Classical Portfolio Research Articles

Time-varying relative risk aversion: Theoretical mechanism and empirical evidence

This paper explores the issue of understanding time-varying relative risk aversion with household-level data on two classical portfolio choice problems. First, we derive an analytic form solution to a parsimonious portfolio choice model with the preference given by Greenwood, Hercowitz and Huffman (1988, GHH), and then, the solution identifies four partial equilibrium effects in our model with the GHH preference on risky shares through two channels and two net effects whose signs hinge on the value of a key structural parameter. Based on household-level data, our empirical results from both mean and quantile regression models show clearly that wealth negatively affects risky shares and the estimated effects are statistically significant and robust, which is in line with the theory. Finally, we show that the GHH preference alone is not sufficient in explaining how risky shares respond to labor income in the household-level data.

Managing Portfolio Volatility Automatically: Insights from Wealth Front Robo-Advisor

This study examines the comparative performance of Wealthfront's Classic and Socially Responsible Portfolios under an 8% target volatility constraint. Utilizing historical data from 2010 to 2024 and employing a Tactical Asset Allocation model, it assesses risk-adjusted returns, including Sharpe and Sortino Ratios. Preliminary findings indicate that while the Classic Portfolio offers higher returns, it also exhibits greater volatility compared to the Socially Responsible Portfolio. This research highlights the trade-off between financial performance and ethical considerations in investment decisions, providing insights relevant to investors seeking to balance risk and return within the framework of ro-bo-advisormanaged portfolios. Implications include the importance of risk-adjusted metrics in in-vestment decisions and the role of robo-advisors in enhancing portfolio performance. Future research should explore diverse volatility targets and investor preferences to refine investment strategies.

Особенности конструирования портфеля финансовых инструментов на основе оценки бета-коэффициентов

The article focuses on a variant of the development of the classical portfolio theory based on coefficients. The role of beta coefficients in financial decisionmaking is analyzed, and a portfolio optimization option is presented in the form of a linear programming problem with respect to the price shares of financial instruments acting as variables. Special attention is paid to the mathematical approaches underlying portfolio theory. Such approaches include statistical analysis to assess the expected profitability and coefficients of various financial instruments, as well as optimization methods to determine the optimal balance between the profitable and risky characteristics of the portfolio. Due to the choice of various options for the value of the beta coefficient of the portfolio, the fundamental possibility of designing optimal portfolios taking into account investment goals, risk level and desired profitability is demonstrated. Three investment strategies have been formulated based on the inclusion in the portfolio of financial instruments with high coefficient values; inclusion in the portfolio of financial instruments with low coefficient values and inclusion in the portfolio of financial instruments with average coefficient values. Based on real financial data, the differences in financial results resulting from the choice of each of these strategies are demonstrated. From a methodological point of view, the material of the article can be useful for improving the content of mathematical disciplines related to the quantitative justification of financial decisions.

Exact and Heuristic Solution Techniques for Mixed-Integer Quantile Minimization Problems

We consider mixed-integer linear quantile minimization problems that yield large-scale problems that are very hard to solve for real-world instances. We motivate the study of this problem class by two important real-world problems: a maintenance planning problem for electricity networks and a quantile-based variant of the classic portfolio optimization problem. For these problems, we develop valid inequalities and present an overlapping alternating direction method. Moreover, we discuss an adaptive scenario clustering method for which we prove that it terminates after a finite number of iterations with a global optimal solution. We study the computational impact of all presented techniques and finally show that their combination leads to an overall method that can solve the maintenance planning problem on large-scale real-world instances provided by the ROADEF/EURO challenge 2020 1 and that they also lead to significant improvements when solving a quantile-version of the classic portfolio optimization problem. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by the Deutsche Forschungsgemeinschaft [CRC TRR 154], Fonds De La Recherche Scientifique [PDR T0098.18], and Bundesministerium für Bildung und Forschung. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0105 .

Neural Networks for Portfolio Analysis in High-Frequency Trading.

High-frequency trading proposes new challenges to classical portfolio selection problems. Especially, the timely and accurate solution of portfolios is highly demanded in financial market nowadays. This article makes progress along this direction by proposing novel neural networks with softmax equalization to address the problem. To the best of our knowledge, this is the first time that softmax technique is used to deal with equation constraints in portfolio selections. Theoretical analysis shows that the proposed method is globally convergent to the optimum of the optimization formulation of portfolio selection. Experiments based on real stock data verify the effectiveness of the proposed solution. It is worth mentioning that the two proposed models achieve 5.50 % and 5.47 % less cost, respectively, than the solution obtained by using MATLAB dedicated solvers, which demonstrates the superiority of the proposed strategies.

Analysis of the criteria selection problem in diversification models

The digitalization of the economy reduces the cost of doing business by automating the relevant processes, but any transformation creates new risks and economic instability. Economic instability leads to a drop in the standard of living and, as a result, negatively affects the activities of trade enterprises. Small and medium businesses are especially sensitive to any changes. The decrease in demand for most everyday goods has a painful effect on the activities of small and medium-sized businesses and leads to the emergence of new risks. These risks have a significant impact on reducing the profitability of enterprises. Therefore, it is important for each enterprise to diversify the activities of the enterprise, which includes the expansion of the product range, the reorientation of sales markets and the optimal distribution of goods between divisions of one enterprise. The subject of the article is multi-criteria models of a diversified portfolio that minimize the risks that arise in the era of the digital economy when managing retail chains. To formalize the problem, five models are proposed that differ in vector objective functions, both in the quantity and quality of the selected criteria. The aim of the work is to analyze the problem of choosing criteria in the corresponding multicriteria or vector diversification problems. The article examines the advantages of introducing an additional criterion of entropy maximization into the criteria of the classical two-criteria model of portfolio theory, which characterizes the degree of diversity of the portfolio composition. A complex combination of methods of classical portfolio theory and multicriteria optimization is applied. The results include a comparison of three methods for solving the following problems: criteria convolution, successive concessions, and computer simulation of the Pareto set. Conclusions: the results obtained will be useful for automating the risk management of retail chains. The practical value is that the obtained results of real data for the network have demonstrated the possibility of using the developed tool for automatic allocation of resources in the form of pareto-optimal portfolios in order to minimize risks.

The Average Chinese Family How to Build an Optimal Investment Portfolio in an Uncertain Market Environment

Classical portfolio theory suggests that the maximum expected return for a given level of risk can be achieved through an appropriate allocation between different asset classes. However, in reality, markets are not always fully efficient and there are factors such as market failures and speculative behaviour, which may result in investors not always achieving the expected returns. By analysing factors such as asset classes, risk preferences and investment objectives, this thesis provides strategies and recommendations to help the average household develop a personalised investment recipe, using a combination of portfolio theory and empirical research.

Quantifying dimensional change in stochastic portfolio theory

AbstractIn this paper, we develop the theory of functional generation of portfolios in an equity market with changing dimension. By introducing dimensional jumps in the market, as well as jumps in stock capitalization between the dimensional jumps, we construct different types of self‐financing stock portfolios (additive, multiplicative, and rank‐based) in a very general setting. Our study explains how a dimensional change caused by a listing or delisting event of a stock, and unexpected shocks in the market, affect portfolio return. We also provide empirical analyses of some classical portfolios, quantifying the impact of dimensional change in portfolio performance relative to the market.

Multicriteria Portfolio Choice and Downside Risk

In this study, we investigated some extensions of the classical portfolio theory and try to evaluate them in a situation of crisis. We studied some additional criteria for portfolio selection, based on market multiples representing the overall situation of companies. Additionally, we investigated semi-variance as an alternative measure of risk. We developed a range of portfolios that were built using different criteria for risk and the fundamental values of companies from the Polish stock market. Then, we compared their returns during the crisis that occurred after the outbreak of the COVID-19 pandemic. The results of empirical research on the major companies traded on the Warsaw Stock Exchange reveal that investors can achieve better investment results by augmenting the standard Markowitz model with an additional criterion connected with the fundamental standing of companies, such as book-to-market or earnings-to-market ratios. The second result is that using nonclassical risk measures such as semi-variance instead of variance provides better results, and this method of measuring risk is especially essential in periods characterized by the collapse of the capital market.

Risk budgeting portfolios from simulations

Risk budgeting is a portfolio strategy where each asset contributes a prespecified amount to the aggregate risk of the portfolio. In this work, we propose an efficient numerical framework that uses only simulations of returns for estimating risk budgeting portfolios. Besides a general cutting planes algorithm for determining the weights of risk budgeting portfolios for arbitrary coherent distortion risk measures, we provide a specialised version for the Expected Shortfall, and a tailored Stochastic Gradient Descent (SGD) algorithm, also for the Expected Shortfall. We compare our algorithm to standard convex optimisation solvers and illustrate different risk budgeting portfolios, constructed using an especially designed Julia package, on real financial data and compare it to classical portfolio strategies.

Semi-Metric Portfolio Optimization: A New Algorithm Reducing Simultaneous Asset Shocks

This paper proposes a new method for financial portfolio optimization based on reducing simultaneous asset shocks across a collection of assets. This may be understood as an alternative approach to risk reduction in a portfolio based on a new mathematical quantity. First, we apply recently introduced semi-metrics between finite sets to determine the distance between time series’ structural breaks. Then, we build on the classical portfolio optimization theory of Markowitz and use this distance between asset structural breaks for our penalty function, rather than portfolio variance. Our experiments are promising: on synthetic data, we show that our proposed method does indeed diversify among time series with highly similar structural breaks and enjoys advantages over existing metrics between sets. On real data, experiments illustrate that our proposed optimization method performs well relative to nine other commonly used options, producing the second-highest returns, the lowest volatility, and second-lowest drawdown. The main implication for this method in portfolio management is reducing simultaneous asset shocks and potentially sharp associated drawdowns during periods of highly similar structural breaks, such as a market crisis. Our method adds to a considerable literature of portfolio optimization techniques in econometrics and could complement these via portfolio averaging.

Multi-source data driven cryptocurrency price movement prediction and portfolio optimization

The existing cryptocurrency portfolio studies have relied heavily on historical asset returns and ignored the importance of the prediction information of asset returns, which leads to poor out-of-sample performance of the resulting portfolio strategies. To this end, we first crawl the tweets related to cryptocurrencies on Twitter, analyze tweets' sentiment, and construct sentiment indicators. Second, we use the historical trading data, daily Google Trends, and sentiment indicators to forecast the movement of cryptocurrency prices using Support Vector Machine (SVM). Third, we propose a portfolio optimization model by considering both the forecasting information and the global minimum variance model, and then derive the corresponding portfolio strategy. Finally, we compare the out-of-sample performance of the proposed strategy with classic portfolio strategies and the Cryptocurrency Index. The empirical results show that: on the one hand, the proposed multi-source data can effectively help forecast the cryptocurrency price movements; on the other hand, the proposed portfolio strategy outperforms traditional portfolio strategies regarding the out-of-sample Sharpe ratio, Sortino ratio, and certainty equivalent return, this proves that the proposed strategy can sufficiently combine information between history and future. More importantly, the above conclusions are well verified in the robustness test.

Solving Periodic Investment Portfolio Selection Problems by a Data-Assisted Multiobjective Evolutionary Approach

Classic portfolio selection problems mainly focus on high-risk financial markets with tradeoffs between returns and risk. However, more risk-averse investors pursue long-term portfolio planning with the objectives of maximizing final returns and maximizing flexibility. This article addresses a new type of the portfolio problem, called periodic investment portfolio selection problems (PIPSPs), in which investors periodically allocate resources to financial products with different periods. A multiobjective model for PIPSPs is first presented. With a mechanism for utilizing the data generated during the implementation of multiobjective evolutionary algorithms (MOEAs), a data-assisted MOEA (DA-MOEA) is proposed to solve PIPSPs. The main idea of a DA-MOEA is to combine a MOEA with a data-assisted process that consists of three components: 1) feature construction; 2) data fusion model development; and 3) obtained information utilization. To solve the addressed PIPSPs, two versions of DA-MOEAs with baselines of nondominated sorting and decomposition-based mechanisms are implemented, namely, the data-assisted NSGA-II (DA-NSGA-II) and data-assisted MOEA/D (DA-MOEA/D). In the developed DA-MOEAs for PIPSPs, a feature construction process and a data fusion model are well designed for mining data with different formats. To validate the algorithms, two sets of test instances are generated. The experimental results demonstrate the efficacy of the data-assisted process. Furthermore, the effects of the algorithm components, such as the data source sizes, information types, and information utilization strategies, are investigated.

Planning resource allocation for husbandry management by portfolio optimization

The husbandry management is assessed in general by comparison of current and past economical results, which are used as a universal business metric. Sustainable management in general targets minimization of risk and maximization of the return for managing business activities. The minimization of the economic risk allows for decreasing the potential losses for the husbandry management and they are leading criteria for planning future resource allocations. The new point added in this research concerns simultaneously inclusion in the portfolio problem the risk formalization both as a standard deviation of return and the probability for losses as value-at-risk. Several portfolio problems are defined, considering the probability of losses as a goal function or constraint in the portfolio problems. The inclusion of these two formalizations allows the portfolio risk to decrease additionally in comparison with the classical portfolio problems, where the risk is quantified as a standard deviation of the portfolio return. The peculiarities of these problems and the corresponding optimal solutions are analyzed, which allows quantifying the resource allocation per different business activities. Numerical experiments are made with real data on animal husbandry, available from the Bulgarian National Statistics and the results are illustrated in a graphical way. The empirical comparison with these data gives benefits in decreasing the risk when both risk formalizations are applied in the portfolio problem.

Swarm Intelligence Algorithms for Portfolio Optimization Problems: Overview and Recent Advances

Due to the volatility and uncertainty of the financial market, investors often use the form of portfolio to actively manage their assets. Portfolio optimization (PO) is becoming more and more important for investors. However, PO is frequently a kind of NP-hard problem in the field of modern financial optimization, which has gradually attracted the attention and interest of researchers. Some efficient mathematical models were built to describe the return and risk of portfolio. A lot of precise and approximate fast algorithms are used to solve the established PO models. The fundamental purpose is to maximize the return and to minimize the risk of portfolio under certain constraints. In recent years, researchers not only limit the goal of PO to the balance between risk and return, but also pay attention to liquidity, environmental, social, and governance (ESG) controversy level, Sortino ratio, and other indicators. The number of PO targets and constraints is further extended. In the past two decades, swarm intelligence (SI) algorithms have been widely introduced to solve PO problems. SI algorithm is mainly inspired from the daily phenomena in nature or self-organization, self-adaptation, and self-learning of biological population. The existing research results show that SI algorithm has the characteristics of high efficiency and can obtain satisfactory solutions in solving PO problems. The recent advances on the classic portfolio optimization concepts, models, and the usual SI-based solving algorithms are presented. Finally, future potential research directions are presented.

Asset splitting algorithm for ultrahigh dimensional portfolio selection and its theoretical property

The presence of a huge number of assets poses challenges to classical portfolio selection algorithms. Constrained l1 minimization approaches have been proposed to directly estimate effective parameters in the optimal portfolio. Linear programming method and alternating direction method of multiplier (ADMM) algorithm is used to solve the corresponding minimization problems. However, these two algorithms may fail due to the limitations of computing time and computing memory when a huge number of assets are considered in the portfolio optimization. This article proposes an asset splitting ADMM (AS-ADMM for short), a parallel computing algorithm, to tackle such challenges, and establishes the convergence property of the new algorithm. Furthermore, we develop a new regularization method for estimating the effective parameters with the folded-concave penalty and establish its oracle property. The local linear approximation (LLA) algorithm is used to redirect the new method to a weighted l1 regularization method. We conduct simulation studies to investigate the advantage of the proposed algorithm and regularized model in solving the high dimensional portfolio selection problems. A real data example is also included to demonstrate the applicability of the proposed algorithms and regularization methods.

The value and cost of more stages in stochastic programing: a statistical analysis on a set of portfolio choice problems

Sequential decision problems under uncertainty are commonly studied with stochastic programing. An important modeling choice is the number of stages. More stages allow additional information to be captured, but is associated with a coarser representation of uncertainty may worsen solution quality. In this paper, we study this trade-off, with the objective to advance the understanding of how the number of stages affect solution quality in stochastic programing. We show: (i) how the optimistic bounds from stochastic programing gradually suggest improved performance with more stages, while the real solution quality simultaneously deteriorates; and (ii) that real performance can be improved by adding stages, but only up to some point, after which more stages are detrimental. Further, we highlight the importance of understanding what creates the value of more stages in the problem of interest, and particularly if this can be captured in models with few stages. The numerical experiments are based on the classic portfolio choice problem of an investor with constant relative risk aversion preferences, maximizing the expected utility of terminal wealth. We study instances with proportional transaction costs and predictability in returns, which takes this problem into an inherently multi-stage nature.

A multivariate model for hybrid wind–photovoltaic power production with energy portfolio optimization

Generation of renewable energy is destined to grow further, motivated, for example, by the Paris Agreement, aimed at reducing the production of greenhouse gases. In particular, hybrid production plants allow the exploitation of different climatic sources to generate electricity. We analyze the electricity generation of a mixed wind–photovoltaic (PV) system, considering a multivariate model that involves the required climatic variables. We include the price of electricity in our model in order to evaluate the profitability of the system through its expected income. In addition, we investigate the optimal choice between these two production technologies via Markowitz’s classic portfolio selection theory. To this end, we then consider a portfolio of the income deriving from both wind and PV production. We determine the most efficient components that maximize the overall income of our portfolio. This analysis is enriched by taking into consideration the loss of load hours of efficient portfolios. Finally, we make an optimal choice between the two technologies. The models are validated via Monte Carlo simulations using empirical data.

Optimization of a Portfolio of Investment Projects: A Real Options Approach Using the Omega Measure

Investment decisions usually involve the assessment of more than one financial asset or investment project (real asset). The most appropriate way to analyze the viability of a real asset is not to study it in isolation but as part of a portfolio with correlations between the input variables of the projects. This study proposes an optimization methodology for a portfolio of investment projects with real options based on maximizing the Omega performance measure. The classic portfolio optimization methodology uses the Sharpe ratio as the objective function, which is a function of the mean-variance of the returns of the portfolio distribution. The advantage of using Omega as an objective function is that it takes into account all moments of the portfolio’s distribution of returns or net present values (NPVs), not restricting the analysis to its mean and variance. We present an example to illustrate the proposed methodology, using the Monte Carlo simulation as the main tool due to its high flexibility in modeling uncertainties. The results show that the best risk-return ratio is obtained by optimizing the Omega measure.

Portfolio Selection with Regularization

We study the Markowitz mean-variance portfolio selection model under three types of regularizations: single-norm regularizations on individual stocks, mixed-norm regularizations on stock groups, and composite regularizations that combine the single-norm and mixed-norm regularizations. With mixed-norm regularizations incorporated, our model can accomplish group and stock selections simultaneously. Our empirical results using both US and global equity market data show that compared to the classical mean-variance portfolio, almost all regularized portfolios have better out-of-sample risk-adjusted performance measured by Sharpe ratio. In addition, stock selection and group screening accomplished by adding [Formula: see text] and [Formula: see text] regularizations respectively can lead to decreased volatility, turnover rate, and leverage ratio. Yet there are instances in which diversifying across different groups is more favorable, depending on the grouping methods. Moreover, we find a positive correlation between portfolio turnover and leverage. Heavily leveraged portfolios also have high turnover rates and thus high transaction costs.