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Chaos Theory and Modern Trading. By Paul Cottrell, BSc, MBA, ABD. Introduction. Author Complexity Science, Behavioral Finance, Dynamic Hedging, Financial Statistics, Chaos Theory Proprietary Trader Energy and Currency Dissertation - PowerPoint PPT Presentation
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ByPaul Cottrell, BSc, MBA, ABD
Chaos Theory and Modern Trading
Author Complexity Science, Behavioral
Finance, Dynamic Hedging, Financial Statistics, Chaos Theory
Proprietary Trader Energy and Currency
Dissertation Dynamically Hedging Oil and
Currency Futures Using Receding Horizontal Control and Stochastic Programming
Introduction
The behavior of dynamic systemsMany systems are non-linear
Unpredictable results can occurDeterministic chaos
Simple chaos where no stochastic functions are in the system
Non-deterministic chaosComplex Chaos where stochastic function are in
the system
What is Chaos Theory?
Simple Chaos
Lorenz System
Double fulcrum Pendulum
Complex Chaos
• Human misbehavior
• Random news events
• Feedback loops
Black Swan vs. Dragon King
Unknowable Knowable
Theory of EmergenceStarted in cosmology
Big Bang leads to further particle evolution and the emergence of materials.Which leads to further complex arrangement
Life Social Organization
Economic or financial emergenceEconomic development Systemic riskContagion
Key takeawayA complex system can evolve into unpredicted pathways
What evolves from Chaos?
Complexity ScienceThe study of complex systems
Using simple rules for agentsSelf organizing behavior Interactions that have a magnifying effect
The Theory of Emergence
How does this relate to trading?
• The “Market”
• Complex organism
• Self organizing• Adam’s invisible
hand
• Price action• Asymmetric
• Information • Asymmetric
How does this relate to trading? (Cont)
• Traders use models
• Models have certain assumptions on price action
• Models can be used incorrectly and cause a system failure• Lehman Crash• Flash Crash
(Maybe?)• Account drawdown• Mass
unemployment• Big Macs too
expensive
The Efficient Market HypothesisAssumptions
Rational investors Information cannot be used to make above normal profitsThe stochastic variations in returns mean to zeroThe market should always be in steady state
ProblemsTraders are greedy and not rational
Due to the Dopamine response mechanismNew information is not completely in the priceProfits can be statistically above average for some groupsStochastic variations in returns can lead to bubbles and
bursts.
Economic Models
Fundamental EquilibriumWhen price is close to “economic value”Could be assumed at a 200 moving average on a
long duration chartFundamental analysis rule the game
Speculative EquilibriumWhen price is above or below “economic value”Chartists or Quants rule the gameMost assets are in Speculative Equilibrium
Evidence in the 50 period moving averageHas mean reverting characteristics
Behavioral Finance
Chaotic Returns• Returns graphed• Daily Returns, Weekly, Monthly• S&P 500• Lower Right Graph
• Dow 30• Monthly
• State Space• X-axis return (t-1)• Y-axis return (t)
• Empirical evidence • That returns are stationary
• In daily returns• Non-stationary
• At larger time scales.• Shows emergence of tend
Fractal Efficiency Ratio
• Ratio to determine level of chaos• “C” is the return at time (t)• Ratio = 1
• Pure trending• Ratio = 0
• Pure Chaos
Mandelbrot Markets
H < 0.5mean reversion
H = 0.5Brownian Motion
H > 0.5Trending
A possible method to describe the market in terms of smoothness.Lower “H” value the smoother the surface of the market.
There is trading time and clock time Clock time is standard time and is constant in velocity Trading time is changing
Velocity (first derivative) depends on the speed of price For example:
During high volatile market days price action is higher Leading to faster time in trade time Lower volatile days have slow trade time
Many traders use terms like Rapid price movement or it was a slow trading day
Time is relative to the level of the price change Can be used to help model discontinuous markets.
Bridge gap with a Brownian motion bridge. Mandelbrot Time can help frame volatility in terms of delta time.
Similar to space-time bending with gravity. Trade-time bends with level of price action.
Mandelbrot Time
The market is a complex system
Usually in speculative equilibrium Volatility and correlations are not
constant
Market participants can profit on average above zero mean
Systems that can monitor the telemetry of the “market” might be able to monitor the endogenous risk in the market (Dragon Kings)
Exogenous risks do exist (Black Swans)
Hedging strategies can, to some degree, mitigate risk factors.
Conclusion