BTW the 'flash crash' resulted in a 37 point drop in the S&P in one day. This is hardly a six sigma event. The rate of change during the day was high, but the opening and closing difference is hardly such an incredible event as to compare it to a 'black swan' in rarity.

As a point of reference, June 29th had a one day drop of 33 points in the S&P and no mention of any kind of 'flash crashiness' ever appears.

Flash Crash is a product of the media relative to it's statistical significance in 'real life'.
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Post by hsv_climber »

VictoriaF wrote: 1. I agree with Taleb that Black Swans are more likely to be found in information domains, because actions in these domains are more scalable, i.e., same effort produces orders of magnitude differences in impacts.
This is what I was arguing against in your previous posts. And Value_investor has 2 posts above about that as well.
It seems to me that information domains create an illusion of producing Black Swans rather than events themselves.
Speaking of scalability... Lets look at pirates in Somalia. Piracy is not a novel concept. It is probably second/third oldest profession. Yet Somali pirates are generating huge amount of wealth with minimal efforts.
Current "Age of Geeks" has just redefined who is getting the scalable effect. Hundreds of years ago, there were only kings / royals / top 50 / etc. who were getting the most wealth with minimal impact. The new kings are Warren Buffett, Steve Jobs, and Sergey Brin.
So, scalability was always there, but it just moved from one profession (royals, aristocrats) to another (lucky math/business geniuses).
Of course, with more wealth generated by the new technologies, there is more wealth to spread around.
VictoriaF wrote: 2. I agree with Taleb that Black Swans strive on complexity.
My dog might think that he has a complex life, because he can make a choice either to spend the whole day sleeping in his crate, or go sleep outside in the backyard, or sleep on a blanket in the living room, or wonder around the house and see what people are doing. This is much more complex than other dogs who should spend the whole day tied to a chain.
In other words, the word "complexity" has no meaning until it is properly defined.
VictoriaF wrote: 3. Flash Crash is a recent example of how the increasing complexity of trading coupled with the magnifying effects of information technologies have produced an outlier event.
The first recognized bubble with the subsequent crash was Holland's tulip bubble. End result of "Flash Crash" was minimal.
In fact, I would not be surprised if there were similar "Flash Crashes" back in 19th century, but people have forgot about them, because they just did not register on the stock market chart.
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Post by VictoriaF »

Value_Investor wrote:How can Taleb make the statement that black swan events are accelerating? Does he have a total of all black swan events in 1900 and compared those to say, 2000?
Nassim Nicholas Taleb has defined the concept of Black Swans (capitalized). Black Swans, as defined, are not countable. Valid arguments are not limited to historic quantities; proofs can be logical. Taleb uses philosophy and logic. He does not need to prove anything.
Value_Investor wrote:Of course not. He's falling into a trap that he himself complains about. That is the nature of people trying to give too much credit to themselves versus the role of luck. In addition to that, he's also assuming perfect knowledge of the past (i.e. he knows of all the black swan events and can accurately show their relative rate of change).
You created a strawman and use it to attack Taleb. Your strawman is logically false, and the Bogleheads Forum is not a place for personal attacks.
Value_Investor wrote:The argument for increased complexity causing more black swans in as impossible to prove as the existance of god.
This is another false strawman, and a violation of the Bogleheads Forum policy on the discussion of religion.
Value_Investor wrote:An anecdotal example. In 1910 if a person was stabbed to death in South Dakota, the occurance was not known to those in New York. Today, that same occurance is known to more people due to social media, traditional media, etc. That something is more widely known doesn't mean it's more prevalent. It simply means that it's more known. The actual occurance of stabbings in North Dakota could very well be lower today than in 1910.
Occurrences of people stubbed in South Dakota are not Black Swans, as defined by Taleb.
Value_Investor wrote:If a tree falls in the woods and no one is there to hear it, does it make a sound?
Occurrences of fallen trees are not Black Swans, as defined by Taleb.

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Post by VictoriaF »

hsv_climber wrote:
VictoriaF wrote: 1. I agree with Taleb that Black Swans are more likely to be found in information domains, because actions in these domains are more scalable, i.e., same effort produces orders of magnitude differences in impacts.
This is what I was arguing against in your previous posts. And Value_investor has 2 posts above about that as well.
It seems to me that information domains create an illusion of producing Black Swans rather than events themselves.
Speaking of scalability... Lets look at pirates in Somalia. Piracy is not a novel concept. It is probably second/third oldest profession. Yet Somali pirates are generating huge amount of wealth with minimal efforts.
Current "Age of Geeks" has just redefined who is getting the scalable effect. Hundreds of years ago, there were only kings / royals / top 50 / etc. who were getting the most wealth with minimal impact. The new kings are Warren Buffett, Steve Jobs, and Sergey Brin.
So, scalability was always there, but it just moved from one profession (royals, aristocrats) to another (lucky math/business geniuses).
Of course, with more wealth generated by the new technologies, there is more wealth to spread around.
If a king collects his fortune in physical gold, he can collect only as much as the amount of physical gold coins available. If Steve Jobs collects his fortune from the sales of I-Pads, his limit is the number of zeros he can type. That's the essence of scalability as used by Taleb.

In Taleb's examples, a baker can open several franchises and have people work for him in multiple places (similarly to the model of a medieval king and his surfs). But a baker's product is a physical bread, which is constrained by physical resources, freshness, and alike, and thus is much less scalable than, e.g., book sales.

hsv_climber wrote:
VictoriaF wrote: 2. I agree with Taleb that Black Swans strive on complexity.
My dog might think that he has a complex life, because he can make a choice either to spend the whole day sleeping in his crate, or go sleep outside in the backyard, or sleep on a blanket in the living room, or wonder around the house and see what people are doing. This is much more complex than other dogs who should spend the whole day tied to a chain.
In other words, the word "complexity" has no meaning until it is properly defined.
The more options your dog has, the more things can go wrong. Modern systems are more complex than your dog's lifestyle. When multiple components are independently designed and imperfectly integrated, unexpected failures are more likely to occur. When complexity moves from systems to systems-of-systems, the opportunity for failures compounds and the predictability of extreme failures decreases.

I am making a logical argument. I don't have any data and I am not planning to seek data. You are free to agree or disagree with this logic.

hsv_climber wrote:
VictoriaF wrote: 3. Flash Crash is a recent example of how the increasing complexity of trading coupled with the magnifying effects of information technologies have produced an outlier event.
The first recognized bubble with the subsequent crash was Holland's tulip bubble. End result of "Flash Crash" was minimal.
In fact, I would not be surprised if there were similar "Flash Crashes" back in 19th century, but people have forgot about them, because they just did not register on the stock market chart.
Bubbles, as Black Swans, are not precisely defined. Furthermore, not all bubbles are Black Swans, and not all Black Swans are bubbles. As Taleb points out, a Black Swan depends on the subject considering some event. Thanksgiving slaughter is a Black Swan for the turkey, but not for its owner.

The Flash Crash is an example of an outlier. The facts that its effects were neutralized a couple days later or that Flash Crash has not created long-lasting effects on markets are irrelevant to the argument I made. My argument is that it was an outlier, nobody has predicted anything like that before it happened, and after it has happened investors are now more cognizant of intra-day volatility and some risks in e.g., trading ETFs. Whether these conditions qualify the Flash Crash as a Black Swan is irrelevant. What is relevant to my argument is, again:
1. It was an outlier.
2. It was created and amplified in an information domain.

Victoria
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Post by hsv_climber »

VictoriaF wrote: If a king collects his fortune in physical gold, he can collect only as much as the amount of physical gold coins available. If Steve Jobs collects his fortune from the sales of I-Pads, his limit is the number of zeros he can type. That's the essence of scalability as used by Taleb.
I doubt that this is the point that Taleb makes. In fact that is not the point that he makes. His point of scalability, described in the book, is that a writer (or singer) can collect all the money that would go into book purchases. In the book he is using J.K. Rowling as one of the examples.
Steve Jobs's limit is not the number of 0, but a very concrete number - total number of world sales in personal computing devices. He might try to create a different market with I-Pad, but it will still be competing for the same or similar $$.
Just like there is no way for J.K. Rowling (i.e. example from the book) to get more money than the total $$ spend on book purchases.
VictoriaF wrote: In Taleb's examples, a baker can open several franchises and have people work for him in multiple places (similarly to the model of a medieval king and his surfs). But a baker's product is a physical bread, which is constrained by physical resources, freshness, and alike, and thus is much less scalable than, e.g., book sales.
Your example 1 does not match example 2. Think about it, not just try to rephrase Taleb. What is the absolute maximum number of I-Pads Steve Jobs can sell? It is equivalent to the maximum number of people on the planet who are older than 3 years old.
OTOH, what is the maximum number of bread a baker can sell? It is equivalent to the maximum number of people on the planet who are older than 1 years old. And he can sell this bread every day.
Baker's product is more scalable than I-Pad.

In other words, you've chosen a bad example. You should've chosen a s/w product or an e-book. But I-Pad is a physical device, which is no different than a piece of bread. And even e-books & s/w products have their physical limits.

But going back to kings... Alexander & his army were able to concur half of the world. So, amount of gold that was available to him to could be gained by him was only up to his imagination. Alexander had a scalable job.
VictoriaF wrote: The more options your dog has, the more things can go wrong. Modern systems are more complex than your dog's lifestyle. When multiple components are independently designed and imperfectly integrated, unexpected failures are more likely to occur. When complexity moves from systems to systems-of-systems, the opportunity for failures compounds and the predictability of extreme failures decreases.

I am making a logical argument. I don't have any data and I am not planning to seek data. You are free to agree or disagree with this logic.
Your logic is based on the assumption that world is getting more complex. But is it really the case? Is LCD monitor (new & better technology) is really more complex than an old RGB tube?
Is modern PC more complex than the first one? The new one might have more elements inside an Intel CPU, but even an average 10-year old now can build a computer from the spare parts. Was it really the case 20 years ago?
Here are 2 examples:
1. a farmer is using tractor to work on his land (in 2010)
2. a farm worker is using horse & his own body to work on the land (long time ago).

What is more complex and harder to fix and predict - a tractor (N1) or farmer's (and horse's) health (N2)?
VictoriaF wrote: Whether these conditions qualify the Flash Crash as a Black Swan is irrelevant. What is relevant to my argument is, again:
1. It was an outlier.
2. It was created and amplified in an information domain.

Victoria
But you've claimed that the number of Black Swans is accelerating because of the information domain. Yes, it was an outlier. We've had another outlier in 1987 before that.
Acceleration would mean that we should see these outliers (or Black Swan - type events) more often. Where is the acceleration?
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Post by rustymutt »

Why were on the subject of tails, has anyone else ever had ox tail soup.

It's mmmm mmmmmm good.
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Post by Lumpr »

Value_Investor wrote:BTW the 'flash crash' resulted in a 37 point drop in the S&P in one day. This is hardly a six sigma event. The rate of change during the day was high, but the opening and closing difference is hardly such an incredible event as to compare it to a 'black swan' in rarity. . . .
This doesn't strike me as being the proper analysis. This approach leads to the conclusion that the flash crash didn't exist because the S&P was up +% during 2010. Seems like the proper comparison is the crest to trough intraday compared to the historical crest to trough intraday.
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Post by VictoriaF »

hsv_climber,

1. Apple derives revenues from iTunes, as well as hardware, see for example, http://seekingalpha.com/article/211977- ... venue-year . iTunes would make a better example than iPads. Google's products are probably more scalable than iTunes. Income from financial products is probably even more scalable than that. Getting farther away from hardware towards information does, in fact, increase scalability.

2. You keep trying to catch me on inconsistencies. Some of my examples can be improved upon, as I have done in the item-1 above. But your pursuit of my inconsistencies borders on malice.

I consider any further discussion of Taleb's statements about the acceleration of Black Swans -- and my interpretations of his statements -- irrelevant to this thread.

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Post by nbatt »

Taleb is not the only person saying the stock market is becoming more volatile, I have seen Bogle make comments in this regard recently as well.
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Post by LadyGeek »

The OP has raised an interesting question, as the afore mentioned jargon is not discussed in the wiki. I'm working to rectify that.

Wiki article link: (link modified, see below)

Editing in progress. I'd like to keep the thread focused on definitions of various statistics terminologies as used in the context of investing.

I'll post back when I think it's ready to go. Article contributions / suggests / corrections are welcome while it's being developed (post here).

(Update 2/23/11: Development may change link. Use this instead: Portfolio risk management (category))
Last edited by LadyGeek on Wed Feb 23, 2011 5:16 pm, edited 1 time in total.
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Post by peter71 »

Hi LG,

Interesting that your cites as well as the top Google hits suggest that "barbell" is rarely used in the way we use it here . . . i.e., in reference to a portfolio of both stocks and bonds, but if you want a cite that includes the usage popular here pretty much any combination of Taleb and barbell will do, including Taleb's personal wiki page:

http://en.wikipedia.org/wiki/Nassim_Nicholas_Taleb
One of its applications is in his definition of the most effective investment strategy: what he calls the 'barbell' strategy. He suggests that investing money in 'medium risk' investments is pointless because risk is difficult if not impossible to compute. His preferred strategy is to be both hyper-conservative and hyper-aggressive at the same time. For example, an investor might put 80 to 90% of their money in extremely safe instruments, such as treasury bills, with the remainder going into highly risky and diversified speculative bets.
All best,
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Post by LadyGeek »

Hi peter71,

Tough call, but I don't think it's appropriate. Many of those google links (taleb barbell) point back to Taleb's Black Swan book and not much else.

The wiki follows the Wikipedia standard and should only use credible sources. I find it difficult to cite someone who is a self-proclaimed philosopher (although he may be just as accurate... :D). There's no supporting quantitative analysis for Taleb, which is why I went with Bill Bernstein.

Give the referenced Morningstar thread a read (under External links). You'll see posts from wbern (Bill Bernstein), Taylor Larimore, Mel Lindauer, and Larry Swedroe discussing barbell investment strategy. The conclusion is not straight-forward. Posted 9-27-2000. (FWIW, the M* thread is in the wiki: Index to important Posts on Morningstar (under Barbell Portfolio))

As for the on-going statistics article, bobcat2 has suggested a more comprehensive update - Portfolio Risk Management. This topic has not been addressed to any level of detail in the wiki. "Tails" and the like is really a subset of risk management. I'm going to rework the article to fit under this new topic. (Anyone up for collaboration?)

Wiki article link: (link modified, see below). The discussion page link (top) shows the proposed update. Current wiki editing activity is under "Recent changes" (left menu).

(Update 2/23/11: Development may change link. Use this instead: Portfolio risk management (category))
Last edited by LadyGeek on Wed Feb 23, 2011 5:19 pm, edited 1 time in total.
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Post by peter71 »

Hi LG,

Well, I rarely read the Wiki myself, in large part because someone always has to make a "call" . . . use the term as you like and I'll do the same.

Take care,
Pete
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Post by greenspam »

whether it is the behavior of the stock market, or that of a 2 year old child,
we can certainly formulate different math models, use curve fitting, perhaps with normal distributions, fat tails, etc... to DESCRIBE their PAST behavior,

but there is a huge difference between using equations and curves to DESCRIBE what has happened in the PAST, vs. PREDICTING what will happen in the FUTURE.

i know this sounds just like "past performance is no guarantee of future results", but there is a difference. for some reason, people give much greater weight to math models than verbal phrases.

i think we need to think more about the difference between mathematically DESCRIBING vs. PREDICTING behavior. i can't predict what a 2 year old child will do next, nor the stock market... no matter how well i can mathematically characterize their past behavior. so, i guess my philosophy is to expect the unexpected, regardless of the math that might suggest otherwise.
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Post by VictoriaF »

LadyGeek wrote:Hi peter71,

Tough call, but I don't think it's appropriate. Many of those google links (taleb barbell) point back to Taleb's Black Swan book and not much else.

The wiki follows the Wikipedia standard and should only use credible sources. I find it difficult to cite someone who is a self-proclaimed philosopher (although he may be just as accurate... :D). There's no supporting quantitative analysis for Taleb, which is why I went with Bill Bernstein.
Hi LadyGeek,

I understand that it may be difficult to find concrete references describing Taleb's barbell investment strategy apart from what he wrote in The Black Swan. By all means, please use whatever is appropriate for and easy to incorporate in the Bogleheads Wiki.

However, this does not warrant calling Taleb "a self-proclaimed philosopher" or implying that he is not credible. I suggest that proper references to Taleb should use his official title, Distinguished Professor of Risk Engineering at NYU Poly Institute. The source is his web site, Fooled by Randomness.

Thank you,

Victoria
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Post by LadyGeek »

VictoriaF wrote:Hi LadyGeek,

I understand that it may be difficult to find concrete references describing Taleb's barbell investment strategy apart from what he wrote in The Black Swan. By all means, please use whatever is appropriate for and easy to incorporate in the Bogleheads Wiki.

However, this does not warrant calling Taleb "a self-proclaimed philosopher" or implying that he is not credible. I suggest that proper references to Taleb should use his official title, Distinguished Professor of Risk Engineering at NYU Poly Institute. The source is his web site, Fooled by Randomness Thank you, Victoria
I have never read Taleb's works, so I was going by the introductory paragraphs in Wikipedia and this Forbes article: Is A Black Swan In The Way Of The 14,000 Dow? which contains:
And Taleb is not even a billionaire investor himself with a record like Warren Buffett's. On the contrary. He's a philosopher, a muser on the mediocrity of conventional thinking. He unmercifully puts down the teachings of Robert Merton and Myron Scholes, two Nobel prize-winning econmists with a huge Wall Street following.
I looked at Taleb's web site and did additional research. Thank you for repudiating my comment. I see your point and agree that my comment was inappropriate.

The lack of available reference's describing Taleb's barbell strategy, and the aforementioned Forbes article noting that Taleb's barbell strategy was a "flop" (see article for details), pointed me in the direction of Bill Bernstein. His article and associated Morningstar forum thread provide quantified information and informed discussions - good material for the wiki.

The wiki is a collaborative effort. Comments / questions / corrections (!) are welcome.
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Post by VictoriaF »

LadyGeek wrote:I have never read Taleb's works, so I was going by the introductory paragraphs in Wikipedia and this Forbes article: Is A Black Swan In The Way Of The 14,000 Dow? which contains:
And Taleb is not even a billionaire investor himself with a record like Warren Buffett's. On the contrary. He's a philosopher, a muser on the mediocrity of conventional thinking. He unmercifully puts down the teachings of Robert Merton and Myron Scholes, two Nobel prize-winning econmists with a huge Wall Street following.
I checked out this Forbes article, which I have not seen before. It treats Taleb in a sarcastic condescending manner. But note the date. The article is published on 20 July 2007, when the markets were close to their Fall of 2007 highs, and Taleb's insights and warnings could be (for the time being) dismissed.

A year and a half after the Forbes article was published the world turned upside down, Lehman Brothers, and all. The Black Swan was almost prophetic in its descriptions of seemingly conservative bankers taking great risks with other people's money.

LadyGeek wrote:I looked at Taleb's web site and did additional research. Thank you for repudiating my comment. I see your point and agree that my comment was inappropriate.

The lack of available reference's describing Taleb's barbell strategy, and the aforementioned Forbes article noting that Taleb's barbell strategy was a "flop" (see article for details), pointed me in the direction of Bill Bernstein. His article and associated Morningstar forum thread provide quantified information and informed discussions - good material for the wiki.

The wiki is a collaborative effort. Comments / questions / corrections (!) are welcome.
Taleb is not universally liked, and thus his name is frequently accompanied with heated discussions. Many people have not read his books and judge him based on the second-hand information, e.g., references like the Forbes article above. Other people formed their opinions about Taleb from observing his combative attitude to TV journalists in several financial programs (available on Youtube). Many of these people also have not read Taleb.

There are also respectable people who have read Taleb and disagree with him. For instance, Dennis Lindley, a British statistician has written a highly critical review of The Black Swan. Lindley was eloquent, factual and convincing in his review, but after reading Lindley's book Understanding Uncertainty and The Black Swan, I think the two have more in common than they realize.

Thank you for acting on my comment. As you can see, I am a firm devotee of Taleb's ideas, and I try to counterbalance unfairness towards him where I see it.

Victoria
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