came across this paper on Emanuel Derman's website.
an interesting read, especially considering his profile in the field.
i think it is always helpful to remember that the models we'll build and/or work with are not laws, but, at best, very good approximations and predictions of possible economic scenarios. sometimes people forget that, get cocky and then get burned. which is yet another reason that finance is such an exciting field ;D
__________________________________________________________
Beware of Economists Bearing Greek Symbols
by Emanuel Derman
"In physics it takes three laws to explain 99% of the data; in finance it takes more than 99
laws to explain about 3%." So quipped MIT finance professor Andrew Lo at a dinner I
once attended. Economists, he added, consequently suffer from physics envy.
Now I was trained as a theoretical physicist in the 1960s and 1970s, the glory
years of elementary particle physics. Our heroes were Einstein, Dirac, Gell-Mann and
Feynman—Nobelists all, visionaries who conjured up new mental worlds and the
equations that went with them. And these new mental worlds, miraculously, not only
corresponded to the physical world we inhabit, but also accurately predicted the existence
of weird and previously unobserved particles.
How could imagination and mathematics be so powerful in apprehending the
world outside our heads?
Years later, I came to work at Goldman Sachs in the field of quantitative finance,
the branch of economics concerned with calculating the fair value of securities. At first I
was charmed by the resemblance between the finance papers I now studied and the
physics papers I used to read and write. Then, as I read further, I discovered that
economists love formal mathematics much more than physicists do. Many economic
journals encourage—or even demand—a faux-rigorous style with multitudes of axioms
and lemmas in numbers that tend to be inversely proportional to their efficacy in the real
world.
Why are economists trained so formally? It makes sense to axiomatize a
discipline when the axioms are true (or almost so) and have strong predictive power.
That's the case for euclidean geometry, for example, as well as Maxwell's
electromagnetic theory, where many valid, useful, and accurate predictions follow from
applying the laws of deduction to a few initial assumptions.
But economists seem to have embraced formality and physics envy without the
corresponding benefits of accuracy or predictability. In physics, Maxwell's theory and
quantum mechanics allow you to predict the way an electron spins about its own axis
inside a hydrogen atom to an accuracy of twelve decimal places. Something that accurate
isn't just a model—it's a law. In economics, by contrast, there are no laws at all, only
models, and you're immensely lucky if you can predict up from down.
When people build models to value securities, they make all sorts of imaginative
assumptions that are then formulated mathematically. For example, quantitative
strategists at investment banks or hedge funds value currently fashionable collateralized
default obligations (which provide default insurance on baskets of large numbers of
bonds) by assuming that each bond-issuing company is represented by an imaginary
variable. That variable evolves randomly through time—like smoke diffusing across a
room—until it crosses an imaginary default boundary in the future, at which point the
company will default on all of its debt. It's an elegant mental construct and not an
unreasonable way to model the random chance of a company doing badly enough to
default. But it's not literally true. It's still a model, a toy, a limited picture—despite the
fancy mathematics. No wonder the picture often breaks down and causes havoc, as
happened in credit markets last May.
Clearly, then, when someone shows you an economic or financial model that
involves mathematics, you should understand that, despite the confident appearance of
the equations, what lies beneath is a substrate of great simplification and—sometimes—
great and wonderful imagination. That's not a bad thing—financial markets are all about
imagination. But you should never forget that even the best financial model can never be
truly valid because, unlike the physical world, the mental world of securities and
economics is much less amenable to the power of mathematics.
Emanuel Derman (emanuel.derman@mac.com) is the director of the financial
engineering program at Columbia University and the head of risk at Prisma Capital
Partners, a fund of funds. He is the author of My Life as a Quant: Reflections on Physics
and Finance (Wiley, 2004).
an interesting read, especially considering his profile in the field.
i think it is always helpful to remember that the models we'll build and/or work with are not laws, but, at best, very good approximations and predictions of possible economic scenarios. sometimes people forget that, get cocky and then get burned. which is yet another reason that finance is such an exciting field ;D
__________________________________________________________
Beware of Economists Bearing Greek Symbols
by Emanuel Derman
"In physics it takes three laws to explain 99% of the data; in finance it takes more than 99
laws to explain about 3%." So quipped MIT finance professor Andrew Lo at a dinner I
once attended. Economists, he added, consequently suffer from physics envy.
Now I was trained as a theoretical physicist in the 1960s and 1970s, the glory
years of elementary particle physics. Our heroes were Einstein, Dirac, Gell-Mann and
Feynman—Nobelists all, visionaries who conjured up new mental worlds and the
equations that went with them. And these new mental worlds, miraculously, not only
corresponded to the physical world we inhabit, but also accurately predicted the existence
of weird and previously unobserved particles.
How could imagination and mathematics be so powerful in apprehending the
world outside our heads?
Years later, I came to work at Goldman Sachs in the field of quantitative finance,
the branch of economics concerned with calculating the fair value of securities. At first I
was charmed by the resemblance between the finance papers I now studied and the
physics papers I used to read and write. Then, as I read further, I discovered that
economists love formal mathematics much more than physicists do. Many economic
journals encourage—or even demand—a faux-rigorous style with multitudes of axioms
and lemmas in numbers that tend to be inversely proportional to their efficacy in the real
world.
Why are economists trained so formally? It makes sense to axiomatize a
discipline when the axioms are true (or almost so) and have strong predictive power.
That's the case for euclidean geometry, for example, as well as Maxwell's
electromagnetic theory, where many valid, useful, and accurate predictions follow from
applying the laws of deduction to a few initial assumptions.
But economists seem to have embraced formality and physics envy without the
corresponding benefits of accuracy or predictability. In physics, Maxwell's theory and
quantum mechanics allow you to predict the way an electron spins about its own axis
inside a hydrogen atom to an accuracy of twelve decimal places. Something that accurate
isn't just a model—it's a law. In economics, by contrast, there are no laws at all, only
models, and you're immensely lucky if you can predict up from down.
When people build models to value securities, they make all sorts of imaginative
assumptions that are then formulated mathematically. For example, quantitative
strategists at investment banks or hedge funds value currently fashionable collateralized
default obligations (which provide default insurance on baskets of large numbers of
bonds) by assuming that each bond-issuing company is represented by an imaginary
variable. That variable evolves randomly through time—like smoke diffusing across a
room—until it crosses an imaginary default boundary in the future, at which point the
company will default on all of its debt. It's an elegant mental construct and not an
unreasonable way to model the random chance of a company doing badly enough to
default. But it's not literally true. It's still a model, a toy, a limited picture—despite the
fancy mathematics. No wonder the picture often breaks down and causes havoc, as
happened in credit markets last May.
Clearly, then, when someone shows you an economic or financial model that
involves mathematics, you should understand that, despite the confident appearance of
the equations, what lies beneath is a substrate of great simplification and—sometimes—
great and wonderful imagination. That's not a bad thing—financial markets are all about
imagination. But you should never forget that even the best financial model can never be
truly valid because, unlike the physical world, the mental world of securities and
economics is much less amenable to the power of mathematics.
Emanuel Derman (emanuel.derman@mac.com) is the director of the financial
engineering program at Columbia University and the head of risk at Prisma Capital
Partners, a fund of funds. He is the author of My Life as a Quant: Reflections on Physics
and Finance (Wiley, 2004).
no matter what you do, you can't go above 95% 
, and thus has to be careful.
