Variance Portfolio Optimization Research Articles

Enhancing mean–variance portfolio optimization through GANs-based anomaly detection

Enhancing mean–variance portfolio optimization through GANs-based anomaly detection

Dynamic Mean–Variance Portfolio Optimization with Value-at-Risk Constraint in Continuous Time

Recognizing the importance of incorporating different risk measures in the portfolio management model, this paper examines the dynamic mean-risk portfolio optimization problem using both variance and value at risk (VaR) as risk measures. By employing the martingale approach and integrating the quantile optimization technique, we provide a solution framework for this problem. We demonstrate that, under a general market setting, the optimal terminal wealth may exhibit different patterns. When the market parameters are deterministic, we derive the closed-form solution for this problem. Examples are provided to illustrate the solution procedure of our method and demonstrate the benefits of our dynamic portfolio model compared to its static counterpart.

A LINEAR-PROGRAMMING PORTFOLIO OPTIMIZER TO MEAN–VARIANCE OPTIMIZATION

In the Markowitz mean–variance portfolio optimization problem, the estimation of the inverse covariance matrix is not trivial and can even be intractable, especially when the dimension is very high. In this paper, we propose a linear-programming portfolio optimizer (LPO) to solve the Markowitz optimization problem in both low-dimensional and high-dimensional settings. Instead of directly estimating the inverse covariance matrix [Formula: see text], the LPO method estimates the portfolio weights [Formula: see text] through solving an [Formula: see text]-constrained optimization problem. Moreover, we further prove that the LPO estimator asymptotically yields the maximum expected return while preserving the risk constraint. To offer a practical insight into the LPO approach, we provide a comprehensive implementation procedure of estimating portfolio weights via the Dantzig selector with sequential optimization (DASSO) algorithm and selecting the sparsity parameter through cross-validation. Simulations on both synthetic data and empirical data from Fama–French and the Center for Research in Security Prices (CRSP) databases validate the performance of the proposed method in comparison with other existing proposals.

Mean–variance portfolio selection under no-shorting rules: A BSDE approach

This paper revisits the mean–variance portfolio selection problem in continuous-time within the framework of short-selling of stocks is prohibited via backward stochastic differential equation approach. To relax the strong condition in Li et al. (Li et al. 2002), the above issue is formulated as a stochastic recursive optimal linear–quadratic control problem. Due to no-shorting rules (namely, the portfolio taking non-negative values), the well-known “completion of squares” no longer applies directly. To overcome this difficulty, we study the corresponding Hamilton–Jacobi–Bellman (HJB, for short) equation inherently and derive the two groups of Riccati equations. On one hand, the value function constructed via Riccati equations is shown to be a viscosity solution of the HJB equation mentioned before; On the other hand, by means of these Riccati equations and backward semigroup, we are able to get explicitly the efficient frontier and efficient investment strategies for the recursive utility mean–variance portfolio optimization problem.

A Mayfly algorithm for cardinality constrained portfolio optimization

Portfolio optimization is an essential issue in quantitative investing, which aims to find the best set of portfolios by allocating the proportion of assets. One of the most widely studied portfolio optimization models is the cardinality constrained mean–variance model, which incorporates real-world constraints on the number of selected assets and lower and upper bounds on the proportion of each asset. This paper presents a novel metaheuristic algorithm based on the Mayfly algorithm to solve the cardinality constrained mean–variance portfolio optimization problem. To better adapt to this problem, we design and introduce some new features to the proposed algorithm, including (1) a new cardinality constraint handling strategy; (2) a new local search strategy; and (3) changes to the crossover operator. We have designed comparison experiments for the proposed metaheuristic and evaluated its performance using five commonly used performance metrics. The experimental results show that the proposed approach achieves competitive performance on datasets of different sizes. The results also demonstrate the feasibility of this approach in solving the cardinality constrained mean–variance portfolio optimization problem.

Application of Maximum Sharpe Ratio and Minimum Variance Portfolio Optimization for Industries

Since the start of 2022, expectations regarding the continuous raising of interest rates by the Fed to curb the 40-year-high inflation has been negatively impacting the US stock market, leading to volatility spikes. Thus, portfolio optimization plays an important role to risk-averse investors. This paper investigated an optimal portfolio strategy that aims to maximize the Sharpe ratio to outperform a common benchmark, the S&P500. Eleven US stocks were selected, one from each of the eleven market sectors, based on market capitalization. Then, mean-variance portfolio optimization was conducted to obtain an optimal distribution of stocks weighing in Maximum Sharpe Ratio Portfolio (MSRP) and Global Minimum Variance Portfolio (GMVP), and backtesting was adopted to construct portfolio performance for MSRP, GMVP and Equal-Weight Portfolio (1/N) strategies by using historical data from the first eight months of 2022. The Sharpe ratio was calculated to compare the performance between the three strategies---MSRP, GMVP and 1/N---and the S&P500. Empirical results, supported by a robustness test, suggested that MSRP strategy outperformed S&P500 with the highest Sharpe ratio, which indicated that MSRP achieved a higher return per unit of risk regardless of market volatility presented in different time intervals. Therefore, this research provides insights into portfolio investment decision-making for risk-averse investors.

Average variance portfolio optimization using machine learning-based stock price prediction case of renewable energy investments

With the progress of time series prediction, several recent developments in machine learning have shown that the integration of prediction methods into portfolio selection is a great opportunity to structure investment decisions in the renewable energy industry. In this paper, we propose a novel approach to portfolio formation strategy based on a hybrid machine learning model that combines a convolutional neural network (CNN) and long-term bidirectional memory (BiLSTM) with robust input characteristics obtained from Huber’s location for stock prediction and the mean-variance (MV) Markowitz model for optimal portfolio construction. Specifically, this study first applies a prediction method for stock pre-selection to ensure high-quality stock inflows for portfolio formation. Then, the predicted results are integrated into the MV model. To comprehensively demonstrate the superiority of the proposed model, we used two portfolio models, the MV model and the equal-weighted (1/N) portfolio model, with LSTM, BiLSTM and CNN-BiLSTM, and used them as references. Between January 2016 and December 2021, historical data from the Stock Exchange of Thailand 50 Index (SET50) was collected for the study. Experience shows that integrating stock pre-selection can improve VM performance, and the results of the proposed method show that they outperform comparison models in terms of Sharpe ratio, average return and risk.

Portfolio construction as linearly constrained separable optimization

Mean–variance portfolio optimization problems often involve separable nonconvex terms, including penalties on capital gains, integer share constraints, and minimum nonzero position and trade sizes. We propose a heuristic algorithm for such problems based on the alternating direction method of multipliers (ADMM). This method allows for solve times in tens to hundreds of milliseconds with around 1000 securities and 100 risk factors. We also obtain a bound on the achievable performance. Our heuristic and bound are both derived from similar results for other optimization problems with a separable objective and affine equality constraints. We discuss a concrete implementation in the case where the separable terms in the objective are piecewise quadratic, and we empirically demonstrate its effectiveness for tax-aware portfolio construction.

Application of LSTM and portfolio optimization in Chinese stock market

The purpose of this paper is to examine the application of LSTM and mean variance portfolio optimization in Chinese stock market. 20 stocks are selected from CSI 300 components, we collect their High, Low, Open, Adjust Close and trade volume from June 16th 2020 to June 16th 2022. Then we use LSTM model to forecast the stock price. The forecast results are used to construct 2 portfolios. One portfolio maximize Sharpe ratio, the other portfolio minimize variance. From April 6th to June 16th 2022, the Maximize Sharpe Ratio portfolio outperformed CSI 300 index, the Minimize Variance Portfolio did not beat the market but the return was very close to CSI. Therefore, the combination of LSTM and Mean Variance Portfolio Optimization theory is effective in Chinese stock market.

A portfolio stock selection model based on expected utility, entropy and variance

In the context of investment decision-making, the selection of stocks is important for a successful construction of portfolios. In this paper the expected utility, entropy and variance (EU-EV) model is applied for stock selection, which can be used as preselection model for mean–variance portfolio optimization problems. Based on the EU-EV risk, stocks are ranked and the best ranked stocks with lower risk are selected in order to form subsets of stocks, which are then used to construct portfolios. The EU-EV model is applied to the PSI 20 index, to the Euro Stoxx 50 index and to the Nasdaq 100 index. Subsets of selected stocks are analysed and their portfolios’ efficiencies are compared with those of the portfolios obtained from the whole set of stocks using the mean–variance model. The results reveal that the EU-EV model is an adequate stock selection model for building up efficient portfolios with a lower number of stocks.

A novel evolutionary optimization algorithm based solution approach for portfolio selection problem

<span>The portfolio selection problem is one of the most common problems which drawn the attention of experts of the field in recent decades. The mean variance portfolio optimization aims to minimize variance (risk) and maximize the expected return. In case of linear constraints, the problem can be solved by variants of Markowitz. But many constraints such as cardinality, and transaction cost, make the problem so vital that conventional techniques are not good enough in giving efficient solutions. Stochastic fractal search (SFS) is a strong population based meta-heuristic approach that has derived from evolutionary computation (EC). In this paper, a novel portfolio selection model using SFS based optimization approach has been proposed to maximize Sharpe ratio. SFS is an evolutionary approach. This algorithm models the natural growth process using fractal theory. Performance evaluation has <span>been conducted to determine the effectiveness of the model by making comparison with other state of art models such as <a name="_Hlk101168095"></a>genetic algorithm (GA) and simulated</span> annealing (SA) on same objective and environment. The real datasets of the Bombay stock exchange (BSE) Sensex of Indian stock exchange have been taken in the study. Study reveals the superior performance of the SFS than GA and SA.</span>

Interactive portfolio optimization model based on rough fundamental analysis and rational fuzzy constraints

Research on mean–variance portfolio optimization (MVPO) has made significant progress in the application of advanced solution algorithms or multiple criteria decision-making methods to achieve superior outcomes. However, there is little specific guidance on how to approach individually preferred optimization bounded by rationality. Therefore, the main goal of this study is to extend MVPO research by incorporating an investor’s preferences and rational expectations during optimizations. Using a set of equities from the Taiwan stock market, this study proposes an interactive MVPO model guided by personal risk-return preferences and bounded by rational fuzzy constraints. Furthermore, this study adopts a rule-based bipolar model to prioritize candidate equities and support the interactive optimization process. This hybrid model is an early attempt to investigate bounded rationality in MVPO, which integrates multiple rule-based decision-making with multiple objective decision-making. The obtained portfolio outperformed two benchmark indexes in 2020, suggesting the feasibility of this approach.

Mean–variance portfolio optimization with deep learning based-forecasts for cointegrated stocks

Most mean–variance (MV) models construct a portfolio based on nonstationary stocks. This study presents a new MV model constructed using stationary portfolios composed of cointegrated stocks. The expected return of this new model is predicted by using machine learning models, such as support vector machine, random forest, and attention-based long short-term memory (LSTM) network. The proposed model is evaluated using data on stocks in the CSI 300 and the S&P 500, with 42 features over 8 years from May 4, 2012 to August 4, 2020. The empirical results show that the portfolio constructed based on the stationary portfolios in both the Chinese and the US stock markets delivers significant profits. Further, the attention-based LSTM network can more accurately model the spread return using technical indicators, financial investment information, and lagged returns, and can successfully select pairs of cointegrated stocks for constructing a more profitable MV portfolio, than can conventional machine learning models. Using the attention-based LSTM to predict 20-day return movement results in model accuracy of up to 92.59% for the CSI 300 and 88.52% for the S&P 500, and a corresponding Sharpe ratio of 9.31 and 2.77, respectively.

Orthogonal portfolios to assess estimation risk

This document presents the various advantages of using portfolio rules composed by linear combinations of the orthogonal components derived from the optimal solution to a linearly constrained mean–variance portfolio optimization problem. We argue that this practice has value in and of itself since it pushes forward the tractability of the out-of-sample performance measure, and the identification of risk sources in the portfolio. This structure is further used to propose new correction schemes based on shrinkage factors that improve out-of-sample performance, and to study its limiting behavior as both the sample size and the number of assets increase. Additionally, our results are compared with those corresponding to the theoretical and implementable three-fund rules of Kan and Zhou (2007) so the benefits of using orthogonal portfolio rules are highlighted.

Linear Pooling of Sample Covariance Matrices

We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a distinct linear combination of all class sample covariance matrices. This approach is shown to reduce the estimation error when the sample sizes are limited, and the true class covariance matrices share a somewhat similar structure. We develop an effective method for estimating the coefficients in the linear combination that minimize the mean squared error under the general assumption that the samples are drawn from (unspecified) elliptically symmetric distributions possessing finite fourth-order moments. To this end, we utilize the spatial sign covariance matrix, which we show (under rather general conditions) to be an asymptotically unbiased estimator of the normalized covariance matrix as the dimension grows to infinity. We also show how the proposed method can be used in choosing the regularization parameters for multiple target matrices in a single class covariance matrix estimation problem. We assess the proposed method via numerical simulation studies including an application in global minimum variance portfolio optimization using real stock data.

Deep learning for efficient frontier calculation in finance

We propose deep neural network algorithms to calculate the efficient frontier in mean–variance and mean–conditional value-at-risk (mean–CVaR) portfolio optimization problems. Starting with the mean–variance portfolio optimization problem in the Black–Scholes framework, we first compare the analytical solution with the computed one, and we show the efficiency of the methodology in high dimensions. Adding additional constraints, we compare different formulations and, obtaining the same frontier, show that the “no short selling” and “no borrowing” problem can be solved with all formulations. Then, a new projected feedforward network is shown to be able to deal with some local and global constraints on the weights of the portfolio while outperforming classical penalization methods. We extend our numerical results to assets following the Heston model, and we show that the results obtained in the Black–Scholes method still hold. Finally, we present numerical results for the more difficult mean–CVaR optimization problem, which we show are realistic only for algorithms with a global resolution of the problem.

The Gerber Statistic: A Robust Co-Movement Measure for Portfolio Optimization

The purpose of this article is to introduce the Gerber statistic, a robust co-movement measure for covariance matrix estimation for the purpose of portfolio construction. The Gerber statistic extends Kendall’s Tau by counting the proportion of simultaneous co-movements in series when their amplitudes exceed data-dependent thresholds. Because the statistic is not affected by extremely large or extremely small movements, it is especially well suited for financial time series, which often exhibit extreme movements and a great amount of noise. Operating within the mean–variance portfolio optimization framework of Markowitz, we consider the performance of the Gerber statistic against two other commonly used methods for estimating the covariance matrix of stock returns: the sample covariance matrix (also called the <i>historical covariance matrix</i>) and shrinkage of the sample covariance matrix given by Ledoit and Wolf. Using a well-diversified portfolio of nine assets over a 30-year period (January 1990–December 2020), we find, empirically, that for almost all investment scenarios considered, the Gerber statistic’s returns dominate those achieved by both historical covariance and by the shrinkage method of Ledoit and Wolf.

Bitcoin investments and climate change: A financial and carbon intensity perspective

Climate-related criticism of Bitcoin is primarily based on the network's absolute carbon emissions, without considering its market value. Taking a relative emission perspective and utilizing the mean–variance portfolio optimization framework, we study the financial and carbon-related implications of Bitcoin investments. The results of our in-sample analysis show that adding Bitcoin to a diversified equity portfolio can both enhance the risk–return relationship of the portfolio and reduce the portfolio's aggregate carbon emissions. This finding persists under various assumptions regarding Bitcoin prices, carbon emission estimates, and carbon prices.

A rapidly converging artificial bee colony algorithm for portfolio optimization

A survey of the relevant literature shows that there have been many studies of the portfolio optimization problem, and that the number of these studies that have been based on heuristic techniques is quite high. We present a heuristic approach to the portfolio optimization problem using the artificial bee colony technique. As a test dataset, we use weekly prices from March 1992 to September 1997 from the following indices: Hang Seng in Hong Kong, DAX 100 in Germany, FTSE 100 in the UK, S&P 100 in the USA and Nikkei in Japan. This test dataset also includes daily prices from May 2013 to April 2016 from the XU030 and XU100 indices in Turkey. In this study, the cardinality-constrained mean–variance portfolio optimization model is treated as a mixed quadratic and integer programming problem, for which heuristic approaches are appropriate. The results of this study are compared with those of genetic algorithms, tabu search, simulated annealing, particle swarm optimization, a differential evaluation algorithm, a greedy randomized adaptive search procedure, an artificial bee colony, ant colony optimization, and a variable neighborhood search algorithm. The purpose of this paper is to present a relatively efficient and effective heuristic method to the portfolio optimization problem. The results show that the proposed artificial bee colony approach achieves these aims.

PRACTICAL INVESTMENT CONSEQUENCES OF THE SCALARIZATION PARAMETER FORMULATION IN DYNAMIC MEAN–VARIANCE PORTFOLIO OPTIMIZATION

We consider the practical investment consequences of implementing the two most popular formulations of the scalarization (or risk-aversion) parameter in the time-consistent dynamic mean–variance (MV) portfolio optimization problem. Specifically, we compare results using a scalarization parameter assumed to be (i) constant and (ii) inversely proportional to the investor’s wealth. Since the link between the scalarization parameter formulation and risk preferences is known to be nontrivial (even in the case where a constant scalarization parameter is used), the comparison is viewed from the perspective of an investor who is otherwise agnostic regarding the philosophical motivations underlying the different formulations and their relation to theoretical risk-aversion considerations, and instead simply wishes to compare investment outcomes of the different strategies. In order to consider the investment problem in a realistic setting, we extend some known results to allow for the case where the risky asset follows a jump-diffusion process, and examine multiple sets of plausible investment constraints that are applied simultaneously. We show that the investment strategies obtained using a scalarization parameter that is inversely proportional to wealth, which enjoys widespread popularity in the literature applying MV optimization in institutional settings, can exhibit some undesirable and impractical characteristics.