A heuristic approach to a portfolio optimization model with nonlinear transaction costs

After the seminal paper of Markowitz, we have been witnesses to a great evolution with respect to the traditional mean-variance (MV) model. With all its merits, however, some of the main downsides of the MV model and its extended or modified models have been recognized: the computational complexity; the inability to incorporate practical considerations such as taxes and transaction costs; and the investment decision being at exactly one point in time for a single-period horizon. It therefore appears desirable to have an alternative method that can deal with highly demanding real-world portfolio problems considering more complex scenarios and settings.;In this thesis we extend the Markowitz MV model to a rebalancing portfolio optimization problem incorporating realistic considerations such as transaction costs and a risk-free asset with short-selling allowed, and we apply the Tabu Search (TS) heuristic to solve practical portfolio problems. First of all, we propose a bi-objective portfolio optimization model which we expect to yield a portfolio equilibrium by combining the following two objectives: maximize the portfolio's expected return and minimize its risk. For realistic portfolio problems we consider the multi-objective portfolio optimization models incorporating a risk-free asset and its short-selling and nonlinear transaction costs based on a single-period and a rebalancing portfolio optimization problem.;For the single-period portfolio problem, we propose an adaptive version of the TS heuristic. We define a feasible portfolio as the solution representation by means of a vector indicating the amount of money invested in each asset. For the initial solution, we randomly generate portfolios by considering the problem size and the purpose of diversified creation. From the initial solution, we obtain the final solution by iteratively searching with the neighborhood and tabu structure. The neighborhood of the current portfolio is generated by increasing and/or decreasing the adjacent pairwise risky assets with a variation factor. The tabu size is determined by the problem size, and the TS algorithm terminates after some number of iterations without an improvement in the objective function value.;For our primary purpose, we extend the single-period model to a rebalancing problem which also considers nonlinear transaction costs and a risk-free asset. We assume that the time point for rebalancing the portfolio is exactly at the midpoint of the entire time horizon of the single-period model. In the rebalancing portfolio problem, since we consider nonlinear transaction costs for risky assets' transactions, a myopic policy which tries to optimize each time period independently is not optimal for the problem because portfolio decisions do affect each other time period. The final objective value at the end of the time period is affected by the portfolio decision at the beginning of the planning horizon because the final result comes from the portfolio decision at the time point of rebalancing the portfolio, which is affected by the portfolio decision at the beginning of the time period. Therefore, we have proposed an advanced, adaptive TS algorithm having an evolutionary neighborhood structure, and we have solved the rebalancing portfolio problem with an iterative folding back procedure in the decision tree structure. For computational studies we consider a risk-free asset and the number of risky assets to be 5, 10, 12, and 15 for both the single-period and rebalancing portfolio problems.