1. COMPARISON BETWEEN SINGLE AND MULTI OBJECTIVE GENETIC ALGORITHM APPROACH FOR OPTIMAL STOCK PORTFOLIO SELECTION Authors:Cvörnjek Nejc Brezocnik Miran Jagric Timotej Papa Gregor

2. INTRODUCTION  Finding a solution for an investment process with which we can have influence on a computation time  Master thesis based on financial modelling with nature inspired algorithms  Stock price predictions with Neural Network  Portfolio optimization with GA, NSGA-II

3. PROBLEM PRESENTATION

4. MODEL PRESENTATION

5. GRAPHICAL PRESENTATION OF M-V MODEL

6. Y. Xia, B. Liu, S. Wang, K.K. Lai: A model for portfolio selection with order of expected returns

7. C-M. Lin, M. Gen: An Effective Decision-Based Genetic Algorithm Approach to Multiobjective Portfolio Optimization Problem

8. S.K.Mishra, G. Panda, S. Meher, R. Majhi, M. Singh. Portfolio management assessment by four multiobjective optimization algorithm  In research authors compare four multi objective genetic algorithms  Performance was measured by S, Δ and C metrics  C metrics MetricsPESAPAESAPAESNSGA-II S0.0004042360.0000823610.00000573720.000000574 Δ 0.892482853 0.8121818330.78625961920.5967844252 PESAPAESAPAESNSGA-II PESA—0.0000 PAES0.85222 —0.36440.1562 APAES0.959900.2731 —0.2653 NSGA-II0.966270.803210.37534—

9. S.K. Mishra, G. Panda, S. Meher, S.S. Sakhu: Optimal Weighting of Assets using a Multi-objective Evolutionary Algorithm  They compare three multi objective genetic algorithms  Performance was measured by S, Δ and C metrics  C metrics PESASPEA2NSGA-II S0.0003046160.00000678740.000000574 Δ 0.8654128590.83379761920.5967844252 PESANSGA-IISPEA2 PESA—0.0000 NSGA-II0.95790—0.2566 SPEA20.946270.08534—

10. PROBLEM  We randomly choose twenty stocks among different branges from S&P500 index.  We construct three sizes of portfolio. Portfolios have sizes of 5, 10 and 20 stocks.  Time period was from 01.01.2013 to 01.01.2014. Stocks CADAAGSPFE TIFCVXJECTAP AXPKOKSUPM NOCFMCSGPS FRXGOOGNVDAMHK

11. RESULTS ParametersGANSGA-II Population size50 Natural selection0.05/ Crossover rate0.9 Mutation size0.2 Tournament size22

14.  In global minimum portfolio a weight of CAD asset is 65% StockPercentageReturnVariance CAD22.66-0.00046954230.000039831697 TIF11.920.00187647690.00018975974 AXP10.760.00176773180.000125013218 NOC38.690.00218118320.000101090825 FRX15.970.00205712370.00015994853 Σ =100

15. Correlation in 2006

16. Correlation in 2009

17. COMPUTATIONAL TIMES Simple GA 5 stocks10 stocks20 stocks 100 generations0,620,70,83 250 generations1,551,782,02 500 generations3,253,434,04 1000 generations6,427,068,06 NSGA-II 5 stocks10 stocks20 stocks 100 generations83,1983,884,67 250 generations206,16209,08210,33 500 generations414,24418,86423,97 1000 generations827,01841,79857,36

18. CONCLUSION  None of techniques overperformed in finding a solution  In M – V model stocks with a lower variance are preffered  Simple GA is significantly faster than NSGA-II  Simple GA is more efficient than NSGA-II