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Pablo has thoroughly explained why mathematics do not work in the world of finance. He speaks the truth from the mind of a practitioner. He speaks the truth when he says that finance is a social science. Mathematics should only be applied to disciplines which are restrained and bound by rules that cannot be broken, such as physics. Mathematics works beautifully in a world where rules are followed, but it starts to break down in worlds where rules can be broken. Social Science is a world governed by human activity. Regularity and universality - forget it. Finance is governed by human activity, so it come to no surprise that humans often break rules. No model can handle human irrationality.
For all those physicist and mathematicians, who feel they can "crack the code", read "God's mind", or find "Newton like" universal laws and regularity in the markets, here are a few takeaways from Pablo's book:
1.) In Social science, regularity and universality do not exist. Modeling human activity - forgetaboutit.
2.) Don't make the mistake of substituting the logic of mathematics for the logic of finance, markets, economics etc.
3.) IN FINANCE, mathematics should only be used for CONCEPTUALIZATION or a way of thinking about uncertainty, risk, and expectation. It should ONLY be used to COMPARE relative risk between financial instruments.
4.) Mathematics is only a description of regularity; It's not a description of causality. Mathematics do not reveal the causal mechanisms responsible for uncertainty and risk.
5) We think we modeled the world correctly. It's the other way around. The world "temporarily" behaves as if our models are correct.
Over the years we have come to believe mathematics is the only tool for conceptualization, or it's the highest level of science. We give little regards to the objects we apply mathematics to. We tend to treat all objects the same. Social objects such as finance, economics we treat the same as physical objects such as atoms and chemicals. For some, they've managed to "collapse" theory into practice. What started out as theoretical - in no way connected to reality - is now accepted as practical knowledge.
Pablo's book explains why we often fall prey to the pitfalls of mathematics. Some say this book is poorly written. I say that is non-sense. The point is this book speaks the truth. A must read for anyone who views mathematics as the highest form of science!
 

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As others before me, I was also led to Triana's book by the works of N.N.Taleb - that's how misleading an introduction is.
Triana's tome fails on so many levels that's imbarassing. "Lecturing Birds
" is poorly written and poorly edited (how else would one explain constructs like "impossibly impossible", "intisically intrinsic" "abstractionism"?). It is also incredibly long winded and particularly effective in driving me to impatience. Uncharacteristically - for myself - I found that, by the middle of his book, I was checking the first sentence on every paragraph to decide if it was worth reading or if it could be skipped without detriment to the general comprehension - skipping was almost always safe. However irritating, these are not the worst failures of the book.
Coming to the subject from brilliant works such as Taleb's books, or articles such as "Recipe for Disaster: The Formula That Killed Wall Street" (Wired) or "Trillion Dollar Bet" (NPR's NOVA series), I was expecting similar insights. I came away from the book more or less convinced that Triana is using his "kill the quants" rant as a smoke screen to hide the total systemic failure of the contemporary economic system. Persuaded, as I am, that quant analysis may have failed at its task, and that it bears a nontrivial responsibility of hte recent economic crisis, I find that Triana's obsessive fingering of the quants as the sole culprits very conveniently forgets to mention that bankers took ridiculously risky and leveraged positions because they wanted to do it in the first place. Had they gotten astrologists rather than quants, they'd have used astrology as an excuse to take those same positions. Let's not forget that 1929 happened in the days of the good old fashioned common sense that are so dear to Triana's heart.
My take: read Taleb. For a reason why "good ole common sense" cutis it just about as VaR, read "This Time is Different". Do not bother with this boring book. That is, unless you want to put up with more than 350 pages of prose like this:
"Deliciously paradoxically, the Nobel could end up diminishing, not fortifying, the qualifications-blindness and self-enslavement to equations-led dictums that, fifth-columnist style, pave the path for our sacrifice at the altar of misplaced concreteness."
 

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Lecturing Birds - Instant Financial Classic!
The beauty of very high level academics is that once it's underbelly becomes exposed it invariably takes a turn back to the basics, Triana is the next
thing to a financial Aristotle, explaining derivatives in the vernacular of "Fat Tony"!
Clearly some of the most exotic finance directions and methods of manipulation, David Li's bastardized copula function for one, have clearly failed, maybe used in bastardized relations, or correlations, yet their bones and fragments remain a fixture in our daily education and finance world!
Lest we not forget that the whole financial "Expert" world enevitably boils down to pedigree and social circles, from the matriculation to the name on the firm's door!
Do your own homework - Buy Lecturing Birds and get a birdseye view of what Quants we have been for listening to the so-called financial "Experts"!
 

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