Genetic Algorithms in Portfolio Optimization

Financial planning involves asset allocation and risk management. Asset allocation problem decides the percentage of the overall portfolio value allocated to each portfolio component. Risk management measures the risk of different investment instruments and creates or maintains portfolios with the specified risk-return characteristics. A multi-stage stochastic optimization is a quantitative model that integrates asset allocation strategies and saving strategies in a comprehensive fashion. It manages portfolio in constantly changing financial markets by periodically rebalancing the asset portfolio to achieve return maximization and risk minimization. The multi-stage optimization technique captures dynamic aspects of the problem, leading to optimal portfolio. To increase understandability of the model, a graphical scenario tree can be constructed to visualize the optimal dynamic balanced investment strategy for the multi-period financial planning. Optimization of asset allocation is complex and NP-hard. It is non-linear with many local optima. Searching the global solution by analytical methods is computationally expensive and ineffectively. Since time is a constraint for financial problems, a trade-off should be made between the performance and the computational time. Hence, we use Genetic Algorithms (GA) as our self-learning portfolio optimizer to optimize one's asset allocation in terms of profit minimization at pre-defined risk level. In comparison of other search algorithms, GA is less problem-dependent while the others like Tabu Search is systematic and strategic towards the problem. In comparison of other local search algorithms, GA reassures a higher chance of reaching a global optimum by starting with multiple random search points and considering several candidate solutions simultaneously. The unique crossover operator in GA offers the possibility of exchanging attributes among potential solutions. The drawback of classical GA is mainly attributed to the fact that the diversity of a population relies on mutation only once the population has been initialized. Since mutation must be kept at a low rate (otherwise the offspring do not inherit the characteristics of their parents, leading to a random search), it does not diversify the population effectively once the population has been converged. Krishnakumar's Micro-genetic algorithm (f•GA) avoids premature convergence by infusing new schema into population with random generation of new strings when convergence occurs. In classical GA, the population size must be large, otherwise GA does not provide a sufficient sample size, causing premature convergence. However, large population size requires more time to converge the population. The rate of convergence is unacceptably slow. The reshuffling procedure of GA allows GA to run with small population size so as to save the computational time. To shorten further computational time, we propose a partial replacement procedure to take the place of the reshuffle procedure. This procedure takes advantage of the fact that some good attributes might have been acquired previously by some strings through the reproduction process. These strings having good candidacy potential should be allowed to recombine with some new strings for further improvements. Obviously, there is a considerable time saving when compared with the reshuffling procedure which actually restarts the population from the beginning. Partial replacement procedure is to be designed to reduce the amount of evaluation for effective operations. Our modified f•GA is incorporates into our portfolio optimization system. Since the change of various financial instrument are under normal distribution, over-training may occurs when GA just memorizes the behavior patterns in training period and fails in generalizing them. As a result, the overtrained solution cannot give a desirable performance on new data. The key to success of Genetic Algorithm in the financial model is the prevention of over-training. In order to find a robust optimal solution, performance consistency should be taken into account during evaluating each solution candidate in the financial model. Our algorithm is to partition the training phase into two phases: one is for searching optimal or near-optimal solution and the other is to increase the consistency of portfolio performance. By this way, consistency of performance is concerned. The performance of our system is demonstrated by optimizing cash and various stocks in Hong Kong market over extended time periods. Experiments are conducted to compare 1) the efficiency of f•GA and the modified GA and 2) the robustness of GA with and without performance consistency fitness evaluation. It should be found that the modified GA is more efficiency than f•GA and GA with performance consistency fitness evaluation outperforms the one without performance consistency fitness evaluation.