Constructing the optimal portfolio: estimation of actual portfolio risk and choice of securities with the genetic algorithm

Drawing upon Markowitz’s mean–variance model, this paper proposes a method for constructing an optimal portfolio using historical data for the estimation of portfolio risk and the choice of securities. First, we establish that the portfolio risk produced by substituting the estimates of the means and the covariance matrix in Markowitz’s formula has a serious downward bias relative to the actual portfolio risk, which is U-shaped with respect to the number of securities. Second, we show that a leave-one-out-method provides less-biased estimates of portfolio risk. Third, we employ a genetic algorithm for determining which securities should be incorporated into a portfolio, and confirm that the selected approach works well with real data.