Yukiko Orito

Equality constrained long-short portfolio replication by using probabilistic model-building GA

Portfolio replication problem is to optimize the portfolio such that its proportion-weighted combination is the same as the given benchmark portfolio. However, the benchmark portfolio generally opens only the return to the public but other information such as the assets included in the portfolio, the proportion-weighted combination, the rebalancing date and the investment strategies is closed to the public. In order to optimize such portfolios, we propose an optimization method based on the probabilistic model-building GA in this paper. On the other hand, we are focusing on the long-short portfolio optimization. The long-short portfolio consists of the assets with long positions in which they have bought and been held and with short positions in which they have been borrowed and sold. While applying any optimization method to the long-short portfolios, the portfolio as a feasible solution must be satisfied an equality constraint. In order to make the feasible solutions effectively, we propose two techniques and then apply them to our optimization method. In the numerical experiments, we show that our method has better ability to replicate the long-short portfolios with good fitness values. We found that, however, some portfolios were not replicated though our method worked well. We also discuss this problem in this paper.

Evaluating the Efficiency of Index Fund Selections Over the Fund’s Future Period

It is well known that index fund optimization is important when hedge trading in a stock market. By “optimization” is meant the optimization of the proportion of funds in the index fund. Index funds consisting of a small number of listed companies are constructed in this paper by means of a genetic algorithm method based on the coefficient of determination between the return rate of the fund price and the changing rate of the market index. The method is examined with numerical experiments applied to the Tokyo Stock Exchange. The results show that the index funds work well in forecasting over a future period when a market index has followed a downward or a flat trend. In addition, we reveal problems arising from this optimization in that the coefficient of determination depends on the characteristics of the scatter diagram between the index fund price and the market index.

Index fund rebalancing using probabilistic model-building genetic algorithm with narrower width histograms

The portfolio optimization/rebalancing problem is to determine a proportion-weighted combination in a portfolio in order to achieve certain investment targets. For this problem, many researchers have used various evolutionary methods and models such as genetic algorithms and simulated annealing. On the other hand, the portfolio optimization/rebalancing problem can be viewed as a multi-dimensional problem because its solution is a proportion-weighted combination for the given assets. The previous works, however, have not taken into account the multi-dimensional aspect of the problem. In order to approach this problem from the multi-dimensional aspect, we propose a model based on the probabilistic model-building genetic algorithm with narrower width histograms (PMBGA-NWH), and then apply it to optimize the constrained index funds with the given rebalancing cost in this paper. In the numerical experiments, we show that our model has better ability to make optimal index funds than the traditional genetic algorithm (GA).

A New Population Initialization Approach Based on Bordered Hessian for Portfolio Optimization Problems

In the portfolio optimization problems, the proportion-weighted combination in a portfolio is represented as a real-valued array between 0 and 1. While applying any evolutionary algorithm, however, the algorithm hardly takes the ends of a given real value. It means that the evolutionary algorithms have a problem that they cannot give the not-selected asset whose weight is represented as 0. In order to avoid this problem, we propose a new population initialization approach using the extreme point of the bordered Hessian and then apply our approach to the initial population of GA for the portfolio optimization problems in this paper. In the numerical experiments, we show that our method employing the population initialization approach and GA works very well for the portfolio optimizations even if the portfolio consists of the large number of assets.

Index Fund Optimization Using Genetic Algorithm and Scatter Diagram Based on Coefficients of Determination

Index fund optimization is one of portfolio optimizations and can be viewed as a combinatorial optimization for portfolio managements. It is well known that an index fund consisting of stocks of listed companies on a stock market is very useful for hedge trading if the total return rate of a fund follows a similar path to the rate of change of a market index. In this paper, we propose a method that consists of a genetic algorithm and a heuristic local search on scatter diagrams to make linear association between the return rates and the rates of change strong. A coefficient of determination is adopted as a linear association measure of how the return rates follow the rates of change. We then apply the method to the Tokyo Stock Exchange. The results show that the method is effective for the index fund optimization.

Index fund optimization using a genetic algorithm and a heuristic local search algorithm on scatter diagrams

It is well known that index funds are popular passively managed portfolios and have been used very extensively for investment. Index funds consist of a certain number of stocks of listed companies on a stock market such that the funds return rates follow a similar path to the changing rates of the market indices. However it is hard to make a perfect index fund consisting of all companies included in the market. Thus, the index fund optimization can be viewed as a combinatorial optimization for portfolio managements. In this paper, we propose a method that consists of a genetic algorithm and a heuristic local search algorithm to maximize the correlation between the funds return rates and the changing rates of the market index. We then apply the method to the Tokyo Stock Exchange and compare it with a GA method and a hybrid GA method. The results show that our proposed method is effective for the index fund optimization.

Adaptive GA-based AR-hidden Markov model for time series forecasting

The optimization of a model that expresses time series data for a given period is a problem associated with the development of a regression model that estimates future data on the extension of the past data time series. This is a two-step optimization problem where the order of past data used in the regression model (number of orders of the solution space) is decided, and weighted coefficients for observed data at each point in time (design variables) are determined. Such a two-step optimization problem cannot calculate the evaluation function after the model is developed despite the fact that design variables cannot be determined during the second step until the orders of solution space are determined in the first step. Thus, it is a problem where simultaneous optimization of both the first and second steps is difficult, and a regression model with the smallest evaluation function is chosen as the optimal model after comparison with all the solutions. However, the self-regressing hidden Markov model used in this study for regression requires a large amount of calculation during design variable determination due to the use of the hidden Markov. Furthermore, the calculation and comparison of all the solutions is inefficient. For such an optimization problem, this study proposes an actual-value genetic algorithm (GA) with a framework capable of simultaneous optimization of the first and second steps. The proposed method takes an approach where in individuals that represent the solution space of different orders in the same group are generated. Further, it retains individuals with an order that has a large number of good solutions at a high probability through the transition of the generations. Numerical tests will involve performance validation using estimated artificial data of several states, realized volatility (RV) of the stock, and artificial as well as actual data of inbound visitors to Japan, and they will demonstrate that the optimization of the regression model by the proposed method is more effective than that by the conventional method.

Equality constraint-handling technique with various mapping points: The case of portfolio replication problem

For solving an equality constrained optimization problem, it is difficult to find an optimal solution by using any evolutionary algorithms. We propose a new technique that handles an equality constraint in this paper. The technique transforms variables of solution on equality constrained search space to them on unconstrained search space through trigonometrical functions. Thus, this paper presents the contribution that an evolutionary algorithm effectively finds good feasible solutions without evolutionary stagnation because an unconstrained space consists only of feasible solutions. However, our technique searches mapping points only on the part of constrained space because it cannot transform the constrained space to fully unconstrained space. Therefore, we expand such a space consisting of various mapping points by exchanging trigonometrical functions on EDA (Estimation of Distribution Algorithm). In numerical experiments, for portfolio replication problems, we demonstrate the effectiveness of our technique.

Dynamic Index Fund Optimization by a Heuristic GA Method Based on Correlation Coefficients

The portfolio optimizations are generally to determine the proportion of funds in the portfolio consisting of the static assets. Then, it is hard to determine the proportion-weighted combination for the optimal portfolio consisting of the static large number of assets. In order to avoid this problem, we propose a Heuristic GA Method that optimizes the portfolio that consists of not only the given static assets but also the dynamically selected assets in this paper. In order to demonstrate the effectiveness of our method, we apply the method to creating an index fund based on correlation coefficients for the Tokyo Stock Exchange. This fund is one of the passively managed portfolios. The results show that our method works well for a dynamic index fund optimization.

Effectiveness of iterative asset selection based on bordered hessian for portfolio optimization problems

This paper introduces a new initialization method of individuals for genetic algorithm (GA) in portfolio optimization problems. In our approach, first a set of assets, variables, composing the portfolio is selected, and then combination of real-valued weights of the portfolio is optimized by GA. In the asset selection, a pairwise asset selection which is an iterative greedy scheme based on the bordered Hessian is adopted. In most case of greedy manner, the initial point of search to build a complete solution has a big effect on its quality. In numerical experiments, we compare how the initial selection of asset has an impact on initialization of the population of GA, and evaluate the quality of whole composition of the portfolio obtained by GA.