30. Figure 2: Genetic Algorithm Methodology
A genetic algorithm could be used to maximize the return from the momentum strategy through iterations of J and K (ranking and holding periods). During the first step indicated at figure 1 an initial population of potential solutions is created randomly through choosing ranking and holding periods from 3 to 24 months, forming decile portfolios and calculating their return, standard deviation and t-statistic. This is performed 100 times to form an initial population of solutions. At step two, the fitness of each of the potential solutions in the initial population is evaluated. The objective function is to maximize the return of the portfolio short in losers and long in winner stocks. The next step involves selection of the fittest members of the population to parent the next generation of solutions. The member of the initial population with highest return is passed over to the next generation and is known as elite. Tournament selection is used to choose parents with a strong selective pressure and they are passed through the crossover and mutation operators, which are steps 3, 4 and 5 on the chart respectively. The offsprings created through crossover and mutation become part of the next generation. The fitness of objective function is evaluated for each member of the generation. The iterations are repeated for 25 to 50 generations. Finally, the optimal ranking and holding period could be chosen based in the evaluation of the objective function which is at the maximum return. The value of the t-statistic of the portfolio needs to be considered as well at this point. The standard deviation of the portfolios will be investigated in the diversification part of the study.