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Derman on mathematical models

Joined
5/4/07
Messages
176
Points
28
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).
 
“In physics it takes three laws to explain 99% of the data; in finance it takes more than 99 laws to explain about 3%.”
Statistics lies in between :) no matter what you do, you can't go above 95% :)

Interesting article :) it is always interesting to read what prof. Derman has to say.
 
Thanks for the article Dmytro,
a nice reminder once again that in finance one deals with probabilistic measures mixed with imagination of numerous market participants ;), and thus has to be careful.
I only wonder how is possible that the laws work in physics, but not in finance? Brownian motion and many other models in physics are explained and described precisely, but in economics CAPM, for example, gives significant errors. Maybe it takes time (with numerous attempts, experiments and loads of imagination ;) ) for any science to come up with laws and working models?
 
Well, maybe in the 22nd century :)
Maybe at that time people will be able to predict at least 90% of financial events :)

I agree that imagination must be very strong :)
 
Thanks Dmytro,
Very interesting article which shows the importance of imagination and intuition; also mentioning the importance of economic understanding of the markets.
 
i think the problem is that physics and the like are closed systems, and the markets are not.
a little thing called human factor turns out to be a bitch to figure out ;]
even greenspan concurs (recent guest on jon stewart).
 
i think the problem is that physics and the like are closed systems, and the markets are not.
a little thing called human factor turns out to be a bitch to figure out ;]
even greenspan concurs (recent guest on jon stewart).

That is exactly the point :) if only we could predict the human factor.

I've heard of something called "behavioral finance", a discipline that studies how people make decisions.
 
Economics

Behavioural finance.... I think we have add psychology in MFE program. Game theory?

My Prof. of Economics told me that he couldn't bother so much about modeling because he believed 90% of the models are incorrect.....!:dance:
 
Game theory is something different. It is still based on mathematical models. I'm talking more along the lines of psychology. For example, various stress situations and how different people react to them and what decisions do they make.
 
Impossible

Impossible to know manZZZ!

In terms of stock market, people who have experience will stay put even the index is nose deep. However, inexperience investor will sell all the way through. Again, this is provided one know how to create portfolio insurance to minimize losses or to gain when the market is down while they are still holding the underlying assets (stocks).

I refer the above to non-institutional investor. I think we have refer back to utility theory too. We may different type of quant traders, e.g. risk avert or risk taker...or someone not sure.

Frankly speaking, I really hope someone can come up to tell me how to include these fear factors when we model the market. Modeling historical data is no fun. I am a wannabe so you guys can teach me.

Thanks,
K:)

Game theory is something different. It is still based on mathematical models. I'm talking more along the lines of psychology. For example, various stress situations and how different people react to them and what decisions do they make.
 
typo errors

rephrase:


Impossible to know manZZZ!

In terms of stock market, people who have experience will stay put even the index is nose deep. However, inexperience investor will sell all the way through. Again, this is provided one know how to create portfolio insurance to minimize losses or to gain when the market is down while they are still holding the underlying assets (stocks).

I refer the above to non-institutional investor. I think we have to refer back to utility theory too. We may have different type of quant traders, e.g. risk avert or risk taker...or someone not sure.

Frankly speaking, I really hope someone can come up to tell me how to include these fear factors when we model the market. Modeling historical data is no fun. I am a wannabe so you guys can teach me.

Thanks,
K:)[/quote]
 
In terms of stock market, people who have experience will stay put even the index is nose deep.

as long as they can hold it. They may be in a situation where they would have to liquidate regardless.
 
Agreed. If the margin call....or they need the fund or cut losses for another arbitrage opportunities....
 
In terms of stock market, people who have experience will stay put even the index is nose deep. However, inexperience investor will sell all the way through. Again, this is provided one know how to create portfolio insurance to minimize losses or to gain when the market is down while they are still holding the underlying assets (stocks).

We might be interested in studying the population to see how bad things can go before different people start selling. Or any other situation where the same thing happens to many people and we want to observe what they do. Based on that, we can see what most people would do in a certain situation and react accordingly.
 
I understand Kean's professors concern. When you have too many variables which are dependent on subjective decision processes; you may find it unuseful to spend time on modeling.
The issue becomes more severe when you think about the behavioral finance. These decisions are not concrete problems that someone can model with certainty.
But this is still ok as long as you accept that your model is incorrect when you start building it. It is nothing more than a trial to approximate the reality.
 
Yes

At that time, I was a bit upset by such comment because it was very discouraging to any student. By the way, I heard that UK Ministry of Finance or Bank of England used to construct a model with 700 independent variables to gauss the movement of FX and interest rates. Not sure how true was this story?

I think having a model in mind is better than nothing.

I believe everyone knows about trading system. Apparently candlesticks chart is probably the best can tell the intra-day price movement of a particular stock. I wonder anyone know that any system can provide the stock selling-buying volume based on intra-day hourly trading. In this manner, I think we can study the trend closely based on this data.

In particular, I spent a few hours talking to people who bought shares and people who involved in the financial markets. The feedback was these people would stick to a few stocks throughout many years. They will continue to make money with these stocks. My hypothesis is that these people entering and leaving the market are almost surely proportion to any price movements of an underlying asset.

Again, there are different type of investors. We do not have statistics to divide them into group from a market perspective. I don't know whether it will help to give us the percentile of price movements.

Interesting subject indeed.

Thanks
Kean


I understand Kean's professors concern. When you have too many variables which are dependent on subjective decision processes; you may find it unuseful to spend time on modeling.
The issue becomes more severe when you think about the behavioral finance. These decisions are not concrete problems that someone can model with certainty.
But this is still ok as long as you accept that your model is incorrect when you start building it. It is nothing more than a trial to approximate the reality.
 
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