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Comparison of Single and Multi-Objective Genetic Algorithm Approaches for Optimal Stock Portfolio Selection

This study explores investment strategies through the lens of genetic algorithms, specifically comparing single and multi-objective approaches for optimal stock portfolio selection. It utilizes a financial modeling framework based on modern portfolio theory introduced by Harry Markowitz in 1952. The research involves stock price predictions using neural networks and examines portfolio optimization with both Simple Genetic Algorithm (GA) and Non-dominated Sorting Genetic Algorithm II (NSGA-II). Results show that while neither technique outperformed significantly, Simple GA proved to be more efficient and faster compared to NSGA-II.

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Comparison of Single and Multi-Objective Genetic Algorithm Approaches for Optimal Stock Portfolio Selection

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  1. COMPARISON BETWEEN SINGLE ANDMULTI OBJECTIVE GENETIC ALGORITHMAPPROACH FOR OPTIMAL STOCK PORTFOLIO SELECTION

  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 • Portfolio is a basket of multiple financial instruments desired to achieve diversification • Harry Markowitz in 1952 • M – V model • Two parameters or ( and

  4. MODEL PRESENTATION • Portfolio‘s expected return • Portfolio‘s risk • Model constraints • And where i,j = 1, 2,... N.

  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 • Adopted weighted average method to calculate expected return • They include three parameters into equation • Arithmetic mean • Changes in tendency of return • Forecasted return based on financial report and individual experience • Fitness function was • You need to be an expert to forecast stock return with financial report.

  7. C-M. Lin, M. Gen:An Effective Decision-Based Genetic AlgorithmApproach to Multiobjective PortfolioOptimization Problem • They proposed a method where portfolio is formed based on yield of return • Fitness function was • Fitness function is very similar to Sharpe ratio formula

  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

  9. S.K. Mishra, G. Panda, S. Meher, S.S. Sakhu:Optimal Weighting of Assets using aMulti-objective Evolutionary Algorithm • They compare three multi objective genetic algorithms • Performance was measured by S, Δand C metrics • C metrics

  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.

  11. RESULTS

  12. In global minimum portfolio a weight of CAD asset is 65%

  13. Correlation in 2006

  14. Correlation in 2009

  15. COMPUTATIONAL TIMES Simple GA NSGA-II

  16. 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

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