Exchange Traded Horserace Betting Fund with Deterministic Payoff A Mathematical Analysis of a Profitable Deterministic Horserace Betting Model

Transcription

1 Exchange Traded Horserace Betting Fund with Deterministic Payoff A Mathematical Analysis of a Profitable Deterministic Horserace Betting Model Craig George Leslie Hopf BSc, MIntFin Griffith School of Environment Science, Environment, Engineering and Technology Griffith University Submitted in fulfilment of the requirements of the degree of Master of Philosophy December 2013

2 Abstract The horserace betting market is a subset of the financial market space, and wagering typically inherits a defined return to risk trade-off. For horserace betting input into institutional portfolio to be plausible, the payoff to risk trade-off from betting must be acceptable for the fund when compared with the return risk trade-off from the existing mainstream assets included in portfolio investment. A new paradigm for horserace betting modelling and investing is acclaimed in this thesis, as premiss for betting input into institutional portfolio. An exchange traded betting fund is developed in the thesis that is able to generate pre-race (and within-race) investment arbitrage that offers an acceptable, defined return risk trade-off for the risk averse investor. The extensive former horserace betting market stochastic modelling theory that forecasts racer expected outcomes and payoff, is today succeeded by this research that develops a deterministic horserace betting model (and algorithm) that generates defined payoff for the fund. This deterministic betting model challenges the existing semi-strong efficient market hypothesis toward horserace betting that no betting strategy consistently outperforms the financial market s benchmark return. Subsequently, the primary research (alternative) hypothesis tested is profitable exchange traded horserace betting fund with deterministic payoff exists for acceptable institutional portfolio investment. The exchange traded betting fund is constructed as a savings fund that provides a continuous rate of return. The driver for the fund, a deterministic betting model, is constructed from both new and existing theory. The deterministic model optimizes field win and place wagering to determine a feasible, actual payoff risk trade-off. Investment arbitrage is defined as a positive return to nil risk trade-off and is the optimal solution for the research. Mathematically derived in the thesis is the multiple system optimization theorem over 1

3 space to validate optimal solution generated from the deterministic betting model. The results and analysis from statistical testing of a global stratified data sample accept two subhypotheses for the research - DBM outperforms the stochastic horserace model benchmark, and ETBF outperforms the SPDR S&P/ASX 200 fund. These conclusions of acceptance legitimize the research s primary hypothesis that encompasses the subhypotheses. Essentially, the primary hypothesis was accepted at the ninety-five percent confidence level from results of test sample, to endorse an exchange traded horserace betting fund with deterministic payoff into financial market. The profound implications by achieving successful solution for the primary and secondary research questions is to warrant practical examination of horserace betting input in portfolio, for benefit of financial markets. 2

4 Declaration of Dissertation Authenticity I make declaration that this dissertation s work has not previously been submitted in whole or in part for the award of degree or diploma from any university. I unequivocally declare that this dissertation does not contain any material which has been previously published or written by any other person, except where due reference is made throughout the literature. Craig Hopf date 3

5 Table of Contents Chapter One: Research Introduction 1.1 Betting market background Betting exchange theory and technology General problem Research question and objectives Significance of research Thesis structure Chapter summary.19 Chapter Two: Literature Review 2.1 Stochastic horserace betting model theory Set permutation fundamentals Racer rank order notation Technical horserace betting models and application Fundamental horserace betting models and application Fund return to risk optimizer techniques Mean variance portfolio optimization Forward search portfolio optimization Chapter summary

6 Chapter Three: Research Methodology 3.1 Research questions and objectives Pre-race stage Primary hypothesis and sub-hypotheses statements Racing populations, parameters and statistics Deterministic betting model design Exchange traded betting fund design Race event Sample and data selection DBM and ETBF workings Post-race stage DBM and ETBF results and analysis Primary hypothesis and sub-hypotheses testings Chapter summary...58 Chapter Four: New Paradigm for Horserace Betting 4.1 Mathematical analysis of deterministic betting model (DBM) Complex number system properties DBM - objective function and constraints Multiple system optimization (MSO) theorem and application..64 5

7 4.1.4 DBM workings DBM arbitrage Mathematics of ETBF Chapter summary...70 Chapter Five: Research Results and Analysis 5.1 Post-race analysis Model and fund analysis Day one race results Day two race results Day three race results Day four race results Day five and six race results Primary hypothesis and sub-hypotheses tests Sub-hypothesis one test Sub-hypothesis two test Primary hypothesis test Post-race discussion ETBF portfolio illustration Chapter summary

8 Chapter Six: Conclusion, Limitation and Implication...92 Appendix A1 Multiple system optimization (MSO) theorem proof.96 A2 TrackInvest algorithm. 98 References.107 7

9 Figures and Tables List List of Figures Figure 2.1 (a) & (b) SVM Optimum Separation Hyperplane...33 Figure 2.2 Nonlinear Space Transformation...35 Figure 2.3 Efficient Frontier...38 Figure Figure 3.1 EEN Betting Matrix...50 Figure 3.2 Pool Wagering...54 Figure 5.1 ETF Portfolio Efficient Frontier 89 Figure 5.2 ETF Portfolio Curve..90 List of Tables Table 3.1 Racing Populations...50 Table 3.2 Population Parameters and Sample Statistics..51 Table 3.3 DBM and SBM variables.55 Table 4.1 TrackInvest Model Field Win & Place Payoff..65 Table 4.2 TrackInvest Model Field Win Payoff...67 Table 4.3 TrackInvest Model Multibet Field Win Payoff.68 Tables DBM & SBM Field Win Bet Payoff%

10 Table 5.7a DBM Accumulative Payoff Cross Tabulation..79 Table 5.7b SBM Accumulative Payoff Cross Tabulation...80 Table 5.8 Model Regional Mean Alpha Race Returns Daily and Weekly Averages..81 Table 5.9 Fund Alpha Race Returns Daily and Week Average...82 Table 5.10 Betting Strategy Sample Statistics...82 Table 5.11 ETF Daily Payoffs.87 Table 5.12 ETF Mean Payoffs, Standard Deviations and Covariances..88 Table 5.13a: Portfolio ETF Weightings, Means and Standard Deviations..88 Table 5.13b: Portfolio ETF and ETBF Weightings, Means and Standard Deviations 89 9

11 Acknowledgement I wish to extend my sincere gratitude to my family, and to my supervisor Dr Gurudeo Anand Tularam who has continually maintained support and assistance throughout the thesis proposal development and finalization; and to the Griffith University academia, the Environmental Futures Research Institute and Griffith Enterprise division for their ongoing support, contribution, and qualified, shared vision for horserace betting to participate as a mainstream asset class for portfolio investment, and the forward benefit a blue chip investment provides for society. 10