Sunday, February 22, 2009

David X. Li

I've been seeing a lot of hits from searches on "Gaussian Copula" or "David X. Li" lately. Li is a quant who developed the Gaussian Copula model used in pricing of CDOs. See here for a post I did on him and the model back in 2005, including some predictions that it might all end in tears :-/

David X. Li is no relation to David X. Cohen of the Simpsons and Futurama, although Cohen did study physics at Harvard :-)

Below is some advice for quants from Li.

How to Become a Successful Financial Engineer?

David X. Li

Actuaries might have been the most quantitative people in the financial industry for a long time. However this unique position has been severely challenged since about a decade or two ago when the investment banks began to hire so-called "rocket scientists" – people with Ph.D. degree in physics and other quantitative fields. Nowadays you can find quantitative analysts or "quants" working in various functions in investment banks and large commercial banks, such as trading, risk management and portfolio management. You may even meet some quants working in some traditional quant-free zones, such as auditing department of a large bank. As the insurance and banking businesses converge it is hard to imagine that traditional approaches to risk measurement – like actuaries work on the insurance side and quants work on the banking side – can still be applied in isolation.

This change poses a challenge to our profession. However there is nothing to panic about. Many problems in practice might need combined skills in actuarial science and financial engineering to solve.

This article outlines some basic skills people should have in order to become a successful financial engineer. It is more from an investment bank angle since that is where the author knows the most.

Mathematical Training

Karl Marx once said ``A subject can only become a science after it successfully uses mathematics". Finance might be the most successful area to use mathematics. The mathematics used in finance ranges from basic mathematics, such as numerical analysis, calculus, and statistics to more advanced ones, stochastic processes and stochastic differential equations, non-linear optimization etc. The areas we use the most in practice are numerical analysis and statistics. Whoever wants to have a career as financial engineer should try to have a solid training in mathematics in school. Wall Street tends to hire people with strong quantitative skills. The general philosophy is that we can teach you finance, but we don’t have time to teach you mathematics. We use a lot of mathematics at the graduate level, so it is to your advantage to take some graduate mathematics courses before you walk out of school. Many practitioners go back to school to learn more mathematics after a few years working in industry. It is hard to learn all the necessary mathematics, but you can pick up other useful mathematical tools or concepts once you have built a solid foundation. I like the saying by Professor Elias Shiu at the University of Iowa "Learning Mathematics is like rowing, if you don’t push forward you’d be pushed backward". Just keep rowing!

On the other hand, don’t indulge yourself into abstract mathematics. Mathematics is just a tool. So you should keep the mentality of an applied mathematician. We find it usually takes longer time for a pure mathematician to feel his "role" in practice than a physicist or an applied mathematician. One famous applied mathematician once said, "Mathematics in every one of its applied areas is a good servant, but a bad master". At the end we are to solve practical problems, not a mathematical game or theorem.

Financial Training

The theory of finance has emerged as a prominent science with the Nobel Prize award to Harry Markowitz, William Sharpe, Merton Miller, Robert Merton and Myron Scholes. This theory attempts to understand how financial markets work, how to make them more efficient, and how they should be regulated. These revolutionary theories in the latter half of the twentieth century have created waves of financial innovation in Wall Street. There are essentially two revolutions. The first revolution, which was the introduction of quantitative methods to the black art of equity fund management, began with the 1952 publication of his Ph.D. dissertation ``Portfolio Selection" by Harry Markowitz. The second revolution in finance began with the 1973 publication of the solution by Fischer Black and Myron Scholes (in consultation with Robert Merton) to the option pricing problem. The Black-Scholes formula brought to the finance industry the modern methodology of martingales and stochastic calculus, methodology which enables investment banks to produce, price and hedge an endless variety of "derivative securities."

There are mainly two aspects of the financial theory, economic and engineering. At the early stage it is essential to understand each instruments from an engineering point of view. But you will find it is important to understand the "big picture" or the economic aspect of the theory later on. There are many books on derivative securities. The key is to fully understand each instrument thoroughly. A good reference book is John Hull’s book. Another important aspect is to understand the market conventions, which you can only learn from a practitioner’s book or some software manuals. These conventions are very important since a one-day miscount could result in a 40-bp (basis point) difference, which is usually larger than many derivative transaction profit margins.

IT Training

Computers have played an important role in our daily life, more so in the life of a financial engineer. Of course you can rely on the IT people in your company to implement your models. But it usually takes a longer time for you to explain the problem than if you just write something simple and get the answer yourself. The package people use the most is the Excel spreadsheet. Other packages, which allow you to do rapid development, are MatLab, Mathematica or Splus. If you can program in C++, Visual Basic for Application or Java, that will be even better. You should pick up these skills at the early stage of your career, which will make your life much easier later on.

In summary, you need a combined set of skills to be a successful financial engineer. Many skills could be developed while you are still in college. Just keep in mind, financial engineering skills is just one set of skills for you to be successful in your business life. Many other skills, such as communication skills and leadership, may play a more important role in your career.

David X. Li is a partner in the RiskMetrics Group where he concentrates on risk management research, product development and structural marketing. Previously he worked for banks in the areas of risk management and credit derivative trading. He taught actuarial science and finance at university briefly before he left academia. Mr. Li has a Ph. D. degree in statistics from the University of Waterloo and master's degrees in economics, finance and actuarial science from the famous NanKai. He is an Associate of the Society of Actuaries (SOA) and an elected Council Member of the Investment Section of the SOA.


Anonymous said...

I bitterly regret that I didn't do a double major in mathematics, register for every single elective, and master.

Any other subject can be picked up simply by reading through one of these 5-gigabyte PDF textbook torrents, e.g. here but not math (at least not for me...)

Anonymous said...

I love this, from Mr. Li's little essay:

Karl Marx once said ``A subject can only become a science after it successfully uses mathematics". Finance might be the most successful area to use mathematics. [emphasis added]

Notice the switch — "successfully uses mathematics" to "the most successful area to use mathematics".

Can you spell "non sequitur"? This little slip speaks volumes; it sums up where these d-----bags are coming from. And that's not the only hint of sloppy thinking and superficial posing in this essay.

Finally, the irony of a financial engineer—a rarified creature of modern capitalism—using a Karl Marx quote as an endorsement of his career choice is too rich for words.

Steve Hsu said...

Li grew up in PRC, so he couldn't help but know a lot of Marx quotations and would view everything a bit differently than we do.

I did find the sentence you emphasized to be strange, but keep in mind it was written at the peak of the finance bubble :-)

Anonymous said...

"A subject can only become a science after it successfully uses mathematics"

It was Descartes who said math is the language of science. Probably a few Ancient Greeks beat Descartes to it, but not sure about that. Marx is purely derivative in everything good as well as evil.

Unknown said...

Wired magazine has a story basically blaming Gaussian copulas for destroying the world...

Donald Pretari said...

This is David Li week. I wondered why he hasn't been heard from lately:

Don the libertarian Democrat

Seth said...

The story of the way copulas got applied is a classic illustration of the way the big poker game among financial executives trumps the work of quants.

The copulas provided a 'talking point' for selling the idea that risk was under control to buyers who could be relied upon not to understand them. I like to call this 'geek glamour' -- whenever awkward questions come up, the shell game operator says: "hey, look over there at those pretty formulas" to distract the mark from what is really going on. The beauty of this approach is that the con man doesn't have to understand the 'copulas' talking point either. All that's necessary is that it sound 'glamorously geeky' to the mark.

Steve Hsu said...

The cult of the efficient market doesn't believe in the existence of con men. No arbs! No arbs! Mr. Market is too smart for that.

But of course you are right that geeky copulas and PhDs lend a "spurious air of technicality" to any con job.

CW said...

Thanks for prompting me to link to this other related piece in Wired:

Road Map for Financial Recovery: Radical Transparency Now!

I don't necessarily endorse this manifesto, because I think transparency requires more than data availability, even if the data is in a standard, machinable form. What is also required is avoidance (prohibition) of gratuitous, reckless complexity. From the sidebar to the above piece:

Wired: Do you think your degree in applied physics means you look at the market differently?

[Dan] diBartolomeo: One of the things you learn in engineering is to be rigorous. If you build a bridge that falls down on a windy day, there's going to be hell to pay. Financial markets are not like that; they are very noisy. It's hard to tell who's skillful and who's just lucky. And a lot of analyses are done in extremely haphazard, primitive ways, but the investing public doesn't know any better.

CW said...

PS: diBartolomeo's parting remark in that Wired interview —

Wired: So could better math have prevented the market crisis?

diBartolomeo: People are investing in complex securities they don't understand. The big failures aren't data failures; they aren't issues of "We don't know." They're issues of "We don't want to make the effort to be rigorous."

Ian Smith said...

You will notice Steve has put in bold the part which confirms his theory that he is th world's smartest man --- physicists are better than mathematicians.

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