Portfolio Selection Algorithm Research Articles

A Multiagent Evolutionary Algorithm for the Resource-Constrained Project Portfolio Selection and Scheduling Problem

A multiagent evolutionary algorithm is proposed to solve the resource-constrained project portfolio selection and scheduling problem. The proposed algorithm has a dual level structure. In the upper level a set of agents make decisions to select appropriate project portfolios. Each agent selects its project portfolio independently. The neighborhood competition operator and self-learning operator are designed to improve the agent’s energy, that is, the portfolio profit. In the lower level the selected projects are scheduled simultaneously and completion times are computed to estimate the expected portfolio profit. A priority rule-based heuristic is used by each agent to solve the multiproject scheduling problem. A set of instances were generated systematically from the widely used Patterson set. Computational experiments confirmed that the proposed evolutionary algorithm is effective for the resource-constrained project portfolio selection and scheduling problem.

A Novel Multi-Objective Evolutionary Algorithm for Portfolio Selection

Portfolio selection is a problem arising in finance and economics. While its basic formulations can be efficiently solved using linear or quadratic programming, its more practical variants have to be tackled by heuristics in many cases. In this work, both portfolio return and risk factors need to be considered, so it is abstracted as a multi-objective 0/1 knapsack problem and solved by a novel multi-objective evolutionary algorithm based on SPEA2. Experimental results show that the multi-objective optimization to solve the portfolio problem can better reveal the relationship between benefits and risks, to provide investors with a better basis for decision making.

Online Lazy Updates for Portfolio Selection with Transaction Costs

A major challenge for stochastic optimization is the cost of updating model parameters especially when the number of parameters is large. Updating parameters frequently can prove to be computationally or monetarily expensive. In this paper, we introduce an efficient primal-dual based online algorithm that performs lazy updates to the parameter vector and show that its performance is competitive with reasonable strategies which have the benefit of hindsight. We demonstrate the effectiveness of our algorithm in the online portfolio selection domain where a trader has to pay proportional transaction costs every time his portfolio is updated. Our Online Lazy Updates (OLU) algorithm takes into account the transaction costs while computing an optimal portfolio which results in sparse updates to the portfolio vector. We successfully establish the robustness and scalability of our lazy portfolio selection algorithm with extensive theoretical and experimental results on two real-world datasets.

Chinese Corporate Social Responsibility by Multiple Objective Portfolio Selection and Genetic Algorithms

ABSTRACTIn this paper, we study corporate social responsibility (CSR) in China through the prism of investments. We work with large stocks and assess their CSR performance from agency CSR data. We formulate Chinese CSR by a multiple objective extension of a traditional portfolio selection model and analytically solve the extension. We also solve the extension by a genetic algorithm and directly evaluate the algorithm's performance against the analytical solution. The multiple objective formulation is tested by randomly choosing nondominated portfolios with out‐of‐sample data to identify nondominated portfolios that outperform the 1/n portfolio (equally weighted portfolio). Copyright © 2013 John Wiley & Sons, Ltd.

AN ONLINE PORTFOLIO SELECTION ALGORITHM WITH REGRET LOGARITHMIC IN PRICE VARIATION

We present a novel efficient algorithm for portfolio selection which theoretically attains two desirable properties: Worst‐case guarantee: the algorithm is universal in the sense that it asymptotically performs almost as well as the best constant rebalanced portfolio determined in hindsight from the realized market prices. Furthermore, it attains the tightest known bounds on the regret, or the log‐wealth difference relative to the best constant rebalanced portfolio. We prove that the regret of the algorithm is bounded by O(log Q), where Q is the quadratic variation of the stock prices. This is the first improvement upon Cover's (1991) seminal work that attains a regret bound of O(log T), where T is the number of trading iterations. Average‐case guarantee: in the Geometric Brownian Motion (GBM) model of stock prices, our algorithm attains tighter regret bounds, which are provably impossible in the worst‐case. Hence, when the GBM model is a good approximation of the behavior of market, the new algorithm has an advantage over previous ones, albeit retaining worst‐case guarantees. We derive this algorithm as a special case of a novel and more general method for online convex optimization with exp‐concave loss functions.

Robust and adaptive algorithms for online portfolio selection

We present an online approach to portfolio selection. The motivation is within the context of algorithmic trading, which demands fast and recursive updates of portfolio allocations as new data arrives. In particular, we look at two online algorithms: Robust-Exponentially Weighted Least Squares (R-EWRLS) and a regularized Online minimum Variance algorithm (O-VAR). Our methods use simple ideas from signal processing and statistics, which are sometimes overlooked in the empirical financial literature. The two approaches are evaluated against benchmark allocation techniques using four real data sets. Our methods outperform the benchmark allocation techniques in these data sets in terms of both computational demand and financial performance.

A class of on-line portfolio selection algorithms based on linear learning

On-line portfolio is a sequential investment algorithm during a long period and makes portfolio decision without any statistical assumption about the behavior of the market. A constant rebalanced portfolio (CRP) is an investment strategy which adopts the same portfolio vector on each trading period. Design of on-line portfolio algorithms which are competitive with the best constant rebalanced portfolio (BCRP) is a hot topic recently. In this paper, we present a new on-line portfolio selection strategy, which computes the new portfolio vector based completely on on-line learning of linear functions. The proposed algorithm is useful since it gives the investor a whole range of choices for the on-line portfolios. Using the technique of taking relative entropy as a distance function, we prove that the new algorithm is a universal portfolio, which exhibits the same asymptotic growth rate in normalized natural logarithmic wealth as the BCRP for any sequence of price relatives. Experiments on several New York Stock Exchange dates also show the good performance of the new strategy.

Optimal Investment Under Transaction Costs: A Threshold Rebalanced Portfolio Approach

We study how to invest optimally in a financial market having a finite number of assets from a signal processing perspective. Specifically, we investigate how an investor should distribute capital over these assets and when he/she should reallocate the distribution of the funds over these assets to maximize the expected cumulative wealth over any investment period. In particular, we introduce a portfolio selection algorithm that maximizes the expected cumulative wealth in i.i.d. two-asset discrete-time markets where the market levies proportional transaction costs in buying and selling stocks. We achieve this using “threshold rebalanced portfolios”, where trading occurs only if the portfolio breaches certain thresholds. Under the assumption that the relative price sequences have log-normal distribution from the Black-Scholes model, we evaluate the expected wealth under proportional transaction costs and find the threshold rebalanced portfolio that achieves the maximal expected cumulative wealth over any investment period. Our derivations can be readily extended to markets having more than two stocks, where these extensions are provided in the paper. As predicted from our derivations, we significantly improve the achieved wealth with respect to the portfolio selection algorithms from the literature on historical data sets under both mild and heavy transaction costs.

Defensive online portfolio selection

The class of defensive online portfolio selection algorithms, designed for finite investment horizon, is introduced. The game constantly rebalanced portfolio and the worst case game constantly rebalanced portfolio, are presented and theoretically analysed. The analysis exploits the rich set of mathematical tools available by means of the connection between universal portfolios and the game-theoretic framework. The empirical performance of the worst case game constantly rebalanced portfolio algorithm is analysed through numerical experiments concerning the FTSE 100, Nikkei 225, Nasdaq 100 and S&P500 stock markets for the time interval, from January 2007 to December 2009, which includes the credit crunch crisis from September 2008 to March 2009. The results emphasise the relevance of the proposed online investment algorithm which significantly outperformed the market index and the minimum variance Sharpe-Markowitz’s portfolio.

High-conviction equity portfolio optimization

We investigate the construction of well-diversified high-conviction equity portfolios using the portfolio diversification index (PDI). This paper is the first to investigate the out-of-sample properties of the PDI. Our research applies a novel portfolio selection algorithm to maximize the PDI of a portfolio of stocks in the Standard & Poor’s S&P 500 index over the period 2000–2009. We construct equally weighted, well-diversified portfolios consisting of 5 to 30 stocks, and compare these with randomly selected portfolios of the same number of stocks. Our results indicate that investors using our algorithm to maximize the PDI can improve the diversification of high-conviction equity portfolios. For example, a portfolio of 20 stocks constructed using the algorithm with the PDI behaves outof-sample as if it contains 10 independent stocks, ie, a PDI score of 10. This is a significant improvement over the PDI score of 7 that occurs with a randomly selected portfolio. Our research is robust with respect to the number of stocks in the investment portfolio and the time period under consideration.

Combinatorial auction algorithm for project portfolio selection and scheduling to maximize the net present value

Scheduling projects at the activity level increases the complexity of decision making of project portfolio selection but also expands the search space to include better project portfolios. An integer programming model is formulated for the project portfolio selection and scheduling problem. An iterative multi-unit combinatorial auction algorithm is proposed to select and schedule project portfolios through a distributed bidding mechanism. Two price update schemes are designed to adopt either a standard or an adaptive Walrasian tâtonnement process. Computational tests show that the proposed auction algorithm with the adaptive price update scheme selects and schedules project portfolios effectively and maximizes the total net present value. The price profile generated by the algorithm also provides managerial insights for project managers and helps to manage the scarce resources efficiently.

Create Better Diversified High-Conviction Equity Portfolios Using the Portfolio Diversification Index

We investigate the construction of well-diversified high-conviction equity portfolios, building on Rudin and Morgan (2006) who introduced the Portfolio Diversification Index (PDI) as a new measure of portfolio diversification applied to long/short equity hedge funds in an in-sample period. We are the first to investigate the out-of-sample properties of the PDI. Our research applies a novel portfolio selection algorithm to maximize the PDI of a portfolio of stocks in the S&P 500 Index over 2000 to 2009. We construct equally-weighted, well-diversified portfolios, consisting of 5 to 30 stocks and compare these with randomly selected portfolios of the same stock sizes. Our results indicate that investors using our algorithm to maximize the PDI can improve the diversification of high-conviction equity portfolios. For example, a portfolio of 20 stocks constructed using the algorithm with the PDI behaves out-of-sample as if it contains 10 independent stocks, i.e. a PDI score of 10. Although this is less than the PDI score of 15 achieved in-sample, it is a significant improvement over the PDI score of 7, which occurs with a randomly selected portfolio. Our research is robust with respect to the number of stocks in the investment portfolio and the time period under consideration.

Multi-Attribute Portfolio Selection with Genetic Optimization Algorithms

The traditional portfolio theory first proposed by Markowitz only provides a solution to capital allocation to a pre-determined set of assets, regardless of asset quality. To remedy this gap, a multi-attribute asset quality analysis, before asset allocation, is proposed. Thus a two-stage multi-attribute portfolio selection framework that considers asset quality, as well as asset allocation, is formulated. For solving the proposed portfolio selection problem, this study applies genetic algorithms for multi-attribute portfolio selection and analysis. In the first stage, i.e. asset quality evaluation, a genetic algorithm is used to identify good quality assets in terms of asset ranking. In the asset allocation stage, allocation of capital to individual high-quality assets is optimized using another genetic algorithm based on Markowitz's mean-variance theory. Through the two-stage asset evaluation and allocation process, an optimal portfolio can be determined in the context of considering both multiple asset return attributes and risk exposures. Experimental results reveal that the proposed multi-attribute portfolio selection framework provides a very feasible and useful tool to assist investors in planning their investment strategy and constructing their portfolios.

Efficient implementation of an active set algorithm for large-scale portfolio selection

This paper deals with the efficient implementation of parametric quadratic programming that is specialized for large-scale mean-variance portfolio selection with a dense covariance matrix. The aim is to calculate the whole Pareto front of solutions that represent the trade-off between maximizing expected return and minimizing variance of return. We describe and compare in a uniform framework several techniques to speed up the necessary matrix operations, namely the initial matrix decomposition, the solution process in each iteration, and the matrix updates. Techniques considered include appropriate ordering of the matrix rows and columns, reducing the size of the system of linear equations, and dividing the system into two parts. Regarding implementation, we suggest to simultaneously use two different matrix representations that are specifically adapted to certain parts of the algorithm and propose a technique that prevents algorithm stalling due to numerical errors. Finally, we analyse and compare the runtime of these algorithm variants on a set of benchmark problems. As we demonstrate, the most sophisticated variant is several orders of magnitude faster than the standard implementation on all tested problem instances.

An algorithm for portfolio selection in a frictional market

Absolute deviation is utilized as a measure of risk and a new function is provided for it. We consider the mean-absolute deviation (MAD) portfolio optimization problem in a frictional market with additional constraints representing the so-called short sales. An algorithm for solving the optimization problem is thus presented, which uses the special structure of the original problem to reduce to a linear programming. The numerical test shows the validity of the method.

A novel algorithm for uncertain portfolio selection

In this paper, the conventional mean–variance method is revised to determine the optimal portfolio selection under the uncertain situation. The possibilistic area of the return rate is first derived using the possibisitic regression model. Then, the Mellin transformation is employed to obtain the mean and the risk by considering the uncertainty. Next, the revised mean–variance model is proposed to deal with the problem of uncertain portfolio selection. In addition, a numerical example is used to demonstrate the proposed method. On the basis of the numerical results, we can conclude that the proposed method can provide the more flexible and accurate results than the conventional method under the uncertain portfolio selection situation.

Optimal portfolio selection and dynamic benchmark tracking

This paper analyzes different approaches to portfolio selection when the requirement to portfolio performance is formulated relative to a given benchmark. For example, it may be desirable to track a market index as closely as possible. We develop several portfolio selection algorithms based on different perceptions of risk and different risk/target measures, ranging from the traditional variance to the more modern value-at-risk. In a dynamic setting we address the issue of optimal portfolio rebalancing. We develop an algorithm for determining whether or not to rebalance a given portfolio, based on transaction costs and new information about market conditions. Our approaches are tested on a set of stock data from the Oslo stock exchange.

An Additive On-Line Portfolio Selection Algorithm

An on-line portfolio management algorithm using additive update rule is presented with consideration of proportional transaction costs. After establishing a relationship between transaction costs and the distance of two portfolio vectors, we solve an optimization problem making a balance between high wealth growth rate and low transaction costs. It is shown that the presented portfolio strategy is universal relative to the set of all buy-and-hold portfolios in the sense that it achieves the same asymptotic exponential growth rate of wealth as the best buy-and-hold portfolio determined with hindsight. The simulation examples using the real data from the London Stock Exchange show the efficiency and the computational simplicity of the algorithm.

A linear programming algorithm for optimal portfolio selection with transaction costs

We study the optimal portfolio selection problem with transaction costs. In general, the efficient frontier can be determined by solving a parametric non-quadratic programming problem. In a general setting, the transaction cost is a V-shaped function of difference between the existing and the new portfolio. We show how to transform this problem into a quadratic programming model. Hence a linear programming algorithm is applicable by establishing a linear approximation on the utility function of return and variance.

The Ex Post Performance of Four Portfolio Selection Algorithms

This paper explores the ex post performance of four widely cited (and sometimes applied) normative portfolio selection models. Each is supposed to solve the same portfolio selection problem relative to the same mean-variance efficiency criteria. It has been shown elsewhere, and this paper confirms, that the models result in vastly different ex ante stock selection strategies. However, the acid test of normative theory is ex post performance relative to a set of efficiency criteria or some other standard. The empirical results reported here show that, with one exception, the ex post performance of the models is consistent with the same mean-variance efficiency criteria, and, over a predictable range of outcomes, consistently outperform the index portfolio based on Standard & Poor's 500 Stock Index.