51����.

Esteban León's "econophysics" research this summer paired the unlikely mates of physics and Wall Street, like blending a lab coat and a pinstripe suit. León, a 51���� senior from Quito, Ecuador, used principles of quantum physics to better understand how financial markets function.

He wanted to see how science's discoveries about how the smallest particles of light and matter behave would provide insights into financial market behavior. What could wave functions from different quantum systems teach us about Apple or Ford stocks?

The idea of analyzing these two complex systems at such a granular level netted León a 10-week summer grant by the 51���� Research Initiative: stipend, room and board, and travel and expense funding for 10 weeks of collaborative research with a faculty mentor -- in his case, two faculty mentors, one from each of his majors, physics and economics.

Searching for Patterns

León was looking for patterns that show up in the two different fields of study. He applied "wave-function" equations on the probability of finding a specific quantum particle in a specific region of space to the probability of a certain stock market return happening under specific conditions.

To tie it all together, he applied "goodness of fit" probability tests, to compare both of the complex systems. He found that some models fit both systems well and some didn't. That's research.

He also found that research also means adjusting protocols on the fly. Early in the summer, León pivoted to home in on the Dow Jones Industrial Average and the Standard and Poor's 500 indices, rather than risk getting too tangled up on the infinitely more complex landscape of options pricing, as he had originally proposed.

He learned research means building on work that's gone before. During 10 weeks planted in front of multiple computer screens, León made liberal use of a wave function equation he worked on last summer with Kevin Gutierrez '20; 51���� Professor and Chair of Physics Mario Belloni, also one of León's summer mentors; economics professor Mark Foley; and Penn State Professor of Physics Richard Robinett.

Transdisciplinary View

León traces his transdisciplinary view of financial markets to a behavioral economics class in game theory he took with Foley at the start of his sophomore year, when he had just declared a physics major.

"Game theory is about how people can make an optimal decision based on others' decisions," León explained.

One illustration of quantum mechanics theory familiar to Big Bang Theory fans is the Schrödinger's cat thought experiment: The hypothetical cat in a hypothetical box can be considered to be both dead and alive, until the box is opened and it is revealed to be one or the other. On the other hand, a game theory example, the prisoner's dilemma, ups the ante with two hypothetical prisoners playing off each other in separate interrogations, to see who will betray whom, and to what potential advantage. Play that kind of game on Wall Street and the ante goes up even more.

At summer's end, León's work "somewhat corroborated" the "Efficient Market Hypothesis," which assumes that all agents in the economy make rational decisions and that information about stocks is available to every agent.

"In reality, this is rarely the case," said León. "My personal view is that, for future research, incorporating elements of psychology and biology will yield better results."

This fall, León will present at the North Carolina Section of the American Association of Physics Teachers (NCS- AAPT) meeting and in 51����'s Summer Research Symposium in early September.

John Syme

josyme@davidson.edu

704-894-2523