Mean-variance Portfolio Research Articles

Scopes of carbon emissions and their impact on green portfolios

The aim of this paper is to study the performance of carbon-based portfolios when all emissions scopes are accounted for. We formalize low-carbon mean-variance portfolio strategies by integrating a carbon penalty to a constrained mean-variance optimization framework. We resort to direct and indirect emissions, split between Scopes 1–2 and Scope 3, across geographical zones (Europe and US) and data providers (Refinitiv and Carbon4 Finance). Our results show that it is possible to cut emission intensities in half at least with virtually no loss in Sharpe ratio for reasonable levels of the carbon constraint. These results are valid across various choices of risk aversions, and irrespective of emissions data provider. For a sustainability-aware investor, these low-carbon portfolios are associated to a higher level of welfare. We find that the corresponding allocations are shifted towards assets with higher returns while keeping the portfolio's volatility unchanged. Our results add to the literature contending that sustainable investing is not costly.

Sparse and risk diversification portfolio selection.

Portfolio risk management has become more important since some unpredictable factors, such as the 2008 financial crisis and the recent COVID-19 crisis. Although the risk can be actively managed by risk diversification, the high transaction cost and managerial concerns ensue by over diversifying portfolio risk. In this paper, we jointly integrate risk diversification and sparse asset selection into mean-variance portfolio framework, and propose an optimal portfolio selection model labeled as JMV. The weighted piecewise quadratic approximation is considered as a penalty promoting sparsity for the asset selection. The variance associated with the marginal risk regard as another penalty term to diversify the risk. By exposing the feature of JMV, we prove that the KKT point of JMV is the local minimizer if the regularization parameter satisfies a mild condition. To solve this model, we introduce the accelerated proximal gradient (APG) algorithm [Wen in SIAM J. Optim 27:124–145, 2017], which is one of the most efficient first-order large-scale algorithm. Meanwhile, the APG algorithm is linearly convergent to a local minimizer of the JMV model. Furthermore, empirical analysis consistently demonstrate the theoretical results and the superiority of the JMV model.

Mean-variance portfolio selection with estimation risk and transaction costs

ABSTRACT There are many approaches that have been proposed to improve the empirical performance of the Markowitz mean-variance model. Designed to mitigate the impact of parameter uncertainty and estimation error, these approaches have delivered substantially better out-of-sample performance. In this paper, we consider the portfolio optimization problem for a single-period investor facing different types of transaction costs. By reformulating the rebalancing problem into a linear regression framework, we show analytically that considering different transaction costs is equivalent to imposing additional constraints on the portfolio weights, thus providing desired properties such as sparsity and stability in the trading strategy.

Optimal portfolio selection using quantile and composite quantile regression models

The portfolio optimization problem can be reformulated by a regression model. Mean-variance portfolios, which are constructed using the sample mean and covariance matrix of asset returns can be considered as a function of the ordinary least squares estimator of the linear regression coefficients. It is well known that this estimator has several drawbacks. In particular many researchers have pointed out its high sensitivity in the presence of outliers and its loss of efficiency in the presence of small deviations from the normality assumption. In this paper we propose a novel regression approach for optimizing portfolios by means of quantile regression models. The proposed portfolios are constructed using certain robust and distribution-free estimators and can be obtained by solving a single linear program, where estimation and portfolio optimization are performed in a single step. Our numerical results on simulated and empirical data confirm that the proposed portfolios behave much better than the traditional mean-variance portfolio, in terms of the Sharpe ratio and expected loss in utility.

Optimising portfolio diversification and dimensionality

A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance approach and portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality that connects diversification to the non-Gaussianity of portfolio returns and can typically be defined in terms of the ratio of risk measures which are homogenous functions of equal degree. The latter arises naturally due to our requirement that diversification measures should be leverage invariant. We introduce this new framework and argue the benefits relative to existing measures of diversification in the literature, before addressing the question of optimizing diversification or, equivalently, dimensionality. Maximising portfolio dimensionality leads to highly non-trivial optimization problems with objective functions which are typically non-convex and potentially have multiple local optima. Two complementary global optimization algorithms are thus presented. For problems of moderate size and more akin to asset allocation problems, a deterministic Branch and Bound algorithm is developed, whereas for problems of larger size a stochastic global optimization algorithm based on Gradient Langevin Dynamics is given. We demonstrate analytically and through numerical experiments that the framework reflects the desired properties often discussed in the literature.

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.

On horizon-consistent mean-variance portfolio allocation

On horizon-consistent mean-variance portfolio allocation

Markowitz meets technical analysis: Building optimal portfolios by exploiting information in trend-following signals

Technical indicators are widely used by market participants to identify trends in asset prices and in trading volumes. However, it is unclear how to reconcile this approach with a portfolio selection policy that guide investment decisions in many assets at the same time. We bridge the gap between Markowitz approach to mean–variance portfolios and technical analysis by devising a portfolio strategy in which optimal weights are directly parameterized as a function of multiple trend-following signals. We present an empirical application in which four commonly used technical indicators are employed to obtain portfolios of all constituents of the S&P500 index.

Sharpe Ratio analysis in high dimensions: Residual-based nodewise regression in factor models

We provide a new theory for nodewise regression when the residuals from a fitted factor model are used. We apply our results to the analysis of the consistency of Sharpe Ratio estimators when there are many assets in a portfolio. We allow for an increasing number of assets as well as time observations of the portfolio. Since the nodewise regression is not feasible due to the unknown nature of idiosyncratic errors, we provide a feasible-residual-based nodewise regression to estimate the precision matrix of errors which is consistent even when number of assets, p, exceeds the time span of the portfolio, n. In another new development, we also show that the precision matrix of returns can be estimated consistently, even with an increasing number of factors and p>n. We show that: (1) with p>n, the Sharpe Ratio estimators are consistent in global minimum-variance and mean–variance portfolios; and (2) with p>n, the maximum Sharpe Ratio estimator is consistent when the portfolio weights sum to one; and (3) with p<<n, the maximum-out-of-sample Sharpe Ratio estimator is consistent.

The Development of Mean-Variance Efficient Portfolios: 30 Years Later

In 1992, in the initial year of this journal’s publication, Guerard and Takano reported mean-variance efficient portfolios for the Japanese and US equity markets and showed that the use of a regression-weighted composite model of earnings, book value, cash flow, sales, and their relative variables outperformed their respective equity benchmarks by approximately 400 basis points annually. Two years later, Markowitz and Xu tested the composite model strategy and found that its excess returns were statistically significant from a variety of models tested and that the composite model strategy was not the result of data mining. For the 30th anniversary issue, the authors of this article report robust regression modeling results for the 2001–2020 period using the latest features in R and the latest commercially available multi-factor models for portfolio selection. Quantitative investing requires constant implementation and discipline to maximize client wealth. The authors’ results suggest that stock selection models can be effectively employed to deliver excess returns.

Mean-semivariance portfolio optimization using minimum average partial

Mean-semivariance and minimum semivariance portfolios are a preferable alternative to mean-variance and minimum variance portfolios whenever the asset returns are not symmetrically distributed. However, similarly to other portfolios based on downside risk measures, they are particularly affected by parameter uncertainty because the estimates of the necessary inputs are less reliable than the estimates of the full covariance matrix. We address this problem by performing PCA using Minimum Average Partial on the downside correlation matrix in order to reduce the dimension of the problem and, with it, the estimation errors. We apply our strategy to various datasets and show that it greatly improves the performance of mean-semivariance optimization, largely closing the gap in out-of-sample performance with the strategies based on the covariance matrix.

Computing optimal portfolios of multi-assets with tail risk: the case of bitcoin

ABSTRACT Assets with tail risk may produce a suboptimal portfolio under mean-variance optimization when asset returns are not normally distributed. We provide a new Monte Carlo simulation method for computing and attaching tails to observed empirical return distributions. We find that a combination of stochastic optimization and the new method for simulating tails in returns with expected shortfall utility function produces optimal portfolios that have better return and risk characteristics than those of mean-variance optimal portfolios. Results from this study suggest that bitcoin can be a diversifier in a multi-asset portfolio when optimization takes all moments of return into consideration.

Markowitz Mean-Variance Portfolio Selection and Optimization under a Behavioral Spectacle: New Empirical Evidence

This paper investigates the robustness of the conventional mean-variance (MV) optimization model by making two adjustments within the MV formulation. First, the portfolio selection based on a behavioral decision-making theory that encapsulates the MV statistics and investors psychology. The second aspect involves capturing the portfolio asset dependence structure through copula. Using the behavioral MV (BMV) and the copula behavioral MV (CBMV), the results show that stocks with lower behavioral scores outperform counterpart portfolios with higher behavioral scores. On the other hand, in the Forex market, the reverse is observed for the BMV approach, while the CBMV remains consistent.

An Application of Portfolio Mean-Variance and Semi-Variance Optimization Techniques: A Case of Fiji

In this paper, we apply the Markowitz portfolio optimization technique based on mean-variance and semi-variance as measures of risk on stocks listed on the South Pacific Stock Exchange, Fiji. We document key market characteristics and consider monthly returns data from SEP-2019 to FEB-2022 (T = 30) of 17/19 listed companies on the stock exchange to construct various portfolios like 1/N (naïve), maximum return, and market and minimum-variance with and without short-selling constraints. Additionally, we compute each stock’s beta using the market capitalization-weighted stock price index data. We note that well-diversified portfolios (market portfolio and minimum-variance portfolio) with short-selling constraints have relatively higher expected returns with lower risk. Moreover, well-diversified portfolios perform better than the naïve and maximum portfolios in terms of risk. Moreover, we find that both the mean-variance and the semi-variance measures of risk yields a unique market portfolio in terms of expected returns, although the latter has a lower standard deviation and a higher Sharpe ratio. However, for the minimum-variance portfolios and market portfolios without short selling, we find relatively higher returns and risks using the mean-variance than the semi-variance approach. The low beta of individual stock indicates the low sensitivity of its price to the movement of the market index. The study is an initial attempt to provide potential investors with some practical strategies and tools in developing a diversified portfolio. Since not all the portfolios based on mean-variance and the semi-variance analyses are unique, additional methods of investment analysis and portfolio construction are recommended. Subsequently, for investment decisions, our analysis can be complemented with additional measures of risk and an in-depth financial statement/company performance analysis.

Mean-Variance Portfolio Selection in Contagious Markets

We consider a mean-variance portfolio selection problem in a financial market with contagion risk. The risky assets follow a jump-diffusion model, in which jumps are driven by a multivariate Hawkes process with mutual-excitation effect. The mutual-excitation feature of the Hawkes process captures the contagion risk in the sense that each price jump of an asset increases the likelihood of future jumps not only in the same asset but also in other assets. We apply the stochastic maximum principle, backward stochastic differential equation theory, and linear-quadratic control technique to solve the problem and obtain the efficient strategy and efficient frontier in semi-closed form, subject to a non-local partial differential equation. Numerical examples are provided to illustrate our results.

Survey on Multi-period Mean–Variance Portfolio Selection Model

Survey on Multi-period Mean–Variance Portfolio Selection Model

A Nash-Type Fictitious Game Framework to Time-Inconsistent Stochastic Control Problems

In this paper, a Nash-type fictitious game framework is introduced to handle a time-inconsistent linear-quadratic optimal control. The Nash-type game in this framework is called fictitious as it is between the decision maker (called real player) and an auxiliary control variable (called fictitious player) with the real player and fictitious player looking for time-consistent policy and precomitted optimal policy, respectively. Namely, the fictitious-game framework is actually an auxiliary-variable-based mechanism where the fictitious player is our particular design. Noting that the real player's cost functional is revised in accordance with that of fictitious player, the equilibrium policy of real player is called an open-loop self-coordination control of original linear-quadratic problem. As a generalization, a time-inconsistent nonzero-sum stochastic linear-quadratic dynamic game is investigated, where one player is to look for precommitted optimal policy and the other player is to search time-consistent policy. Necessary and sufficient conditions are presented to ensure the existence of open-loop equilibrium of the nonzero-sum game, which resort to a set of Riccati-like equations and linear equations. By applying the developed theory of nonzero-sum game, open-loop self-coordination control of the linear-quadratic optimal control is fully characterized, and multi-period mean-variance portfolio selection is also investigated. Finally, numerical simulations are presented, which show the efficiency of the proposed fictitious-game framework.

The Interaction of Major Crypto-assets, Clean Energy, and Technology Indices in Diversified Portfolios

Cryptocurrencies have gained high interest from media, regulatory authorities, and both retailer and institutional investors especially in the COVID-19 pandemic followed by a tremendous academic interest. Classification of cryptos as an asset is one important issue while another crucial topic is the significantly high return and volatility fluctuations which does not make life easier for portfolio investors. High energy consumption to produce cryptos and carbon emission issues are also not developing the favor of cryptocurrencies. Moreover, in financial literature recent studies show that prices of renewable energy stocks have long-term cointegrating relationship with technology companies. In this context first we employ an asymmetric VAR-GARCH model to study spillover effects between major crypto-currencies, clean energy, and technology indices. Using daily data of the two major cryptocurrencies for the period of 1/1/2016 and 30/09/2021, we relate risk and return of different mean-variance portfolio strategies to Bitcoin (BTC), Etherium (ETH), S&amp;P Global Clean Energy Index (SPGCE) and MSCI World Information Technology Index (MSCIWIT). Secondly, we apply the Markowitz mean-variance framework to assess risk-return benefits of cryptocurrency-portfolios. Our main goal is to offer optimal portfolio allocation approaches including cyptocurrencies with traditional financial assets. We will combine cryptocurrencies, clean energy, and technology indices to maximize return and Sharpe ratio. Furthermore, we will use our asymmetric VAR-GARCH models results to understand and cross check the Markowitz portfolio allocation results in details.

Mean-field formulation for mean-variance asset-liability management with cash flow under an uncertain exit time

Abstract The asset-liability management problem with cash flow under an uncertain exit time has been investigated in this article, which is based on the fundamental framework of the mean-variance model in the multi-period version. The liability and random cash flow will affect asset optimization, while the investor may be forced to withdraw from investments with a random probability at each period in our model. The closed-form expressions for the mean-variance optimal portfolio selection and its corresponding efficient frontier are obtained by employing the mean-field formulation and dynamic programming approach. Moreover, some numerical examples are provided to illustrate the validity and accuracy of the theoretical results.

Mean–Variance Portfolio Efficiency under Leverage Aversion and Trading Impact

This paper addresses the optimal rebalancing problem of a long–short portfolio with high net asset value under trading impact losses. The fund manager may employ leveraging as a tool to increase portfolio returns. However, to mitigate potential leverage risks, frequent rebalancing may become necessary, which leads to significant slippage losses that dampen portfolio performance ex post. We consider the problem in an integrated framework by incorporating trading impact and leverage restrictions ex ante within a mean–variance framework, where leverage control is imposed using a chance constraint. The resulting mean–variance–leverage optimization model (MVL) is non-convex, and we develop an efficient scheme to obtain the optimal portfolio. We investigate how portfolio leverage modifies the MV efficient frontier in the presence of trading impact, and highlight the significant outperformance of the proposed model relative to the standard mean–variance model. Increased target means require less restrictions on leverage, which result in higher rates of slippage losses. Our analysis supports the notion that leverage restrictions contribute to choosing high beta assets, even in the presence of trading impact.