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

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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

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 Started in cosmology
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 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
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Systemic risk
Contagion
Key takeaway
 A complex system can evolve into unpredicted pathways

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 The study of complex systems
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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
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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
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 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.

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

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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.
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Similar to space-time bending with gravity.
Trade-time bends with level of price action.

 The market is a complex system
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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.