By Paul Cottrell, BSc, MBA, ABD

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

The behavior of dynamic systems Many systems are non-linear Unpredictable results can occur Deterministic chaos Simple chaos where no stochastic functions are in the system Non-deterministic chaos Complex Chaos where stochastic function are in the system

Lorenz System Double fulcrum Pendulum

Human misbehavior Random news events Feedback loops

Unknowable Knowable

Theory of Emergence Started 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 emergence Economic development Systemic risk Contagion Key takeaway A complex system can evolve into unpredicted pathways

Complexity Science The study of complex systems Using simple rules for agents Self organizing behavior Interactions that have a magnifying effect

The “Market” Complex organism Self organizing Adam’s invisible hand Price action Asymmetric Information Asymmetric

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 Hypothesis Assumptions Rational investors Information cannot be used to make above normal profits The stochastic variations in returns mean to zero The market should always be in steady state Problems Traders are greedy and not rational Due to the Dopamine response mechanism New information is not completely in the price Profits can be statistically above average for some groups Stochastic variations in returns can lead to bubbles and bursts.

Fundamental Equilibrium When price is close to “economic value” Could be assumed at a 200 moving average on a long duration chart Fundamental analysis rule the game Speculative Equilibrium When price is above or below “economic value” Chartists or Quants rule the game Most assets are in Speculative Equilibrium Evidence in the 50 period moving average Has mean reverting characteristics

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

Ratio to determine level of chaos “C” is the return at time (t) Ratio = 1 Pure trending Ratio = 0 Pure Chaos

H < 0.5 mean reversion H = 0.5 Brownian Motion H > 0.5 Trending 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.

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.