Genetic Programming in Statistical Arbitrage Philip Saks PhD Seminar 17.10.2007

Contents Introduction Genetic Programming Clustering of Financial Data Data Framework Results Conclusion

Introduction

Genetic Programming

Clustering of Financial Data

Data

Framework

Results

Conclusion

Introduction To develop an automated framework for trading strategy design, by employing evolutionary computation in conjunction with other machine learning paradigms The present framework utilize genetic programming Much of the existing financial forecasting using GP has focused on high-frequency FX [Jonsson, 1997][Dempster and Jones, 2001][Bhattacharyya et al, 2002] and the general consencus is that there is predictability, and excess return is achievable in the pressence of transaction costs For stocks, the results are mixed [Allen and Karjalainen, 1999] do not significantly out-perform the buy-and-hold on S&P500 daily data, but [Becker and Sheshadri, 2003] do on monthly.

To develop an automated framework for trading strategy design, by employing evolutionary computation in conjunction with other machine learning paradigms

The present framework utilize genetic programming

Much of the existing financial forecasting using GP has focused on high-frequency FX [Jonsson, 1997][Dempster and Jones, 2001][Bhattacharyya et al, 2002] and the general consencus is that there is predictability, and excess return is achievable in the pressence of transaction costs

For stocks, the results are mixed [Allen and Karjalainen, 1999] do not significantly out-perform the buy-and-hold on S&P500 daily data, but [Becker and Sheshadri, 2003] do on monthly.

GP I EC is a concept inspired by the Darwinian survival of the fittest principle – The rationale being, that natural evolution has proved succesfull in solving a wide range of problems throughout time, hence an algorithm that mimics this behavior, might solve a wide range of artificial problems The concept was pioneered by Holland (1975) in the form of Genetic Algorithms (GA) A GA is essentially a population based search method, where each candidate solution is incoded in a fixed length binary string. The population evolves, via mainly three operators, selection, reproduction and mutation. The selection process is based on the survival of the fittest principle.

EC is a concept inspired by the Darwinian survival of the fittest principle – The rationale being, that natural evolution has proved succesfull in solving a wide range of problems throughout time, hence an algorithm that mimics this behavior, might solve a wide range of artificial problems

The concept was pioneered by Holland (1975) in the form of Genetic Algorithms (GA)

A GA is essentially a population based search method, where each candidate solution is incoded in a fixed length binary string.

The population evolves, via mainly three operators, selection, reproduction and mutation.

The selection process is based on the survival of the fittest principle.

GP II GP’s are basically GA’s in which the genome contitutes hierachical computer programs Using this representation, we can solve problems in a wide range of fields such as, symbolic or ordinary regression, classification, optimal control theory etc. since each of these areas “can be viewed as requiring discovery of a computer program that produces some desired output for particular inputs” (Koza, 1992) Tree representation of programs, function & terminal Set Evolutionary operators: selection, cross-over & mutation

GP’s are basically GA’s in which the genome contitutes hierachical computer programs

Using this representation, we can solve problems in a wide range of fields such as, symbolic or ordinary regression, classification, optimal control theory etc. since each of these areas “can be viewed as requiring discovery of a computer program that produces some desired output for particular inputs” (Koza, 1992)

Tree representation of programs, function & terminal Set

Evolutionary operators: selection, cross-over & mutation

Clustering of Financial Data

Data Hourly VWAP prices and volume for banking stocks within the Euro Stoxx Universe, covering the period from 01-Apr-2003 to 29-Jun-2007 (8648 oberservations).

Hourly VWAP prices and volume for banking stocks within the Euro Stoxx Universe, covering the period from 01-Apr-2003 to 29-Jun-2007 (8648 oberservations).

Framework Evolve trading rules with binary decisions We consider the classical single tree setup, but also a dual tree framework, where buy and sell rules are co-evolved. The training set comprises 6000 samples, while the remaining 2647 are used for out-of-sample testing 10 runs are performed for each experiment.

Evolve trading rules with binary decisions

We consider the classical single tree setup, but also a dual tree framework, where buy and sell rules are co-evolved.

The training set comprises 6000 samples, while the remaining 2647 are used for out-of-sample testing

10 runs are performed for each experiment.

Results Trading on VWAP, assuming 1bp market impact

Trading on VWAP, assuming 1bp market impact

Sensitivity Analysis

Stress Testing I

Turnover Analysis

Transaction Cost Implications

Conclusion It is possible to discover profitable arbitrage trading rules on the Euro Stoxx banking sector. A cooperative co-evolution of buy and sell rules are beneficial to the classical single tree structure. Optimizing in the pressence of transaction costs makes a difference – There should be correspondence between assumption and application for optimal performance.

It is possible to discover profitable arbitrage trading rules on the Euro Stoxx banking sector.

A cooperative co-evolution of buy and sell rules are beneficial to the classical single tree structure.

Optimizing in the pressence of transaction costs makes a difference – There should be correspondence between assumption and application for optimal performance.