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First what well-known mathematical principles are you talking about? Second have you read any of his academic papers? All can be found on SSRN. Two of the big o

by bhewes 17y ago

First what well-known mathematical principles are you talking about? Second have you read any of his academic papers? All can be found on SSRN. Two of the big ones are "Errors, Robustness, and the Fourth Quadrant" and "Finiteness of Variance is Irrelevant in the Practice of Quantitative Finance." Taleb states "My central idea in The Black Swan is that: rare events cannot be estimated from empirical observation since they are rare. We need an a priori model representation for that; the rarer the event, the more the dependence on aprorism. Further, we do not care about probability (if an event happens or does not happen); we worry about consequences (how much total wealth or total destruction will come from it). Given that the less frequent the event, the more severe the consequence (just consider that the 100 year flood is more severe, and less frequent, than the 10 year flood), our estimation of the CONTRIBUTION of the rare event is going to be massively faulty (contribution is probability times effect; multiply that by estimation error) ; and nothing can remedy it. So the rarer the event, the less we know about its role --and the more we need to make it up with an extrapolative, generalizing theory. Hence model error is more consequential in the tails and some representations ARE MORE FRAGILE than others..... Nobody before has examined my problem in the history of thought, let alone systematize the idea of decision-making under certain classes of ignorance." I am sure he would be excited if someone could show him that his idea is not original.

andreyf 17y ago
Um, I had this idea sometime around middle school, when we learned fractions, and probability was an example the teacher used. I still remember his response, which was rather satisfying - that in many systems, things break down at edge cases, and that's to be expected. It was a great class - a similar insight Mr. Hawks helped me have is that there's much less of a difference between how people reason about $6 billion and $7 billion than between $5 and $500, even though the former is a much larger gap. This stuff is common sense, and the con is probably older than modern civilization - the author tells you a neat tidbit of somewhat counter-intuitive reasoning, then pretends like he's endowed you with a secret which makes you smarter than most trained economists. You eat it up because you love the idea that you're smarter than economic experts. Bullshit.
mediaman 17y ago
The excerpt you provide from his paper is mathematically expressed as a leptokurtotic probability curve and data with high heteroskedasticity. Do you think he's the first guy to figure out that insufficient sample data in the tails of a leptokurtotic probability curve leads to a higher overall error term? Rather than some groundbreaking new theory of math, this is material covered in freshman econometrics. I'm just asking that he admit this when he boils it down to an enjoyable read. EDIT: the concept of kurtosis was apparently at least named in 1905, over a century ago, by German mathematician Karl Pearson.
- danm 17y ago
  Actually, I believe his point is that the probability distribution is from the Cauchy Distribution, where the mean, the variance, and the kurtosis are all undefined. In fact, you're providing an example of exactly what he writes about in believing that the tools being taught in "freshman econometrics" apply to the sort of randomness you encounter in the real world. Certainly Mandelbrot has had some things to say about this topic as well. When basic financial tools and theories are based on assumptions that are Just Plain Wrong, it makes you question the gigantic stack that has been built on top of them. It's easy enough to dismiss this stuff as worrying about edge cases, but these edge cases occur more often than the theory dictates, and unfortunately, people underestimate their impact.
  - mediaman 17y ago
    You're right about him preferring a Cauchy distribution vs. a leptokurtotic distribution, I was mistaken. Taleb argues that these tools aren't being used in the real world, but all the evidence in places like the options market seems to indicate otherwise: options get way more expensive (from a lognormal perspective) the deeper in/out of the money they are, primarily because there are fat tails already being modeled into the price. And given that options market data, it's tough to see how going long on Black Swans will fetch a good Sharpe ratio--which wouldn't be the case if it were true that everyone were slaves to normal distributions.
    - bhewes 17y ago

by bhewes 17y ago

andreyf 17y ago

Um, I had this idea sometime around middle school, when we learned fractions, and probability was an example the teacher used. I still remember his response, which was rather satisfying - that in many systems, things break down at edge cases, and that's to be expected. It was a great class - a similar insight Mr. Hawks helped me have is that there's much less of a difference between how people reason about $6 billion and $7 billion than between $5 and $500, even though the former is a much larger gap. This stuff is common sense, and the con is probably older than modern civilization - the author tells you a neat tidbit of somewhat counter-intuitive reasoning, then pretends like he's endowed you with a secret which makes you smarter than most trained economists. You eat it up because you love the idea that you're smarter than economic experts. Bullshit.

mediaman 17y ago

The excerpt you provide from his paper is mathematically expressed as a leptokurtotic probability curve and data with high heteroskedasticity. Do you think he's the first guy to figure out that insufficient sample data in the tails of a leptokurtotic probability curve leads to a higher overall error term? Rather than some groundbreaking new theory of math, this is material covered in freshman econometrics. I'm just asking that he admit this when he boils it down to an enjoyable read. EDIT: the concept of kurtosis was apparently at least named in 1905, over a century ago, by German mathematician Karl Pearson.

danm 17y ago
Actually, I believe his point is that the probability distribution is from the Cauchy Distribution, where the mean, the variance, and the kurtosis are all undefined. In fact, you're providing an example of exactly what he writes about in believing that the tools being taught in "freshman econometrics" apply to the sort of randomness you encounter in the real world. Certainly Mandelbrot has had some things to say about this topic as well. When basic financial tools and theories are based on assumptions that are Just Plain Wrong, it makes you question the gigantic stack that has been built on top of them. It's easy enough to dismiss this stuff as worrying about edge cases, but these edge cases occur more often than the theory dictates, and unfortunately, people underestimate their impact.
- mediaman 17y ago
  You're right about him preferring a Cauchy distribution vs. a leptokurtotic distribution, I was mistaken. Taleb argues that these tools aren't being used in the real world, but all the evidence in places like the options market seems to indicate otherwise: options get way more expensive (from a lognormal perspective) the deeper in/out of the money they are, primarily because there are fat tails already being modeled into the price. And given that options market data, it's tough to see how going long on Black Swans will fetch a good Sharpe ratio--which wouldn't be the case if it were true that everyone were slaves to normal distributions.
  - bhewes 17y ago