Scaling Laws and Trading Models Richard Olsen Overview

Scaling Laws and Trading Models Richard Olsen

Overview Why we need trading models? Understanding the nature of time What are scaling laws? Lego building blocks for development of financial engines • Wiki. Fin. Climate for trading models and more • The vision of the future • • Olsen

Global Financial Assets • • • Equities Government bonds Financial sector bonds: Corporate bonds: Securitized loans Nonsecuritized loans: 50 trillion 47 trillion 42 trillion 11 trillion 13 trillion 60 trillion Global Financial Assets: 225 trillion or 310% WDP Olsen

How To Manage These Assets? Olsen

Why should we manage assets? • Self-interest • Economy is non-zero sum system, where information can accumulate and increase wealth. Let us start… Olsen

How Do People Manage Assets? Judgemental, gut feeling…no automation Chess is a difficult game, but the reality of the economy and finance is ever more complex. Intricate feedback processes with relaxation effects at different time scales. Give up in despair or crack the problem? Olsen

Trading Strategies Of Quant Fund • Directional trading: – Fundamental systems – Universal systems • Intraday models • Equity statistical arbitrage: – Technical strategies – Fundamental strategies • Volatility arbitrage • Directional volatility Only 5 percent performance for 2014 Olsen

Technical Trading Terminology • • • Overall trend Support Resistance Momentum Buying/Selling pressure Relative Strength – – – Strength of the current trend Maturity or stage of current trend Reward to risk ratio of a new position Potential entry levels for new long position Fundamental systems Olsen

Weakness of Technical Analysis • • • Analyst bias Open to interpretation Too late Always another level Trader’s remorse No consistent theory Olsen

Fundamental Analysis • Economic analysis • Industry analysis • Company analysis • Buy and hold investors • Contrarian investors • Value investors Olsen

Fundamental Valuation Example Olsen

Weakness Of Fundamental Analysis • Designed for 1 week, month, quarterly and longer time horizons • Open to interpretation • Model quality unstable • Too late • Assumptions of theory raise questions • Open question how to map analysis into real time algorithm? Olsen

Improved Performance • Global Financial Assets: 225 trillion • Improved performance of 1% is 2. 25 trillion USD Pharmaceutical, computer and other industries invest heavily in R&D – why not finance? Where are the big R&D companies in finance? Olsen

Question Of Century How can investment strategies be made to be consistently profitable? Olsen

Markets are not a closed system: profits – losses zero Markets are part of real economy and determine asset prices. They are source of equity for companies and provide liquidity. Price overshooting is cost to economy. Olsen

Market & Limit Orders • Market orders: trader knows that he can execute ‘now’, but does not know the price. • Limit orders: trader knows the price at which he wants to execute, but does not know, when order will be processed or if at all. Olsen

Transaction Costs Trading strategies without transaction costs are highly profitable. How to remove transaction costs? Market making strategies to manage positions! Olsen

Answer To Question Investment strategies generate alpha, if they provide a benefit to economy and society: • liquidity provision • price stabilization Olsen

Price Action Of Financial Instrument Coastline length of all price movements in one year: 1600% (potential profit without leverage after paying for transaction costs) Olsen

1600% Coastline length is result of imbalances of buying and selling activity Objective of investment strategy: increase volume of trading at ever smaller imbalances and reduced overshoots. • Increased liquidity • Price stability Olsen

Risk management: diversification Maximum Up/Down Move In 1 Year: For one asset: +/- 30% For diversified cash portfolio: +/- 0% Olsen

New Methodology Olsen

Automation • 1000+ instruments to manage. • Coastline of price curve is function of resolution: ‘high frequency more opportunity and diversity’ • Complexity of markets • Speed of events Automation of investment and trading strategy is necessity. Olsen

Investment Approach Strategies provide liquidity and stabilize markets. Price overshoots are opportunity to take ‘counter-trend’ positions with dynamic market making. High diversification Olsen

Model Design? Olsen

Model Requirements No curve fitting No model degredation over time Fractal: same model at different scales No black boxes: ‘story line’ Parsimonious Lego-type model building blocks for continued model enhancement. • Operate real time without hand holding • • • Olsen

Inspiration From Natural Sciences Olsen

Model Components: Agents Olsen

One System Or Multi-system Problem? • In relativity theory twins grow old at different speeds as a function of the movement of their systems • In financial markets and economics in general every economic agent is a system on his own that interacts with other system • Financial markets is ‘multi-system’ problem! Olsen

Tool: Scaling Laws Olsen

What Are Scaling Laws? Variables: A, B --> fixed proportionality Different terms to describe this phenomon: • Scaling laws • Scale invariance • Laws of nature Olsen

Lever: Tick-count scaling law Olsen

Signature of Scaling Law? Log-log plot: straight line is signature Olsen

Estimation Of Scaling Law Exponent Dimension Y Scaling law Dimension X • Values of exponents are a function of market environment. • Every data point enters into computation of each threshold of scaling law: efficient use of available market data. • Traditional models discard a lot of data: they have a preferred time intervals of sampling, e. g. daily data. • Data efficiency is foundation for adaptive models. Olsen

Lets start… Olsen

Time Olsen

Time Series Analysis Involves Sampling Population Sample Correct sampling method is important for success! Olsen

How To Sample A Time Series? • • Tick-by-tick? Every second? Every minute, hour, day, week, month…data? How to interpolate, if no data is available? Olsen

Sampling Data In Physical Time Physical time is not dynamic and does not capture information of extremes. Olsen

If We Increase Sampling Frequency? Increasing frequency of sampling adds noise. Olsen

Increased Sampling Reduces Signal Quality Data collected within time interval: Noise Signal • • Basic problem: information is in tails. Signal to noise ratio deteriorates with increased sampling. Issue: Signal is conditional to specific cutoff times. This raises the question what is time? Olsen

Conjecture There is no abstract time. Time tracks the identity of a particular system and records the events of interaction with other systems. Olsen

Physical Time • • Physical time maps the rotation of the earth. It is a uniform scale: X = (X_1, X_2, X_3 …. ) Events have equal weights. There are fixed equi-distant time intervals of 1 minute, 1 hour, 1 day, 1 week…. Olsen

Pendulum triggers time events in clock. Olsen

Actual Time Series • Discrete events, not continuous • Intervals are not equally spaced. • Volumes are spurious. Olsen

Definition Of Event Time An event is a price reversal or excursion of x percent from a local price extreme as defined by the observer. Olsen

Illustration Of A Event Time A t-event is defined as a price reversal from local extreme by x %. In our papers we call a price reversal a directional change. Olsen

Schemata Of Event Time Olsen

Benefit Of Event Time In calendar time the outcome of an analysis depends on the exact starting time; in event time extremes are the pointers and bring event time into sync whatever the exact starting point. Olsen

Price Overshoot Size of overshoot between events. T-events are separated by so-called ‘overshoots’. Olsen

How Big Is An Overshoot On Average? ? Olsen

Empirical Evidence Valuable ex ante information Overshoots are on average equal to threshold; this is true for all observed thresholds. Olsen

A Frame Of Reference: Scaling Laws Olsen

Lever: Tick-count scaling law Olsen

Established scaling laws Müller et al. , J. Bank Finance, 1990: Mean absolute change of mid-price to time Guillaume et al. , Finance Stoch. 1997: Number of directional changes to thresholds Olsen

Other Scaling Laws 2. Average yearly number of price moves 3. Average maximal price move during a time interval 4. Average duration of a price move 5. Average duration of a directional change Olsen

More Scaling Laws Decomposition of total price move into directional-change and overshoot 6 -14. Leads to 9 additional scaling laws Olsen

More Scaling Laws 15 -17. Cumulative price moves We find 12 independent new scaling laws. Olsen

A Grid of 12 Scaling Laws Olsen

Any Number Of Scaling Laws? Property Y d e v r bse l Sca aw L g in O Central Limit Theorem Event Operator: X • Conjecture 1: due to central limit theorem output of property y conditional to event filter X is a scaling law. Olsen

Scaling Law As Abstract Lever Dimension Y Scaling law Changing market environments Dimension X • The scaling laws are the levers that ensure consistent mapping of events in X to action in Y. • Markets are in different states of excitement; it is non-trivial to scale parameters correctly. Olsen

Scaling Law As A Lever Property Y Scaling Law Event Operator: X • We can define sophisticated event operators and construct any number of scaling laws. • The scaling laws are the levers that ensure consistent mapping of events in X to property Y. • Estimation of scaling law exponents is data efficient and can be updated on an ongoing basis. • We can build a grid of scaling laws to create a comprehensive and dynamic framework to trigger actions. Olsen

Events Are Units Of Measurement 4 Excursion 3 2 Event 1 The events are the natural units to measure the size of excursions; the time points of actions are set in terms of event units. Olsen

Code Language 4 Excursion 1 Event Wait… 3 2 Wait… Go short 0. 25 Wait… Models include ‘atoms’ that follow different decision rule defined by code language: big diversity! Olsen

Example: Coast-line Trader Model algorithm estimates scaling law exponent for ‚overshoot scaling law‘. Agents of coast-line traders are initialized by event triggers, event triggers manage position and eventually close position. Olsen

Performance Sharpe Ratio around 0. 8 for FX portfolio Olsen

Key Concepts Of New Models • • Engine Agent-based Fractal Intrinsic time Grid of scaling laws Events trigger actions Emergent Olsen

Model Applications • • • Risk models Predictive models Macroeconomic models Quantitative investment strategies Big data Olsen

Discussion • Breakthrough in technology • Consistent performance • Technology: win-win outcome for investor and economy • Recycling of energy between financial markets and real economy • Real work has just started. Olsen