An approach to portfolio selection using an ARX predictor for securities’ risk and return

It is well known that every investment carries a risk associated, and depending on the type of investment, it can be very risky; for instance, securities. However, Markowitz proposed a methodology to minimize the risk of a portfolio through securities diversification. The selection of the securities is a choice of the investor, who counts with several technical analyzes to estimate investment’s returns and risks. This paper presents an autoregressive exogenous (ARX) predictor model to provide the risk and return of some Brazilian securities – negotiated at the Brazilian stock market, BOVESPA – to select the best portfolio, herein understood as the one with minimum expected risk. The ARX predictor succeeded in predicting expected returns and risks of the securities, which resulted in an effective portfolio. Additionally the Markowitz theory was confirmed, showing that diversification reduces the risk of a portfolio.     

Expected model for portfolio selection with random fuzzy returns

This paper researches portfolio selection problem in combined uncertain environment of randomness and fuzziness. Due to the complexity of the security market, expected values of the security returns may not be predicted accurately. In the paper, expected returns of securities are assumed to be given by fuzzy variables. Security returns are regarded as random fuzzy variables, i.e. random returns with fuzzy expected values. Following Markowitz's idea of quantifying investment return by the expected value of the portfolio and risk by the variance, a new type of mean–variance model is proposed. In addition, a hybrid intelligent algorithm is provided to solve the new model problem. A numeral example is also presented to illustrate the optimization idea and the effectiveness of the proposed algorithm.     

Portfolio Risk Measures: The Time’s Arrow Matters

The traditional ex post risk measure associated to a portfolio, a fund or a market performance, is the standard deviation of a series of past returns, called volatility. We propose an alternative risk measure, that turns out to better quantify the risk actually supported by an investor or asset manager with respect to a portfolio or a fund. This alternative measure is computed from the actual dispersion of successive cumulated returns relative to the corresponding successive cumulated returns produced by an accrued performance of null volatility, which better reflects the dynamics of the risk-return relationship over time. Hence, the proposed name of “accrued returns variability”, for such a risk measure that incorporates the passage of time. Applications are presented, to enlighten the advantage of this risk measure.     

A fuzzy modeling for fuzzy portfolio optimization

Conventional portfolio optimization models have an assumption that the future condition of stock market can be accurately predicted by historical data. However, no matter how accurate the past data is, this premise will not exist in the financial market due to the high volatility of market environment. This paper discusses the fuzzy portfolio optimization problem where the asset returns are represented by fuzzy data. A mean-absolute deviation risk function model and Zadeh’s extension principle are utilized for the solution method of portfolio optimization problem with fuzzy returns. Since the parameters are fuzzy numbers, the gain of return is a fuzzy number as well. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the return of the portfolio optimization problem. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a pair of ordinary one-level linear programs so they can be manipulated. It is found that the calculated results conform to an essential idea in finance and economics that the greater the amount of risk that an investor is willing to take on, the greater the potential return. An example, which utilizes the data from Taiwan stock exchange corporation, illustrates the whole idea on fuzzy portfolio optimization problem.     

Evaluating methods of investment project and optimizing models of portfolio selection in fuzzy uncertainty

This paper deals with the problems of both project valuation and portfolio selection under the assumption that the investment capitals and the net cash flows of the projects are fuzzy variables. Using the credibilistic expected value and the credibilistic lower semivariance of fuzzy variables, this paper proposes both the credibilistic return index and the credibilistic risk index, which are measures of investment return and investment risk with annuity form for evaluating single project. Moreover, a composite risk-return index for selecting the optimal investment strategy is also presented. Then, we set up a general project portfolio optimization model with fuzzy returns and two specific models: triangle and interval fuzzy returns. Furthermore, we provide two algorithms: the improved heuristic rules based on genetic algorithm and the traversal algorithm. Finally, two numerical examples are presented to illustrate the efficiency and the effectiveness of these proposed optimization methods.     

An extended ASLD trading system to enhance portfolio management

An adaptive supervised learning decision (ASLD) trading system has been presented by Xu and Cheung (1997) to optimize the expected returns of investment without considering risks. In this paper, we propose an extension of the ASLD system (EASLD), which combines the ASLD with a portfolio optimization scheme to take a balance between the expected returns and risks. This new system not only keeps the learning adaptability of the ASLD, but also dynamically controls the risk in pursuit of great profits by diversifying the capital to a time-varying portfolio of N assets. Consequently, it is shown that: 1) the EASLD system gives the investment risk much smaller than the ASLD one; and 2) more returns are gained through the EASLD system in comparison with the two individual portfolio optimization schemes that statically determine the portfolio weights without adaptive learning. We have justified these two issues by the experiments.     

Direct data-driven portfolio optimization with guaranteed shortfall probability

This paper proposes a novel methodology for optimal allocation of a portfolio of risky financial assets. Most existing methods that aim at compromising between portfolio performance (e.g., expected return) and its risk (e.g., volatility or shortfall probability) need some statistical model of the asset returns. This means that: (i) one needs to make rather strong assumptions on the market for eliciting a return distribution, and (ii) the parameters of this distribution need be somehow estimated, which is quite a critical aspect, since optimal portfolios will then depend on the way parameters are estimated. Here we propose instead a direct, data-driven, route to portfolio optimization that avoids both of the mentioned issues: the optimal portfolios are computed directly from historical data, by solving a sequence of convex optimization problems (typically, linear programs). Much more importantly, the resulting portfolios are theoretically backed by a guarantee that their expected shortfall is no larger than an a-priori assigned level. This result is here obtained assuming efficiency of the market, under no hypotheses on the shape of the joint distribution of the asset returns, which can remain unknown and need not be estimated.     

Combined DEMATEL technique with a novel MCDM model for exploring portfolio selection based on CAPM

This research proposes a novel MCDM model, including DEMATEL, ANP, and VIKOR for exploring portfolio selection based on CAPM. We probe into the influential factors and relative weights of risk-free rate, expected market return, and beta of the security. The purpose of this research is to establish an investment decision model and provides investors with a reference of portfolio selection most suitable for investing effects to achieve the greatest returns. Taking full consideration of the interrelation effects among criteria/variables of the decision model, this paper examined leading semiconductor companies spanning the hottest sectors of integrated circuit (IC) design, wafer foundry, and IC packaging by experts. Empirical findings revealed that risk-free rate was affected by budget deficit, discount rate, and exchange rate; expected market return was affected by country risk, industrial structure, and macroeconomic factors; and beta of the security was affected by firm-specific risk and financial risk. Also, the factors of the CAPM possessed a self-effect relationship according to the DEMATEL technique. In the eight evaluation criteria, macroeconomic criterion was the most important factor affecting investment decisions, followed by exchange rate and firm-specific risk. In portfolio selection, leading companies in the wafer foundry industry outperformed those in IC design and IC packaging, becoming the optimal portfolio of investors during the time that this study was conducted.     

A hybrid stock selection model using genetic algorithms and support vector regression

In the areas of investment research and applications, feasible quantitative models include methodologies stemming from soft computing for prediction of financial time series, multi-objective optimization of investment return and risk reduction, as well as selection of investment instruments for portfolio management based on asset ranking using a variety of input variables and historical data, etc. Among all these, stock selection has long been identified as a challenging and important task. This line of research is highly contingent upon reliable stock ranking for successful portfolio construction. Recent advances in machine learning and data mining are leading to significant opportunities to solve these problems more effectively. In this study, we aim at developing a methodology for effective stock selection using support vector regression (SVR) as well as genetic algorithms (GAs). We first employ the SVR method to generate surrogates for actual stock returns that in turn serve to provide reliable rankings of stocks. Top-ranked stocks can thus be selected to form a portfolio. On top of this model, the GA is employed for the optimization of model parameters, and feature selection to acquire optimal subsets of input variables to the SVR model. We will show that the investment returns provided by our proposed methodology significantly outperform the benchmark. Based upon these promising results, we expect this hybrid GA-SVR methodology to advance the research in soft computing for finance and provide an effective solution to stock selection in practice.     

The trading on the mutual funds by gene expression programming with Sortino ratio

The aim of this paper is to combine several techniques together to provide one systematic method for guiding the investment in mutual funds. Many researches focus on the prediction of a single asset time series, or focus on portfolio management to diversify the investment risk, but they do not generate explicit trading rules. Only a few researches combine these two concepts together, but they adjust trading rules manually. Our method combines the techniques for generating observable and profitable trading rules, managing portfolio and allocating capital. First, the buying timing and selling timing are decided by the trading rules generated by gene expression programming. The trading rules are suitable for the constantly changing market. Second, the funds with higher Sortino ratios are selected into the portfolio. Third, there are two models for capital allocation, one allocates the capital equally (EQ) and the other allocates the capital with the mean variance (MV) model. Also, we perform superior predictive ability test to ensure that our method can earn positive returns without data snooping. To evaluate the return performance of our method, we simulate the investment on mutual funds from January 1999 to September 2012. The training duration is from 1999/1/1 to 2003/12/31, while the testing duration is from 2004/1/1 to 2012/9/11. The best annualized return of our method with EQ and MV capital allocation models are 12.08% and 12.85%, respectively. The latter also lowers the investment risk. To compare with the method proposed by Tsai et al., we also perform testing from January 2004 to December 2008. The experimental results show that our method can earn annualized return 9.07% and 11.27%, which are better than the annualized return 6.89% of Tsai et al.     

A fuzzy portfolio selection method based on possibilistic mean and variance

This paper deals with the portfolio selection problem when the returns of assets obey LR-type possibility distributions and there exist the limits on holdings. A new possibilistic mean–variance model to portfolio selection is proposed based on the definitions of the possibilistic return and possibilistic risk, which can better integrate an uncertain decision environment with vagueness and ambiguity. This possibilistic mean–variance model can be regarded as extensions of conventional probabilistic mean–variance methodology and previous possibilistic approaches since it contains less parameter and has a more extensive application. A numerical example of a possibilistic fuzzy portfolio selection problem is given to illustrate our proposed effective means and approaches. This project was supported by NCET (No.06-0749) and The National Natural Science Foundation of China (No.70571024).     

Modeling Hong Kong’s stock index with the Student t-mixture autoregressive model

It is well known that financial returns are usually not normally distributed, but rather exhibit excess kurtosis. This implies that there is greater probability mass at the tails of the marginal or conditional distribution. Mixture-type time series models are potentially useful for modeling financial returns. However, most of these models make the assumption that the return series in each component is conditionally Gaussian, which may result in underestimates of the occurrence of extreme financial events, such as market crashes. In this paper, we apply the class of Student t-mixture autoregressive (TMAR) models to the return series of the Hong Kong Hang Seng Index. A TMAR model consists of a mixture of g autoregressive components with Student t-error distributions. Several interesting properties make the TMAR process a promising candidate for financial time series modeling. These models are able to capture serial correlations, time-varying means and volatilities, and the shape of the conditional distributions can be time-varied from short- to long-tailed or from unimodal to multi-modal. The use of Student t-distributed errors in each component of the model allows for conditional leptokurtic distribution, which can account for the commonly observed unconditional kurtosis in financial data.     

An integrated multi-objective Markowitz–DEA cross-efficiency model with fuzzy returns for portfolio selection problem

In this paper, a novel multi objective model is proposed for portfolio selection. The proposed model incorporates the DEA cross-efficiency into Markowitz mean–variance model and considers return, risk and efficiency of the portfolio. Also, in order to take uncertainty in proposed model, the asset returns are considered as trapezoidal fuzzy numbers. Due to the computational complication of the proposed model, the second version of non-dominated sorting genetic algorithm (NSGA-II) is applied. To illustrate the performance of our model, the model is implemented for 52 firms listed in stock exchange market of Iran and the results are analyzed. The results show that the proposed model is suitable in compared with Markowitz and DEA models due to considering return, risk and efficiency, simultaneously.     

An adaptive neuro‐fuzzy system for stock portfolio analysis

We propose an adaptive neuro‐fuzzy inference system (ANFIS) for stock portfolio return prediction. Previous work has shown that portfolio optimization can be improved by using predicted stock earnings rather than historical earnings. We show that predicted portfolio returns can be improved by using ANFIS and taking as input a variety of technical and fundamental attributes about various indices of the stock market. To generate membership functions, we use a robust noise rejection‐clustering algorithm. The neuro‐fuzzy model is tested on portfolios constituted from the Tehran Stock Exchange. In our experiments, the proposed method performs better in predicting the portfolio return than the classical Markowitz portfolio optimization method, a multiple regression, a neural network, and the Sugeno–Yasukawa method. © 2010 Wiley Periodicals, Inc.     

Mean-Entropy Models for Fuzzy Portfolio Selection

This short paper proposes two types of credibility-based fuzzy mean-entropy models. In the short paper, entropy is used as the measure of risk. The smaller the entropy value is, the less uncertainty the portfolio return contains, and thus, the safer the portfolio is. Furthermore, as a measure of risk, entropy is free from reliance on symmetrical distributions of security returns and can be computed from nonmetric data. In addition, the short paper compares the fuzzy mean-variance model with the fuzzy mean-entropy model in two special cases and presents a hybrid intelligent algorithm for solving the proposed models in general cases. To illustrate the effectiveness of the proposed algorithm, the short paper also provides two numerical examples.      

Robust hedging strategies

While investing in foreign assets may bring additional benefits in terms of risk diversification, it may also expose the portfolio to a further source of risk derived from changes in the value of the foreign currencies. Hedging strategies for international portfolios have usually focused on the use of forward contracts to mitigate the currency risk. We propose an alternative formulation aimed at the reduction of the overall portfolio risk by assuming the returns are uncertain and maximizing the portfolio return for the worst possible outcome of the returns. This technique known as robust optimization provides a first guarantee on the portfolio value thanks to the non-inferiority property. We further complement our approach with forward contracts on the foreign exchange rates and options on the assets. Because the total return on any asset will be the product of its local return and currency return, the models proposed are bilinear and non convex. A reformulation of both the uncertainty set and the objective function as a semidefinite problem will yield an approximate tractable model. We compare the hedging alternatives proposed with simulated and historical market data and conclude on their relative benefits.     

Multiobjective portfolio optimization of ARMA–GARCH time series based on experimental designs

The modern portfolio theory has been trying to determine how an investor might allocate assets among the possible investments options. Since the seminal contribution provided by Harry Markowitz’s theory of portfolio selection, several other tools and procedures have been proposed to deal with return-risk trade-off. Furthermore, diversification across sources of returns and risks based on entropy indexes is another pivotal aspect in portfolio management. An efficient approach to model these portfolio properties with the proportion of each asset can be obtained according to mixture design of experiments. Desirability method can be applied to optimize this nonlinear multiobjective problem. Nevertheless, a tuning procedure is required, since preference articulation parameters in desirability algorithm are unknown a priori. As a result, a computer-aided desirability tuning method is proposed to find an optimal portfolio with time series of returns and risks modeled by ARMA–GARCH models. To assess the proposal feasibility, the method is tested with a heteroskedastic dataset formed by weekly world crude oil spot prices and returns. Computer-aided desirability tuning was able to enhance the global desirability by 79% in relation to the result with no tuning procedure.     

Uncertain programming models for portfolio selection with uncertain returns

In an indeterminacy economic environment, experts’ knowledge about the returns of securities consists of much uncertainty instead of randomness. This paper discusses portfolio selection problem in uncertain environment in which security returns cannot be well reflected by historical data, but can be evaluated by the experts. In the paper, returns of securities are assumed to be given by uncertain variables. According to various decision criteria, the portfolio selection problem in uncertain environment is formulated as expected-variance-chance model and chance-expected-variance model by using the uncertainty programming. Within the framework of uncertainty theory, for the convenience of solving the models, some crisp equivalents are discussed under different conditions. In addition, a hybrid intelligent algorithm is designed in the paper to provide a general method for solving the new models in general cases. At last, two numerical examples are provided to show the performance and applications of the models and algorithm.     

A multivariate threshold stochastic volatility model

We introduce in this paper a multivariate threshold stochastic volatility model for multiple financial return time series. This model allows the dynamic structure of return and volatility to change according to a threshold model while accounting for the interdependence of financial returns. Through the threshold volatility modeling, we can understand the impact of market news on volatility asymmetry. Estimation of unknown parameters are carried out using Markov chain Monte Carlo techniques. Simulations show that our estimators are reliable in moderately large sample sizes. We apply the model to three market indice data and estimate time-varying correlations among the indice returns.     

A new Chance-Variance optimization criterion for portfolio selection in uncertain decision systems

The Markowitz’s mean-variance (M-V) model has received widespread acceptance as a practical tool for portfolio optimization, and his seminal work has been widely extended in the literature. The aim of this article is to extend the M-V method in hybrid decision systems. We suggest a new Chance-Variance (C-V) criterion to model the returns characterized by fuzzy random variables. For this purpose, we develop two types of C-V models for portfolio selection problems in hybrid uncertain decision systems. Type I C-V model is to minimize the variance of total expected return rate subject to chance constraint; while type II C-V model is to maximize the chance of achieving a prescribed return level subject to variance constraint. Hence the two types of C-V models reflect investors’ different attitudes toward risk. The issues about the computation of variance and chance distribution are considered. For general fuzzy random returns, we suggest an approximation method of computing variance and chance distribution so that C-V models can be turned into their approximating models. When the returns are characterized by trapezoidal fuzzy random variables, we employ the variance and chance distribution formulas to turn C-V models into their equivalent stochastic programming problems. Since the equivalent stochastic programming problems include a number of probability distribution functions in their objective and constraint functions, conventional solution methods cannot be used to solve them directly. In this paper, we design a heuristic algorithm to solve them. The developed algorithm combines Monte Carlo (MC) method and particle swarm optimization (PSO) algorithm, in which MC method is used to compute probability distribution functions, and PSO algorithm is used to solve stochastic programming problems. Finally, we present one portfolio selection problem to demonstrate the developed modeling ideas and the effectiveness of the designed algorithm. We also compare the proposed C-V method with M-V one for our portfolio selection problem via numerical experiments.