1. An Effective Stock Portfolio Trading Strategy using Genetic Algorithms and Weighted Fuzzy Time Series Yungho Leu and Tzu-I Chiu National Taiwan University of Science and Technology Taiwan, Taipei

2. NASNIT, October 24-26, 2011, Maca Outline  Problem definition  Related work  Our approach  Experiments  Conclusion

3. NASNIT, October 24-26, 2011, Maca Problem Definition  Portfolios: A portfolio is a linear (weighted) combination of a set of securities aiming at minimizing risk with a given level of return rate.

4. NASNIT, October 24-26, 2011, Maca Problem Definition  Markowitz mean-variance Portfolio model :, Where r i is the return rate of security i,  ij is the covarance of r i and r j ; w is called the risk aversion factor Risk Return

5. NASNIT, October 24-26, 2011, Maca Problem with Markowitz model  Need to consider minimal transaction lots.  Does not consider when to re-construct (to sell one and to buy a new one) a new portfolio.  Many methods have been proposed for porfolio construction.  The minimal transaction lots problem is receiving more attention recently.

6. NASNIT, October 24-26, 2011, Maca Our approach  We propose a method to re-construct (to sell one and to buy a new one) portfolio.  We use Genetic Algorithm to construct new portfolios.  We use Fuzzy Time Series to predict the return rate of a portfolio.  We incorporate a stop-lose point policy in the method.

7. NASNIT, October 24-26, 2011, Maca Some related works  Constructing investment strategy portfolios by combination genetic algorithms (Chen et al., 2009).  Automatic stock decision support system based on box theory and SVM algorithm (Wen et al., 2010).

8. NASNIT, October 24-26, 2011, Maca Predict Stock Return rate  Construct Fuzzy Logical Relationship database.  Find the most recent FLRs.  Construct FLR group.  Assign weight to each FLR in FLR group.  Predict the stock price.

9. An Illustrative Example 9 1.The most recent FLRs : (t=1)A 1 →A 1, (t=2)A 1 →A 2, (t=3)A 2 →A 1, (t=4)A 1 →A 1, (t=5)A 1 →A 1, 2. Assign a weight to FLR ： (t=1)A 1 →A 1 with weight 1, (t=2)A 1 →A 2 with weight 2, (t=4)A 1 →A 1 with weight 3, (t=5)A 1 →A 1 with weight 4, Construct FLR Group(FLRG ) (Left-hand-side of day 5 is A 1 ) ： A 1 →A 1, A 2, A 1, A Defuzzify FLRG: Predicted value of day 6= A i ’ is the corresponding value of fuzzy set A i

10. NASNIT, October 24-26, 2011, Maca The Genetic Algorithm  Encoding: Stock numbering: 1~50 Allocation number ： 1~100 Stock no. 73024155 Title of the stock Chang Hwa Bank Chung- hwa Telecom Co. LiteOn Technology Co. China trustChina steel Allocati on no. 1025153035 proporti on 0.0870.21740.13040.26090.3043

11. NASNIT, October 24-26, 2011, Maca The Genetic Algorithm  Single-point Crossover: Stock no. 73024155 Alloc. no. 1025153035 Stock no. 81035162 Alloc. no. 1525203540 parents 35162 203540 24155 3035 Offsprings

12. The Genetic Algorithm  Single-point mutation NASNIT, October 24-26, 2011, Maca Stock no. 73035162 Alloc. no. 1025 203540 Stock no. 7305162 Alloc. no. 1025153540

13. The Genetic Algorithm  Fitness function: NASNIT, October 24-26, 2011, Maca F i (t+n): the predicted closing price of stock i at day t+n N i (t): the closing price of stock i at day t C i : the weight of stock i

14. Portfolio trading  Trade the current portfolio when a new portfolio has a higher expected return rate. NASNIT, October 24-26, 2011, Maca Hold for 5 days Day tDay t+5 Buy portfolio S If the return rate of S is greater than that of S’ then hold S else sell S and buy S’ Predict the return rate of S and the return rate of the new portfolio S’ from GA at day t+10 5 days later

15. Stop-lose point policy  Keep tracking the return rate of the portfolio, when it reaches the stop-lose point, sell it. NASNIT, October 24-26, 2011, Maca t+3tt+4 Buy a new portfolio at date t+5 Periodically Check stop-lose point within 5 days t+5 Buy a stock portfolio If the return rate is less than the stop-lose point (- 7%), sell the portfolio Buy a new portfolio

16. NASNIT, October 24-26, 2011, Maca Experiment setting Population size10 No. of iteration in GA1000 Selection methodRoulette wheel CrossoverSingle-point crossover MutationSingle-point mutation Crossover rate0.8 Mutation rate0.1 Transaction cost 6 ‰ *

17. NASNIT, October 24-26, 2011, Maca Experiment results Calendar year2004200520062007200820092010Average The proposed strategy 0.386170.402420.465590.47664-0.14740.957140.563540.44345 The proposed strategy* 0.23913 2 0.27167 5 0.32398 7 0.33384 2 - 0.35497 0.81734 5 0.39374 4 0.28925 Taiwan 50 Index-0.040.0970.130.09-0.440.50.120.06529 TAIEX-0.060.0860.180.08-0.450.540.1190.07071 *-denotes with transaction cost  The return rates of the proposed methods are higher than the benchmarking indices, with or without considering transaction cost.

18. Experiment results Calendar Year2004200520062007200820092010Average Buy and Hold0.04020.08880.2227-0.0191-0.79780.48940.18160.0294 The proposed Strategy* 0.23910.27170.3240.3338-0.3550.81730.39370.2893 NASNIT, October 24-26, 2011, Maca  The return rate of the proposed method with transaction cost is better than that of the buy and hold.

19. NASNIT, October 24-26, 2011, Maca Conclusion  We propose an effective method to trade security portfolios using GA and Fuzzy Time Series.  The future work is to consider limitations such as transaction lots and the risks of portfolios.

20. NASNIT, October 24-26, 2011, Maca Q&A