1. Proc IWIF-II, 2007, Chengduwww.swingtum.com/institute/IWIF 1 Model of Financial Market : Insights and its Possible Application C. H. Yeung 1, K. Y. Michael Wong 1. Y. C. Zhang 1,2 1 Department of Physics, the Hong Kong University of Science and Technology, Hong Kong, China 2 Institut de Physique Théorique, Université de Fribourg, 1700 Fribourg, Switzerland IWIF-II

2. www.swingtum.com/institute/IWIF2 Proc IWIF-II, 2007, Chengdu Outline Introduction Our model (Wealth Game) VS Minority Game ? Price Sensitivity and Market Impact – Phase Diagram of final states and wealth Market Makers, Transaction Cost and Evolutions – Positive gain for agents and market makers Application on real data: Trading with Hang Seng Index Conclusion

3. www.swingtum.com/institute/IWIF3 Proc IWIF-II, 2007, Chengdu Introduction Minority Game (MG) – The model by D. Challet and Y. C. Zhang in 1997 Successful and simple model of Financial Market which states that the minority choices will win One of the main concern for investors: negative-sum (MG) VS positive-sum (Real market) ?

4. www.swingtum.com/institute/IWIF4 Proc IWIF-II, 2007, Chengdu To include more realistic aspects … 1. What modifications are we making? 2. What important aspects of real markets should be added to capture basic features? 3. Negative sum? Positive sum? Zero sum? 4. Can we apply these financial models on real financial data ?

5. www.swingtum.com/institute/IWIF5 Proc IWIF-II, 2007, Chengdu 1. What modifications are we making?

6. www.swingtum.com/institute/IWIF6 Proc IWIF-II, 2007, Chengdu The Model Individual actions Collective actions Price changes N agents Each agent makes decision from his/her best strategy (higher virtual payoff)

7. www.swingtum.com/institute/IWIF7 Proc IWIF-II, 2007, Chengdu The Strategy +1/ -1/ 0, buy/ sell/ hold decisions (different from MG) Max. Allowed Position K

8. www.swingtum.com/institute/IWIF8 Proc IWIF-II, 2007, Chengdu Wealth = Cash + Stock Values in hand No. of stock in hand, Position Remark : For MG,

9. www.swingtum.com/institute/IWIF9 Proc IWIF-II, 2007, Chengdu 2. What important aspects of real markets should be added to capture basic features? (1) Price sensitivity & (2) Market impact

10. www.swingtum.com/institute/IWIF10 Proc IWIF-II, 2007, Chengdu What are price sensitivity and market impact? Price Sensitivity - Sensitivity of stock price on agents collective actions Define γ : Individual Actions Price rises!! Price movement = (Collective actions) γ Collective Actions

11. www.swingtum.com/institute/IWIF11 Proc IWIF-II, 2007, Chengdu Market Impact - The impact of synchronized decisions from peer investors during transaction Define β Transaction price = Current price + β (Synchronized price movement) Market Impact !! Synchronized Actions !!

12. www.swingtum.com/institute/IWIF12 Proc IWIF-II, 2007, Chengdu Price movement = (Collective actions) γ (1) Price sensitivity γ Transaction price = Current price + β (Synchronized price movement) (2) Market Impact β These 2 aspects we would like to put in the model !!

13. www.swingtum.com/institute/IWIF13 Proc IWIF-II, 2007, Chengdu Decision of agent a i (t) = +1, 0, -1 Real Price: Transaction Price P T (t) = Price in between P(t+1) and P(t) Collective actions !! Price Sensitivity!! Market Impact !!

14. www.swingtum.com/institute/IWIF14 Proc IWIF-II, 2007, Chengdu Positive Negative Results Final State of the system Agents Wealth 3 phases have positive wealth ???

15. www.swingtum.com/institute/IWIF15 Proc IWIF-II, 2007, Chengdu Phase Diagram of Final State Arbitrageurs phase ?? Trendsetter phase ?? Irregular phase ?? Mixture phase ??

16. www.swingtum.com/institute/IWIF16 Proc IWIF-II, 2007, Chengdu Arbitrageurs phase For β 0.5 Period-2 cycle for P(t) !? Buy! sell! Gain!! Too unrealistic!!

17. www.swingtum.com/institute/IWIF17 Proc IWIF-II, 2007, Chengdu Trendsetter state Arbitrageur state VS Periodic with characteristic pattern Period much longer than period 2 !! What are they doing?

18. www.swingtum.com/institute/IWIF18 Proc IWIF-II, 2007, Chengdu Trendsetter state Start to sell !! (Set up the downward trend) Follow the trend !! I was late... Trend setters (winners) Trend followers (winners) Late followers (losers) Depend on strategies, eg: buy/sell/hold …. We didnt teach them to set up and follow trend !! But they do it !!!

19. www.swingtum.com/institute/IWIF19 Proc IWIF-II, 2007, Chengdu Period 2 Unrealistic! Too periodic! or Unrealistic!

20. www.swingtum.com/institute/IWIF20 Proc IWIF-II, 2007, Chengdu Whats the interpretations? The real market is possibly…… Positive Negative Possible parameters of real market !! Agents wealth

21. www.swingtum.com/institute/IWIF21 Proc IWIF-II, 2007, Chengdu 3. Negative sum? Positive sum? Zero sum?

22. www.swingtum.com/institute/IWIF22 Proc IWIF-II, 2007, Chengdu Positive-sum? Where does the money come from? Note: Supply and Demand is not balanced in this model There is a Market Maker behind the game Market Maker is clearing the extra supply and demand (doing opposite as the actual agents do) So, agents gain, Market Maker loses All together ~> zero sum Market Maker ?

23. www.swingtum.com/institute/IWIF23 Proc IWIF-II, 2007, Chengdu No Market Maker, supply and demand have to be balanced ~> when one agent is holding a buying position, someone else must be holding a selling position ~> zero-sum for agents Can both Agents and Market Maker gain? Transaction cost + evolution of agents (agents losing money are leaving the market)

24. www.swingtum.com/institute/IWIF24 Proc IWIF-II, 2007, Chengdu Transaction Cost (% of P(t))+ Evolution Positive gain for Investors and Market maker !! ~> Participation incentives

25. www.swingtum.com/institute/IWIF25 Proc IWIF-II, 2007, Chengdu 4. Can we apply these financial models on real financial data ?

26. www.swingtum.com/institute/IWIF26 Proc IWIF-II, 2007, Chengdu Application on real data: Hang Seng Index (HSI) To convince ourselves that the model share similarities with real market, we test the applicability of the model on HSI Real HSI as external signals, stock price in the model Agents are given a certain amount of initial wealth, for initial investment Wealth dependence maximum position K(t) = Wealth(t) / Price(t)

27. www.swingtum.com/institute/IWIF27 Proc IWIF-II, 2007, Chengdu Results (HSI from 1987 – 2007) HSI x 7.5 times Best 3 among 10000 Agents x 17 times 5 random agents

28. www.swingtum.com/institute/IWIF28 Proc IWIF-II, 2007, Chengdu Initially, w(1987)/P(1987) = 5 Wealth grows faster than inflation Wealth grows slower than inflation

29. www.swingtum.com/institute/IWIF29 Proc IWIF-II, 2007, Chengdu Comparison with other models - % of gaining agents 11% of agents in this model Beat HSI inflation in this 20 years

30. www.swingtum.com/institute/IWIF30 Proc IWIF-II, 2007, Chengdu Wealth Game has the largest % of gaining agents But for the best investor……. Wealth GameMinority Game x 7.5 times x 17 times x 25 times x 7.5 times Minority Game has more outstanding best investor !

31. www.swingtum.com/institute/IWIF31 Proc IWIF-II, 2007, Chengdu Difference in wealth counting….. Wealth GameMinority Game VS with 1.Positive sign VS negative sign 2.Position dependence VS Single bid dependence 3.Small time lag Trend following? Longer memory

32. www.swingtum.com/institute/IWIF32 Proc IWIF-II, 2007, Chengdu Wealth Game Vs Minority Game Another similar test : Wealth independent Max Pos. with w(0) = 0 Best investors are more outstanding Most agents are losing Best investors are not as rich as MG, but most are gaining

33. www.swingtum.com/institute/IWIF33 Proc IWIF-II, 2007, Chengdu Conclusion Behaviors resembling real investors emerge naturally form this simple model Possible values of γ and β (price sensitivity and market impact) in real market can be conjectured form the phase diagrams (irregular phase with positive wealth) Wide participation incentives: positive sum for both existing agents and market maker The model is tested by using real HSI Wealth Game: better average performance Minority game: more outstanding best agents

34. www.swingtum.com/institute/IWIF34 Proc IWIF-II, 2007, Chengdu Thank You!! Questions & Answers Session Acknowledgement: Supported by the Research Grant Council of Hong Kong (DAG05/06.SC36 and HKUST603606)" All cartoon figures from coolclip.com