Mean-variance Portfolio Research Articles

A Fast Successive QP Algorithm for General Mean-Variance Portfolio Optimization

A Fast Successive QP Algorithm for General Mean-Variance Portfolio Optimization

Static Markowitz mean-variance portfolio selection model with long-term bonds

We propose a static Markowitz mean-variance portfolio selection model suitable for long-term zero-coupon bonds. The model uses a multi-factor term structure model of Vasicek (Ornstein-Uhlenbeck) type to compute the portfolio's expected return and its variance in the model. German Government zero-coupon bonds with short to very long time to maturity are considered; the data spans August 2002 to December 2020. The main investment assumption is the re-investment of cash flows of zero-coupon bonds with maturities less than the planning horizon at the current spot interest rate. Solutions for the zero-coupon holding vector and the tangency portfolio are obtained in closed form. Model parameters are estimated under an assumption of modeling ambiguity which takes the form of Knightian uncertainties at the level of the latent factors, allowing the use of a Kalman filter. Different investment strategies are examined on various risk portfolios. Results show that one- and two-factor Vasicek models produce attractive out-of-sample portfolio predictions in terms of the Sharpe ratio especially on long-term investments. It is also noted that a small number of risky bonds can adequately produce very attractive portfolio risk-return profiles.

Construct an Empirical Study on the Concept, Modern Portfolio Theory Using Markowitz Model

In 1952, Harry Markowitz outlined a concept to aid financiers. By examining different combinations of the provided securities, the model aids in the selection of the optimal portfolio. He proposed an assumption of Modern Portfolio Theory, which aids in the creation of an optimal portfolio via the analysis of several portfolios. The Markowitz model is a theoretical framework for investigating the connections between different types of investment risk and return. The Modern Portfolio Theory (MPT) may help risk-averse investors create diversified portfolios that maximize returns without taking on undue risk. A forecasted return on each asset is required for current portfolio theory to be applied. There is no assurance that future results can be predicted based on past performance. Several market and investor presuppositions form the basis of MPT. We will first describe our finding on the "Markowitz optimization riddle" and the "Markowitz mean-variance portfolio theory," and then provide the theoretical proofs of our findings. Returns on investments are treated as random variables in the Markowitz mean-variance portfolio theory. So, picking the right portfolio weighting components is essential.

A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection

We consider the control of McKean-Vlasov dynamics (or mean-field control) with probabilistic state constraints. We rely on a level-set approach which provides a representation of the constrained problem in terms of an unconstrained one with exact penalization and running maximum or integral cost. The method is then extended to the common noise setting. Our work extends (Bokanowski, Picarelli, and Zidani, SIAM J. Control Optim. 54.5 (2016), pp. 2568–2593) and (Bokanowski, Picarelli, and Zidani, Appl. Math. Optim. 71 (2015), pp. 125–163) to a mean-field setting.The reformulation as an unconstrained problem is particularly suitable for the numerical resolution of the problem, that is achieved from an extension of a machine learning algorithm from (Carmona, Laurière, arXiv:1908.01613 to appear in Ann. Appl. Prob., 2019). A first application concerns the storage of renewable electricity in the presence of mean-field price impact and another one focuses on a mean-variance portfolio selection problem with probabilistic constraints on the wealth. We also illustrate our approach for a direct numerical resolution of the primal Markowitz continuous-time problem without relying on duality.

A Deep Neural Network Algorithm for Linear-Quadratic Portfolio Optimization With MGARCH and Small Transaction Costs

We analyze a fixed-point algorithm for reinforcement learning (RL) of optimal portfolio mean-variance preferences in the setting of multivariate generalized autoregressive conditional-heteroskedasticity (MGARCH) with a small penalty on trading. A numerical solution is obtained using a neural network (NN) architecture within a recursive RL loop. A fixed-point theorem proves that NN approximation error has a big-oh bound that we can reduce by increasing the number of NN parameters. The functional form of the trading penalty has a parameter ϵ > 0 that controls the magnitude of transaction costs. When ϵ is small, we can implement an NN algorithm based on the expansion of the solution in powers of ϵ. This expansion has a base term equal to a myopic solution with an explicit form, and a first-order correction term that we compute in the RL loop. Our expansion-based algorithm is stable, allows for fast computation, and outputs a solution that shows positive testing performance.

Mean-Variance and Single-Index Model Portfolio Optimisation:Case in the Indonesian Stock Market

Manuscript type: Research paper Research aims: This study aims to compare the performance of meanvariance and single-index models in creating the optimal portfolio. Design/Methodology/Approach: This study creates optimal portfolios using the mean-variance and single-index models with daily stock return data of 38 companies listed on the LQ45 index, IDX Composite index and Bank Indonesia’s 7-Day (Reverse) Repo Rate from January 1, 2012 to December 31, 2019. The two models are compared using the Sharpe ratio. Research findings: The result shows that the single-index model dominates the Indonesian Stock Exchange (IDX), more so than the meanvariance model. BBCA has the highest proportion for both mean-variance and single-index portfolios. Theoretical contribution/Originality: This study compares two popular portfolio models in the Indonesian stock market. Practitioner/Policy implication: This study helps investors to create optimal portfolios using a model that is more suited to the IDX. Research limitation/Implication: This study creates the optimal portfolio without differentiating risk preferences (i.e., risk averse, risk moderate and risk taker). In addition, this research only uses daily return data and does not compare it with weekly and monthly data.

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.

Portfolios under Different Methods and Scenarios: A Case of Fiji’s South Pacific Stock Exchange

In this study, we analyze portfolio performance under different methods and scenarios for the small island economy of Fiji. In addition to documenting the historical performance and the smallness of the stock market, the study looks at the possibility of opting for an equally weighted (naïve) portfolio against market and minimum variance portfolios. To this end, we extract monthly stock price data of 17/19 listed companies from August 2019 to July 2022 and invoke different approaches to develop portfolios under different scenarios. We consider the mean-variance, minimum variance, semi-variance, utility maximization, and minimum turbulence portfolios, based on beta-adjusted (CAPM-based) returns. The different portfolios presented in the study should provide some insights on asset allocation in Fiji’s stock market. Interestingly, unlike average returns, the beta-adjusted returns indicate that an equally weighted portfolio can yield relatively higher expected returns than market portfolios, although, with a relatively higher standard deviation and lower Sharpe ratio than the optimized results. In a semi-variance analysis (where we account for downside risk only), equally weighted portfolio yields superior returns, albeit with a relatively lower Sortino ratio. Given that Fiji’s stock market is currently a small, with a relatively small number of listed companies, potential and less sophisticated investors and analysts considering portfolios based on beta-adjusted returns, may simply opt for 1/N (naïve) portfolios as a diversification strategy while realizing decent expected returns. The optimized portfolio under mean-variance, semi-variance, and utility are presented as alternative considerations for nuanced investors. Additionally, equally weighted turbulence-adjusted and minimum-turbulence portfolios are constructed to capture periods of unusualness and calmness in the market. The methodologies and the results presented can be adjusted and applied to other small markets and hence can influence investment decisions of investors in creating diversified portfolios under different scenarios.

Asset Allocation in Indonesian Stocks Using Portfolio Robust

The mean-variance portfolio has several weaknesses. It does not accommodate the uncertainty of parameters, tends to be sensitive to the changes of parameter input, and tends to be unreliable on extreme observations. Moreover, it cannot accommodate the changes in investor preferences regarding the evidence of abnormal and asymmetric asset return distribution. To overcome these three weaknesses, we can use the robust mean-variance portfolio that is based on the uncertainty of parameters. However, the robust mean-variance portfolio has not included skewness in its optimization. Therefore, here in this paper, we use the robust mean-variance-skewness portfolio which includes skewness in its optimization. So it can be used for the condition where the data return is skewed asymmetric and contains extreme values. An empirical study of robust mean-variance and robust mean-variance-skewness portfolios has been conducted on four banking stocks in Indonesia, i.e AGRS.JK, BTPN.JK, BBNI.JK, and BBCA.JK. The data used in this study is the daily closing price of the company's stock price for the period January 2, 2020 – January 2, 2022 (489 days) obtained from Yahoo! Finance. From the results of the data analysis, it can be concluded that the variance still plays an important role in determining the weight of the allocation of a portfolio. Meanwhile, the large value of skewness leads to the allocation of the same weight for each stock in a portfolio.

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.

Short Communication: Cone-Constrained Monotone Mean-Variance Portfolio Selection under Diffusion Models

We consider monotone mean-variance (MMV) portfolio selection problems with a conic convex constraint under diffusion models, and their counterpart problems under mean-variance (MV) preferences. We obtain the precommitted optimal strategies to both problems in closed form and find that they coincide, with and without the presence of the conic constraint. This result generalizes the equivalence between MMV and MV preferences from nonconstrained cases to a specific constrained case. A comparison analysis reveals that the orthogonality property under the conic convex set is a key to ensuring the equivalence result.

Optimizing offshore renewable portfolios under resource variability

The deployment of offshore wind, wave, and ocean current technologies can be coordinated to provide maximum economic benefit. We develop a model formulation based on Mean-Variance portfolio theory to identify the optimal site locations for a given number of wind, wave, and ocean current turbines subject to constraints on their energy collection system and the maximum number of turbines per site location. A model relaxation is also developed to improve the computational efficiency of the optimization process, allowing the inclusion of more than 5000 candidate generation sites. The model is tested using renewable resource estimates from the coast of North Carolina, along the eastern US coast. Different combinations of technology-specific offshore technologies are compared in terms of their levelized cost of electricity and energy variability. The optimal portfolio results are then included in a capacity expansion model to derive economic targets that make the offshore portfolios cost-competitive with other generating technologies. Results of this work indicate that the integration of different offshore technologies can help to decrease the energy variability associated with marine energy resources. Furthermore, this research shows that substantial cost reductions are still necessary to realize the deployment of these technologies in the region investigated.

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.

A mean-variance portfolio optimization approach for high-renewable energy hub

This paper proposes a high-renewable portfolio model of energy hub. In this model, geothermal-solar-wind multi-energy complementarities are fully explored based on electrolytic thermo-electrochemical effects of geothermal-to-hydrogen (GTH), which are converted, conditioned, and coupled through energy hub. The proposed high-renewable energy hub portfolio is an intractable optimization problem due to their inherent strong energy couplings and conflicted energy cost/risk. The original problem is thus characterized through the mean-variance approach to explicitly express the risk associated with the forecast uncertainties. The formulated mean-variance portfolio problem is subsequently modeled as a two-stage mixed-integer nonlinear programming (MINLP) stochastic programming to optimally determine appropriate energy generation, conversion, and storage candidates. Numerical studies on a community microgrid are implemented to verify the effectiveness and superiority of the proposed methodology over conventional wind-solar-battery scheme. Simulations results show that the portfolio cost can be reduced by at most 14.9% with a significantly higher operational flexibility.

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>

Dynamic optimal mean-variance portfolio selection with stochastic volatility and stochastic interest rate

Dynamic optimal mean-variance portfolio selection with stochastic volatility and stochastic interest rate

Hybrid Enhanced Binary Honey Badger Algorithm with Quadratic Programming for Cardinality Constrained Portfolio Optimization

A portfolio selection problem with cardinality constraints has been proved to be an NP-hard problem, and it is difficult to solve by the traditional optimization methods. This study considers it to be a hybrid of a classical feature selection problem and a standard mean-variance (MV) portfolio selection model. In particular, we propose a new hybrid meta-heuristic algorithm that combines an enhanced binary honey badger algorithm (EBHBA) with quadratic programming to address this issue. First, we employ the proposed EBHBA algorithm to select a portfolio of [Formula: see text] stocks from [Formula: see text] candidate stocks. Second, based on its choice we transform the problem into a mean-variance model, whose objective function could be defined as the fitness function of EBHBA. Finally, the optimal solution to the model could be found with the quadratic programming method. We also test our approach using the benchmark data sets available at the OR-Library involving real capital markets, where indices are derived from major stock markets around the world. Computational results demonstrate that the proposed method can achieve a satisfactory result for portfolio selection with cardinality constraints and perform well in searching non-dominated portfolios with high expected returns.

Exploiting Mean-Variance Portfolio Optimization Problems through Zeroing Neural Networks

In this research, three different time-varying mean-variance portfolio optimization (MVPO) problems are addressed using the zeroing neural network (ZNN) approach. The first two MVPO problems are defined as time-varying quadratic programming (TVQP) problems, while the third MVPO problem is defined as a time-varying nonlinear programming (TVNLP) problem. Then, utilizing real-world datasets, the time-varying MVPO problems are addressed by this alternative neural network (NN) solver and conventional MATLAB solvers, and their performances are compared in three various portfolio configurations. The results of the experiments show that the ZNN approach is a magnificent alternative to the conventional methods. To publicize and explore the findings of this study, a MATLAB repository has been established and is freely available on GitHub for any user who is interested.

A new global algorithm for factor-risk-constrained mean-variance portfolio selection

A new global algorithm for factor-risk-constrained mean-variance portfolio selection

Markowitz Mean-Variance Portfolio Optimization with Predictive Stock Selection Using Machine Learning

With the advances in time-series prediction, several recent developments in machine learning have shown that integrating prediction methods into portfolio selection is a great opportunity. In this paper, we propose a novel approach to portfolio formation strategy based on a hybrid machine learning model that combines convolutional neural network (CNN) and bidirectional long short-term memory (BiLSTM) with robust input features obtained from Huber’s location for stock prediction and the Markowitz mean-variance (MV) model for optimal portfolio construction. Specifically, this study first applies a prediction method for stock preselection to ensure high-quality stock inputs 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-weight portfolio (1/N) model, with LSTM, BiLSTM, and CNN-BiLSTM, and employed them as benchmarks. Between January 2015 and December 2020, historical data from the Stock Exchange of Thailand 50 Index (SET50) were collected for the study. The experiment shows that integrating preselection of stocks can improve MV performance, and the results of the proposed method show that they outperform comparison models in terms of Sharpe ratio, mean return, and risk.