Buy Low, Sell High, Model First
by David Pescovitz
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Before
joining the Berkeley faculty this year, Andrew Lim was a
professor of Industrial Engineering & Operations Research
at Columbia University. (Click for larger
image.)
David Pescovitz photo
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As any Wall Street
gambler can attest, Yogi Bera was spot on when he said that the
hardest thing to predict is the future. While a computational crystal
ball remains a pipe dream, UC Berkeley professor Andrew Lim is betting
that a form of mathematical analysis traditionally used for the
likes of aircraft control and Internet traffic management could
enable investors to make wiser decisions.
"When people started using quantitative methods to make decisions
in financial markets, they had very simple models (to simulate the
marketplace)," says Lim, a recent addition to the Department
of Industrial Engineering and Operations Research. "The world
isn't a simple place though and their models were not consistent
with market observations. As a consequence, the optimal stock portfolios
based on these models might not work very well in the real world."
The oversimplified models, Lim explains, were based on assumptions
that certain parameters within the marketplace were predictable.
For example, an investor using a traditional mathematical model
to choose a portfolio that would hopefully maximize return with
minimal risk might assume that a stock's average rate of increase
and its volatility are relatively fixed for a given period of time.
Of course, things like a CEO's resignation or an announcement from
the Federal Reserve can easily cause volatility in a particular
company's stock price, or the market in general. Investors weren't
ignorant though, they just did the best they could with the available
models.
"People recognized that these parameters are random,"
Lim says. "Traditional techniques can't handle those random
parameter models very well, and new methods that were developed
for this purpose resulted in equations that were difficult to solve.
The models are just far too complicated to use."
Lim's approach
to financial market analysis is based in control theory, the mathematical
theory of optimal decision-making over time in uncertain environments.
His specific research focuses on stochastic and linear-quadratic
control problems, decision-making problems where you'd like to maximize
a figure — your investment in this case — at minimal risk
based on unpredictable variables that change over time.
While the bulk of Lim's research centers on the development of models
and methods for portfolio selection, he's recently expanded the
scope of his control theory applications to include credit risk
management. For instance, an imaginary company, Acme Industries,
might contract with John Doe Inc. to provide a particular good or
service that Acme depends on for their success. By making this agreement,
Acme has exposed itself to a certain amount of credit risk because
there is a chance that John Doe Inc. might default on their promises.
"The question here is how can you hedge the default risk,"
Lim says. "How do you minimize risks that you may now be facing
due to a contract you've entered with a company that may look unreliable?"
Data for these kinds of mathematical models is plentiful, Lim explains.
For instance, if most of John Doe Inc.'s business comes from supplying
parts to car manufacturers, you might observe the auto industry
to get a sense of John Doe Inc.'s financial stability. Additional
insights may come from accounting data or SEC filings. Once all
the information is gathered and analyzed using accurate the control
theory-based models, Acme might be better equipped to make decisions
on future dealings with John Doe Inc. Or, they might set some funds
aside, just in case John Doe Inc. does leave them in a lurch.
"Even small improvements in financial models can result in
huge savings," Lim says.
Andrew Lim's Home Page
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Writer, Researcher: David Pescovitz
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Updated 9/30/02.
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