A relaxation algorithm for building undominated portfolios

Data in brief, 2016

A large number of portfolio selection models have appeared in the literature since the pioneering work of Markowitz. However, even when computational and empirical results are described, they are often hard to replicate and compare due to the unavailability of the datasets used in the experiments. We provide here several datasets for portfolio selection generated using real-world price values from several major stock markets. The datasets contain weekly return values, adjusted for dividends and for stock splits, which are cleaned from errors as much as possible. The datasets are available in different formats, and can be used as benchmarks for testing the performances of portfolio selection models and for comparing the efficiency of the algorithms used to solve them. We also provide, for these datasets, the portfolios obtained by several selection strategies based on Stochastic Dominance models (see "On Exact and Approximate Stochastic Dominance Strategies for Portfolio Selecti...

Open Journal of Statistics, 2017

The Cardinality Constraint-Based Optimization problem is investigated in this note. In portfolio optimization problem, the cardinality constraint allows one to invest in K N ≤ assets out of a universe of N assets for a prespecified value of K. It is generally agreed that choosing a "small" value of K forces the implementation of diversification in small portfolios. However, the question of how small must be K has remained unanswered. In the present work, using a comparative approach we show computationally that optimal portfolio selection with a relatively small or large number of assets, K, may produce similar results with differentiated reliabilities.

Economic Computation and Economic Cybernetics Studies and Research Academy of Economic Studies, 2009

We consider the problem of a decision maker, who is concerned with the management of a single-period portfolio that consists of holdings in n risky assets and is adjusted at the beginning of the time-period. The portfolio optimization problem consists in choosing the optimal rebalancing decisions in response to new information on market future prices (returns) of the risky assets in the portfolio in order to maximize the expected value of the end of period wealth in the presence of transaction costs, while satisfying a set of constraints. Rebalancing decisions are manifested in the revision of holdings through sales and purchases of assets. We assume that the assets are sufficiently liquid that market impacts can be neglected. We propose to solve the portfolio optimization problem in two steps: first, the phase of stock selection and second, the asset allocation phase. For the stock selection, we use principal component analysis to reduce the number of characteristics that will be taken into account. After that, applying clustering techniques, we find the similarities between the assets and we obtain a partition of the set of assets in clusters. Taking one element from each class, we get the set of assets that will be used to build the optimal portfolio. Once the stock selection completed, the optimal portfolio is obtained using an algorithm that combines the specific features of the convex programming with approximation techniques. The unique nature of our work is the combination of the classification theory with the portfolio optimization techniques and the study of this approach. To illustrate the behaviour of the proposed method, we consider the case of a portfolio of assets from Bucharest Stock Exchange.

Computers & Operations Research, 2000

In this paper we consider the problem of "nding the e$cient frontier associated with the standard mean}variance portfolio optimisation model. We extend the standard model to include cardinality constraints that limit a portfolio to have a speci"ed number of assets, and to impose limits on the proportion of the portfolio held in a given asset (if any of the asset is held). We illustrate the di!erences that arise in the shape of this e$cient frontier when such constraints are present. We present three heuristic algorithms based upon genetic algorithms, tabu search and simulated annealing for "nding the cardinality constrained e$cient frontier. Computational results are presented for "ve data sets involving up to 225 assets. Scope and purpose The standard Markowitz mean}variance approach to portfolio selection involves tracing out an e$cient frontier, a continuous curve illustrating the tradeo! between return and risk (variance). This frontier can be easily found via quadratic programming. This approach is well-known and widely applied. However, for practical purposes, it may be desirable to limit the number of assets in a portfolio, as well as imposing limits on the proportion of the portfolio devoted to any particular asset. If such constraints exist, the problem of "nding the e$cient frontier becomes much harder. This paper illustrates how, in the presence of such constraints, the e$cient frontier becomes discontinuous. Three heuristic techniques are applied to the problem of "nding this e$cient frontier and computational results presented for a number of data sets which are made publicly available.

2006

2010

One of the most frequently studied areas in finance is the classical mean-variance portfolio selection model pioneered by Harry Markowitz; which is also, undoubtedly recognized as the foundation of modern portfolio theory. The model in its basic form deals with the selection of portfolio of assets such that a reasonable trade-off is achieved between the conflicting objectives of maximum possible return at a minimum risk, given that the right choice of constituent assets is made and proper weights are allocated. However, despite its enormous contribution to this branch of knowledge, the model is not immune from criticisms ranging from those associated with its in ability to capture the realism of an investment setting - such as transaction costs, cardinality constraints, floor and ceiling constraints, etc. In this research we extended the classical model by incorporating into it the cardinality as well as the floor & ceiling constraints after which we implemented six different metahe...

International Journal of Economic Sciences, 2021

Classical models for the construction of an investment portfolio do not account for fundamental values of companies considered. In our approach, we extend the portfolio choice by adding a new criterion connected with the fundamental values of companies to the classical criteria of expected return and risk. It is assumed that an investor selects stocks according to their attractiveness, measured by some indicators of economic and financial situation of companies. In this approach, portfolios are assessed according to three criteria: their expected returns, risk (measured by variance of returns) and economic situation of the companies (measured by some indicators). In this article, we consider the book value to price ratio as a measure of the fundamental value of a company. We discuss an algorithm for constructing portfolios with this fundamental value criterion based on analytical solutions for relevant optimization problems. In the optimization problem, we consider minimizing variance with constrains on expected return and attractiveness of investment. We also present empirical examples of calculating effective portfolios of stocks listed on the Warsaw Stock Exchange and compare their performance with effective portfolios built according to the classical Markowitz approach. By adding an additional criterion of the book to market value, we received portfolios with a higher average realized rate of return compared with the classical Markowitz model. Thus, it can be useful for investors in the capital market to incorporate an additional criterion connected with fundamental values of companies when preparing a model of stock returns.

International Journal for Quality Research, 2023

In this study, we performed an innovative approach to analyzing an obtainable and efficient set on a small portfolio using 3-month historical data on the daily movements of stock prices of industrial companies, represented by the Dow Jones Industrial Average Index (DJIA). Under a small portfolio, we mean a two-member, three-member, and a four-member portfolio. In the analysis of the two-member portfolio, the explicit form of the variance function concerning the portfolio return was determined. The analytical function of the sixth-degree polynomial was obtained, and the diagram of this function was a parabola of the same order.An efficient portfolio set is defined as the part of a smooth curve where the first derivative of the function is greater than or equal to zero.Alternatively, the explicit form of the variance function concerning the portions of portfolio securities was determined, which has a quadratic form whose diagram is a quadratic parabola.The efficient set, in this case, determined by the implicit equation of variables, which represents the portions of the securities, will be part of the straight line that forms the constraint of the portfolio.The identical procedure was conducted in the analysis of the three-member and fou rmember portfolios. The partitive portfolio model was defined as every subset of the general portfolio with a growing number of members.This study of the partitive portfolios significantly simplifies the procedure for obtaining the efficient set of multi-member portfolios.

2012

In this paper, a Meta heuristic method is used to solve an extended Markowitz mean-variance portfolio selection model. Since the problem is modeled by quadratic integer programming, we should use Meta heuristics to solve it. This paper proposes a simulated annealing Meta heuristic method to solve the problem and the results for a large scale example is compared with genetic algorithm. The Computational results show that the proposed method is more efficient on large scale examples.