Genetic Programming in Statistical Arbitrage

1. Genetic Programming in Statistical Arbitrage Philip Saks PhD Seminar 17.10.2007

2. Contents • Introduction • Genetic Programming • Clustering of Financial Data • Data • Framework • Results • Conclusion

3. 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.

4. 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.

5. 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

6. Clustering of Financial Data

7. 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).

8. 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.

9. Results • Trading on VWAP, assuming 1bp market impact

10. Sensitivity Analysis

11. Stress Testing I

12. Turnover Analysis

13. Transaction Cost Implications

14. 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.