Mean-variance Portfolio Model Research Articles

A novel Sigma-Mu multiple criteria decision aiding approach for mutual funds portfolio selection

A Sigma-Mu approach is proposed for mutual funds portfolio selection. The mean and variance of the overall performance of each asset are considered, according to an additive aggregation model, subject to weights’ preferences provided by the decision maker. These preferences concern two independent sets of weights, i.e., those pertaining to the investment indicators and those pertaining to the time periods associated with the estimation of the indicators. For the first time in the Sigma-Mu framework, a weighting matrix is exploited, assisting on the development of a method to appraise the sources of variance, due to the weighting scheme of either the indicators or the periods. The Mu's, Sigma's and covariances estimated according to the Sigma-Mu approach, enter as inputs to mixed-integer quadratic programming (MIQP) mean-variance portfolio optimization models, in order to implement an empirical testing procedure, for a period of 8 years. The underlying MIQP models are equipped to consider non-convex investment policy constraints, such as the number of securities to be included in the portfolio, specific binary buy-in thresholds, the desired exposure of the portfolio to each investment advisor etc. The dataset that has been chosen for the empirical testing includes European mutual funds, that offer a broad exposure to the whole span of investment strategies and styles. The results document that the suggested approach may effectively be utilized in mutual funds investment management, since the portfolios constructed by the suggested methodology are associated with superior absolute and risk-adjusted performance against benchmarks.

ESG integration in portfolio selection: A robust preference-based multicriteria approach

We present a framework for multi-objective optimization where the classical mean–variance portfolio model is extended to integrate the environmental, social and governance (ESG) criteria on the same playing field as risk and return and, at the same time, to reflect the investors’ preferences in the optimal portfolio allocation. To obtain the three–dimensional Pareto front, we apply an efficient multi-objective genetic algorithm, which is based on the concept of ɛ-dominance. We next address the issue of how to incorporate investors’ preferences to express the relative importance of each objective through a robust weighting scheme in a multicriteria ranking framework. The new proposal has been applied to real data to find optimal portfolios of socially responsible investment funds, and the main conclusion from the empirical tests is that it is possible to provide the investors with a robust solution in the mean–variance–ESG surface according to their preferences.

Optimization of large portfolio allocation for new-energy stocks: Evidence from China

Investment in the fast-growing new-energy of China has gradually attracted great attention. At present, more than 100 new-energy stocks are listed on China’s stock markets. How to effectively manage the investment risk of these stocks and achieve better returns is of great interest to investors and policymakers. In finance, mean–variance portfolio (MVP) is often applied to solve portfolio allocation problems. However, when investing in numerous stocks, the classical MVP is no longer applicable. For large portfolio allocation, this study constructs a comprehensive MVP model, called an unconstrained regression model with latent factors (URELAF). It applies a factor structure with latent factors to modify the covariance matrix estimation in the classical MVP, using an unconstrained penalized regression to estimate the allocation. In addition, to more realistically simulate the investment of stock markets, transaction costs are considered. The empirical results show that URELAF model can control the risk with Sharpe ratio reaching 6 times as many as MVP model, and even improve about 26% compared with the sub-optimal portfolio model. URELAF also outperforms other portfolios with transaction costs. Finally, hypothesis tests further verify that URELAF can significantly improve portfolio performance compared with other portfolio methods for China’s new-energy market.

Stock market optimization amidst the COVID-19 pandemic: Technical analysis, K-means algorithm, and mean-variance model (TAKMV) approach

The Philippine stock market, just like most of its neighbors in the region, was seriously impacted by the global pandemic COVID-19. Investors remain hopeful while continuing to seek great ones in the damaged market. This paper developed a methodology for portfolio selection and optimization with the use of technical analysis, machine learning techniques, and portfolio optimization model. The combined methods of technical analysis, K-means clustering algorithm, and mean-variance portfolio optimization model will result in the development of the proposed TAKMV method. The study aims to integrate these three important analyses to identify portfolio investments. This paper uses the average annual risk and annual rate of return data for the years 2018 and 2020 to form the clusters and assessed the stocks that correspond to the investor's technical strategy such as Moving Average Convergence/Divergence (MACD) and Hybrid MACD with Arnaud Legoux Moving Average (ALMA). This paper solved the risk minimization problem on selected shares of the companies, based on the mean-variance portfolio optimization model. There are 230 and 239 companies for 2018 and 2020, respectively, listed in Philippine Stock Market, and all simulations were performed in MATLAB environment platform. Results showed that MACD strategy dominates the MACD-ALMA strategy in terms of the number of assets with a positive annual rate of return. The MACD works efficiently in the pre-COVID-19 condition while MACD-ALMA works efficiently during-COVID-19 condition, regardless of the number of assets with a positive annual rate of return. The results also show that the maximum expected portfolio return (RP) can be achieved using the MACD and MACD-ALMA in the pre-and during-COVID-19 conditions, respectively. The MACD-ALMA shows an advantage during high-risk market conditions and can also provide maximum RP. The performance of the TAKMV method was validated by applying its results and comparing it to the next year's historical price. The 2018 results were compared to 2019 data and the 2020 results were compared to 2021 data. For consistency, the comparison was applied to the same company per portfolio. Simulation results show that the MACD strategy is more effective compared to MACD-ALMA.

Uncertain mean–variance portfolio model with inflation taking linear uncertainty distributions

Empirical studies show that in reality there are cases where distributions obtained from past data are not close to real frequencies, which implies that we cannot treat those indeterminate quantities as random variables. In this paper, we study a portfolio investment problem with a popular multiplicative background risk, i.e., inflation, in such cases. Treating risky asset return and inflation rate as uncertain variables, we propose an uncertain mean–variance model. Then we show by analysis that when the risky asset and uncertain inflation take linear uncertainty distributions, uncertain inflation increases the investment risk and leads the investors to invest less in risky asset. Furthermore, we prove that the investment proportion of risky asset increases with the mean of inflation rate and decreases with the increase of the width of inflation rate. Finally, we provide a case analysis to show the effect of uncertain inflation on portfolio investment and the robustness of the results.

International Portfolio Choice with Frictions: Evidence from Mutual Funds

Abstract Using data on international equity portfolio allocations by U.S. mutual funds, we estimate a portfolio expression derived from a standard mean-variance portfolio model extended with portfolio frictions. The optimal portfolio depends on the previous month and the buy-and-hold portfolio shares, and a present discounted value of expected excess returns. We estimate expected return differentials and use them in the portfolio regressions. The estimates imply significant portfolio frictions and a modest rate of risk aversion. While mutual fund portfolios significantly respond to expected returns, portfolio frictions lead to a weaker and a more gradual portfolio response to changes in expected returns. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

An alternative stochastic model for linear portfolios

Stock market returns often tend to follow a non-normal probability distribution due to extreme losses in the tails. These cause fatter tails than normal and consequently heavy-tailed probability distributions are mostly used for modeling returns. In this work, we consider the generalized T (GT) distribution which can be heavy-tailed through its parameters and propose to use it in modeling the random stock returns. The GT distribution also contains the normal, Student t and generalized Laplace distributions as special or limiting cases of the shape parameters. The closed form expressions for the important risk measures are obtained. In case of a portfolio modeling, a multivariate extension of the distribution within the class of elliptical distributions is used. The tail mean-variance portfolio model based on the multivariate GT distribution is developed and optimal portfolio problem is solved. Risk measures for the random return of an asset whose density function is a mixture of the GT densities are obtained. The computability of all expressions derived is shown, and a real data application consisting of seven real stocks from the same sector is given.

Online risk-based portfolio allocation on subsets of crypto assets applying a prototype-based clustering algorithm

Mean-variance portfolio optimization models are sensitive to uncertainty in risk-return estimates, which may result in poor out-of-sample performance. In particular, the estimates may suffer when the number of assets considered is high and the length of the return time series is not sufficiently long. This is precisely the case in the cryptocurrency market, where there are hundreds of crypto assets that have been traded for a few years. We propose enhancing the mean-variance (MV) model with a pre-selection stage that uses a prototype-based clustering algorithm to reduce the number of crypto assets considered at each investment period. In the pre-selection stage, we run a prototype-based clustering algorithm where the assets are described by variables representing the profit-risk duality. The prototypes of the clustering partition are automatically examined and the one that best suits our risk-aversion preference is selected. We then run the MV portfolio optimization with the crypto assets of the selected cluster. The proposed approach is tested for a period of 17 months in the whole cryptocurrency market and two selections of the cryptocurrencies with the higher market capitalization (175 and 250 cryptos). We compare the results against three methods applied to the whole market: classic MV, risk parity, and hierarchical risk parity methods. We also compare our results with those from investing in the market index CCI30. The simulation results generally favor our proposal in terms of profit and risk-profit financial indicators. This result reaffirms the convenience of using machine learning methods to guide financial investments in complex and highly-volatile environments such as the cryptocurrency market.

Solving Constrained Mean-Variance Portfolio Optimization Problems Using Spiral Optimization Algorithm

Portfolio optimization is an activity for balancing return and risk. In this paper, we used mean-variance (M-V) portfolio models with buy-in threshold and cardinality constraints. This model can be formulated as a mixed integer nonlinear programming (MINLP) problem. To solve this constrained mean-variance portfolio optimization problem, we propose the use of a modified spiral optimization algorithm (SOA). Then, we use Bartholomew-Biggs and Kane’s data to validate our proposed algorithm. The results show that our proposed algorithm can be an efficient tool for solving this portfolio optimization problem.

Impact of Investor Sentiment on Portfolio

ABSTRACT This study integrated investor sentiment into the binary system of the mean-variance portfolio model, to clarify the method affecting asset pricing through investor sentiment. The theoretical deduction and empirical research demonstrated that, investor sentiment can promote the vertical movement of the minimum variance set. This can lead to effective portfolio drift and subsequent changes in the investor recognized required rate of return. These findings, verified through theoretical conclusions and empirical evidence, explain investors’ extrapolated expectations and their behavior in positive feedback trading.

MINIMUM TSALLIS PORTFOLIO

Mean-variance portfolio optimization model has been shown to have serious drawbacks. The model assumes that assets returns are normally distributed that is not valid for most of the markets and portfolios. It also relies on asset’s covariance matrices for the calculation of portfolio’s risk that is open to estimation errors. Moreover, these optimization errors are maximized by the method that result in poor out-of-sample performances. In this study, we propose a new portfolio optimization method based on minimization of Tsallis entropy, which is valid for any underlying distribution. First, we show that the Tsallis entropy can be employed as a risk measure for portfolio analysis. Then we demonstrate the validity of the model by comparing its performance with those mean-variance and minimum-variance portfolios using BIST 30 data.

A New Approach for Robust Mean-Variance Portfolio Selection Using Trimmed k-Means Clustering

In this study, we consider the data preprocessing using trimmed k-means clustering for robust mean-variance portfolio selection. The proposed method trims the outliers in the data preprocessing stage. The optimum portfolio is formed by selecting the stock representation for each cluster using the Sharpe ratio. The optimum portfolio formation is accomplished by robust fast minimum covariance determinant (FMCD) and robust S mean-variance (MV) portfolio model. In the empirical experiment, we use fundamental trading data for the year 2017 (to form the clusters) and daily closing price data of LQ45 index stocks from August 2017 to July 2018 taken from the Indonesian Stock Exchange to form the optimum portfolio. As benchmark for portfolio performance formed in this study, we use the performance of the Indonesia Composite Index (ICI). The results reveal that the proposed method can reliably obtain the optimum portfolio and solve the outliers problem. Moreover, the comparison stage shows that the combination of trimmed k-means clustering and robust portfolio model is better in forming the optimum portfolio than the combination of k-means clustering and robust MV portfolio model. Finally, we also find that the combination of trimmed k-means clustering (with α=10%) and robust FMCD MV portfolio model outperforms portfolios produced by other methods.

Decision Making in Real Estate: Portfolio Approach

Abstract An investment policy is suggested about assets on real estate markets. Such analysis recommends investments in non-financial assets and optimization of the results from such decisions. The formalization of the investment policy is based on the portfolio theory for asset allocation. Two main criteria are applied for the decision making: return and risk. The decision support is based on Mean-Variance portfolio model. A dynamical and adaptive investment policy is derived for active portfolio management. Sliding procedure in time with definition and solution of a set of portfolio problems is applied. The decision defines the relative value of the investment to which real estates are to be allocated. The regional real estate markets of six Bulgarian towns, which identify the regions with potential for investments, are compared. The added value of the paper results in development of algorithm for a quantitative analysis of real estate markets, based on portfolio theory.

CCMV Portfolio Optimization with Stocks and Options using Forecasted Data

Although the future of a financial market is ambiguous and mysterious, historical data play a key role to forecast the future of the market. Along with all the advantages of these data, they may result to some errors and consequently, some losses. In this paper, we consider the cardinality constraints mean-variance (CCMV) portfolio optimization model in the presence of short selling, risk-neutral interest rate and transaction costs. We insure the investment using options against unfavorable outcomes. The Geometric Brownian Motion model is utilized to forecast the stocks prices. Also, to improve the results, we calibrate its parameters using historical data by the maximum likelihood estimation method. We perform numerical experiments using historical and forecasted data on the S&P 500 index, to assess the efficiency of the GBM model in forecasting stocks prices. Also, to examine the effect of options in the portfolio, we compare the portfolio with stocks only versus the portfolio with stocks and options using historical and forecasted data in terms of returns and Sharpe ratios.

Impact of ESG Rating of Companies on the Portfolio Performance

Socially responsible investing is becoming more popular among people because people are becoming more concerned about the environment and society. Socially responsible investors screen the company by considering the ESG factors. The question raced is whether socially responsible investing improves the portfolio performance and how the funds perform during uncertain times like the Covid-19 pandemic. Since many critics of ESG funds say that the ESG funds’ performance highly depends on Software and Service company stocks, so the relevance of Software and Service companies in the fund has been analyzed in this research. The portfolios have been formed by using the Markowitz mean-variance portfolio model, and the performance of the minimum variance portfolio has been studied. The fund performance has been analyzed using the Sharpe ratio, and the result concludes that the ESG fund performance with minimum variance has an abnormally high Sharpe Ratio of 10.8. A similar type of performance was identified during the Covid-19 pandemic. The abnormally high Sharpe ratio will encourage investors to move towards socially responsible investing.

Optimal trading strategy for integrated energy company based on integrated demand response considering load classifications

Integrated energy systems (IESs) have become a new transition for the traditional electricity industry. In the context of energy mix, end-users participating markets should consider diverse energy mix. Therefore, this paper proposes a day-ahead integrated energy market structure that allows electricity, heat energy and natural gas to trade simultaneously. Aiming at the maximal profit of integrated energy company (IECO) in the market, an optimal trading strategy based on integrated demand response (IDR) is optimized considering complex energy flow constraints of power distribution system, heat system and natural gas system. In this model, the IDR can be carried out based on three steps, i.e. information sharing of the integrated energy market, energy conversion of Energy Hub (EH) and flexible loads scheduling in the retail market. In particular, flexible loads are classified into shiftable loads, reducible loads and convertible loads according to their characteristics. Furthermore, a conditional value-at-risk based mean–variance portfolio model is set up to address the uncertain market prices. Finally, simulation results on a test system with a 33-bus power distribution system, an 11-node natural gas system and a 6-node District Heat System (DHS) demonstrate the effectiveness of the proposed model.

Some new efficient mean–variance portfolio selection models

AbstractThe poor out‐of‐sample performance of mean–variance portfolio model is mainly caused by estimation errors in the covariance matrix and the mean return, especially the mean return vector. Meanwhile, in financial practice, what most investors actually like is to hold a few stocks in their portfolio. The goal of this paper is to propose some new efficient mean–variance portfolio selection models by considering the following aspects: (i) use the L1‐regularization in objective function to obtain sparse portfolio; (ii) use the shrinkage method of Ledoit and Wolf, Journal of Economics Financial, 2003, 10, 603–621 to estimate the covariance matrix; (iii) use the robust optimization method to mitigate the estimation errors of the expected return. Finally, empirical analysis demonstrates that the proposed strategies have better out‐of‐sample performance.

Multiperiod portfolio selection models under uncertain measure and with multiple criteria

This paper explores a multiperiod portfolio optimization problem under uncertain measure involving background risk, liquidity constraints and V-shaped transaction costs. Unlike traditional studies, we establish multiperiod mean-variance portfolio optimization models with multiple criteria in which security returns, background asset returns and turnover rates are assumed to be uncertain variables that can be estimated by experienced experts. When the returns of the securities and background assets follow normal uncertainty distributions, we use the deterministic forms of the multiperiod portfolio optimization model. The uncertain multiperiod portfolio selection models are practical but complicated. Therefore, the models are solved by employing a genetic algorithm. The uncertain multiperiod model with multiple criteria is compared with an uncertain multiperiod model without background risk and an uncertain multiperiod model without liquidity constraint respectively, we discuss how background risk and liquidity affect optimal terminal wealth. Finally, we give two numerical examples to demonstrate the effectiveness of the proposed approach and models.

Portfolio optimization based on generalized information theoretic measures

In this article, we compare the efficiency of the traditional Mean-Variance (MV) portfolio model proposed by Markowitz with the models which incorporate diverse information theoretic measures such as Shannon entropy, Renyi entropy, Tsallis entropy, and two-parameter Varma entropy. We put these measures as the objective function of the portfolio optimization problem with constraints derived from the mean and variance of the financial market data. Our approach is substantiated by an application to the 10 most liquid NIFTY indices of the Indian financial market and our findings show that using portfolio performance measures like Award Risk Ratio (ARR) and diversity index, the model with generalized information entropy measures yields higher performance than those with other traditional portfolio optimization techniques, like MV model. Furthermore, including the additional condition on variance as a constraint in maximum entropy models reduces portfolio diversity and makes allocation of assets less feasible than the models without incorporating variance.

Research on the portfolio model based on Mean-MF-DCCA under multifractal feature constraint

In order to incorporate the multifractal characteristics of the capital market into the research framework of portfolios and overcome the shortcomings of existing research results that had not considered the existence of multiple fractal fluctuation characteristics and multiple fractal correlation characteristics of asset prices, in this paper, multifractal detrended cross-correlation analysis (MF-DCCA) was embedded into the mean–variance criterion, the Mean-MF-DCCA portfolio model was constructed under the constraints of multiple fractal features, and the analytical solution of the model was given. On this basis, the effectiveness of Mean-MF-DCCA portfolio model was tested using empirical analysis. The results showed that the Mean-MF-DCCA portfolio model was effective, and compared with the mean–variance portfolio model, it is more conducive to investors to construct a sophisticated portfolio under the multiple fluctuation importance degree and multiple time scales, so as to improve their portfolio performance.