Chaos Theory in Economics JINGWEI SHE 02/14/2016

The Subprime Crisis ◦Originated in the United States in 2007 ◦One of the worst financial disasters ◦For the first time, problems that originated in one country had global effects leading the world’ economy to a serious recession.

Failure of the Current Financial Models ◦Neoclassical theory (today’s mainstream financial paradigm) fail to fully explain the increasing complexity of world financial markets ◦The current model oversimplifies reality ◦Works under ideal or normal conditions ◦For example, market is not 100% efficient ◦It’s necessary to look for some alternatives ◦Chaos Theory might be one of them

Background: Chaos Theory ◦“The qualitative study of unstable aperiodic behavior in deterministic non-linear dynamical systems” ◦Highly sensitive to changes in the initial conditions ◦Involves nonlinear feedback forces that can produce unexpected results ◦Chaos Theory allows us to study changing environments with nonlinear dynamics, discontinuities and feedback systems

Background: the Science of Fractals ◦A fractal is a shape made of parts similar to the whole in some way ◦Self-similar when it scales up or down ◦Self-affine if it scales more in one direction than another

Background: Chaos Theory and the Science of Fractals ◦The Science of Fractals works closely with Chaos Theory ◦Starting values of fractal functions can change the value of the function randomly within the boundaries ◦For example: Mandelbrot Set ◦Very simple feedback equation: z n+1 = z n 2 + c ◦Highly complex results

Chaos Theory and Finance ◦The theory describes markets as a system with local randomness and global determinism Neoclassical Model Efficient Market Random Walk Theory Normal Distributions Chaos Theory Model Fractal Market Multifractal Process Fractal Distributions

Fractal Financial Market ◦Benoit Mandelbrot, father of fractal geometry, discovered the self- similar property of financial markets ◦The movements of a stock all look alike when the chart is enlarged or reduced so that it fits the same time and price scale

Multifractal Process

Multifractal Process (cont’d) ◦As a result, each piece ends up with a shape roughly like the whole ◦The property is built in ◦A few generators will yield the relatively tranquil picture of the market, as predicted by the Modern Portfolio Theory ◦Yet those generators are very special ◦The advantage of the Fractal Market Theory is that it can also describe market in tumultuous trading conditions ◦The method can be altered to show the volatility of the market

Multifractal Process (cont’d)

Implications ◦The new theory explains the discontinuity in stock price movements and the large volatility within the market ◦Using historical market data, a fractal generator can be developed ◦Can be used by traders or other market strategists to stress-test the portfolio or forecast the future trend of the market

Research Proposals ◦Research on the existence of chaos in market prices ◦Explore how Chaos Theory can be used in other fields of Economics and Finance

References ◦Chaos Theory and the Science of Fractals in Finance, Tania Velasquez, 2010 ◦How Fractals Can Explain What’s Wrong with Wall Street, Benoit B.Mandelbrot, 2008

Q&A ◦Thanks!