Many papers in recent years have examined the benefits of adding alternative assets to traditional portfolios containing stocks and bonds. Bitcoin has emerged as a new alternative investment for ...investors which has attracted much attention from the media and investors alike. However relatively little is known about the investment benefits of Bitcoin and therefore this paper examines the benefit of including Bitcoin in a traditional benchmark portfolio of stocks and bonds. Specially, we employ data up to June 2018 and analyse the potential out-of-sample portfolio benefits resulting from including Bitcoin in a stock-bond portfolio for a range of eight popular asset allocation strategies. The out-of-sample analysis shows that, across all different asset allocation strategies and risk aversions, the benefits of Bitcoin are quite considerable with substantially higher risk-adjusted returns. Our results are robust to rolling estimation windows, the incorporation of transaction costs, the inclusion of a commodity portfolio, alternative indices, short-selling as well as two additional optimization techniques including higher moments with (and without) variance-based constraints (VBCs). Therefore, our results suggest that investors should include Bitcoin in their portfolio as it generates substantial higher risk-adjusted returns.
This paper proposes a transformation of the portfolio selection problem into SAT. SAT was the first problem to be shown tobe NP-complete, and has been widely investigated ever since. We derive the ...SAT instances from the Portfolio Selection onesusing the concept of cover, and reduce their size via established reduction techniques. The resulting instances are based onthe use of variance as the main risk measure, and are solved via both a standard SAT solver and an adaptive genetic algorithm.Results show that adaptive genetic algorithms are effective in solving these variance-based instances. Further work will bedevoted to investigate other SAT formulations based on different risk measures.
•Reviews financial applications of metaheuristic algorithms.•Provides an updated review of rich portfolio optimization problems.•Provides an updated review of risk management problems.•Outlines ...future trends in applications of metaheuristics to finance.
Computational finance is an emerging application field of metaheuristic algorithms. In particular, these optimisation methods are becoming the solving approach alternative when dealing with realistic versions of several decision-making problems in finance, such as rich portfolio optimisation and risk management. This paper reviews the scientific literature on the use of metaheuristics for solving NP-hard versions of these optimisation problems and illustrates their capacity to provide high-quality solutions under scenarios considering realistic constraints. The paper contributes to the existing literature in three ways. Firstly, it reviews the literature on metaheuristic optimisation applications for portfolio and risk management in a systematic way. Secondly, it identifies the linkages between portfolio optimisation and risk management and presents a unified view and classification of both problems. Finally, it outlines the trends that have gradually become apparent in the literature and will dominate future research in order to further improve the state-of-the-art in this knowledge area.
•This paper studies sample-based portfolio optimization with the entropic value-at-risk (EVaR).•The EVaR enjoys better monotonicity properties in comparison with the conditional value-at-risk ...(CVaR).•An efficient algorithm is presented based on a primal-dual interior-point method for the EVaR approach.•The EVaR approach has similar/better computational efficiency when compared to the CVaR approach.•The EVaR approach may provide portfolios with better financial properties.
The entropic value-at-risk (EVaR) is a new coherent risk measure, which is an upper bound for both the value-at-risk (VaR) and conditional value-at-risk (CVaR). One of the important properties of the EVaR is that it is strongly monotone over its domain and strictly monotone over a broad sub-domain including all continuous distributions, whereas well-known monotone risk measures such as the VaR and CVaR lack this property. A key feature of a risk measure, besides its financial properties, is its applicability in large-scale sample-based portfolio optimization. If the negative return of an investment portfolio is a differentiable convex function for any sampling observation, the portfolio optimization with the EVaR results in a differentiable convex program whose number of variables and constraints is independent of the sample size, which is not the case for the VaR and CVaR even if the portfolio rate linearly depends on the decision variables. This enables us to design an efficient algorithm using differentiable convex optimization. Our extensive numerical study indicates the high efficiency of the algorithm in large scales, when compared with the existing convex optimization software packages. The computational efficiency of the EVaR and CVaR approaches are generally similar, but the EVaR approach outperforms the other as the sample size increases. Moreover, the comparison of the portfolios obtained for a real case by the EVaR and CVaR approaches shows that the EVaR-based portfolios can have better best, mean, and worst return rates as well as Sharpe ratios.
We introduce the robust optimization models for two variants of stable tail-adjusted return ratio (STARR), one with mixed conditional value-at-risk (MCVaR) and the other with deviation MCVaR ...(DMCVaR), under joint ambiguity in the distribution modeled using copulas. The two models are shown to be computationally tractable linear programs. We apply a two-step procedure to capture the joint dependence structure among the assets. We first extract the filtered residuals from the return series of each asset using AutoRegressive Moving Average Glosten Jagannathan Runkle Generalized Autoregressive Conditional Heteroscedastic (ARMA-GJR-GARCH) model. Subsequently, we exploit the regular vine copulas to model the joint dependence among the transformed residuals. The tree structure in the regular vines is accomplished using Kendall’s tau. We compare the performance of the proposed two robust models with their conventional counterparts when the joint distribution in the latter is described using Gaussian copula only. We also examine the performance of the obtained portfolios against those from the Markowitz model and multivariate GARCH models using the rolling window analysis. We illustrate the superior performance of the proposed robust models than their conventional counterpart models on excess mean returns, Sortino ratio, Rachev ratio, VaR ratio, and Treynor ratio, on three data sets comprising of indices across the globe.
•We empirically analyze cryptocurrency-portfolios in a mean-variance framework.•A rich set of different parameterizations is evaluated in an out-of-sample analysis.•Portfolios feature substantially ...lower risk than single cryptocurrencies.•Markowitz optimal portfolios show higher Sharpe ratios than single cryptocurrencies.•The naively diversified 1/N portfolio outperforms all analyzed portfolio strategies.
We apply the Markowitz mean-variance framework in order to assess risk-return benefits of cryptocurrency-portfolios. Using daily data of the 500 most capitalized cryptocurrencies for the time span 1/1/2015 to 12/31/2017, we relate risk and return of different mean-variance portfolio strategies to single cryptocurrency investments and two benchmarks, the naively diversified portfolio and the CRIX. In an out-of-sample analysis accounting for transaction cost we find that combining cryptocurrencies enriches the set of ‘low’-risk cryptocurrency investment opportunities. In terms of the Sharpe ratio and certainty equivalent returns, the 1/N-portfolio outperforms single cryptocurrencies and more than 75% of mean-variance optimal portfolios.
In complex security markets, uncertainty and randomness may coexist. The investors hold different risk attitudes toward different investment objectives in reality. In order to reflect this ...phenomenon, this paper applies mental accounts to portfolio optimization in an uncertain random environment. Firstly, considering the influence of transaction costs and diversification degree, this paper establishes an uncertain random mean-absolute semi-deviation-entropy bi-objective optimization model. Then the bi-objective model is converted to two single-objective models through three steps. Secondly, the equivalent forms of the models are deduced when the return rates of random risky securities are assumed to be normal random variables and the return rates of uncertain risky securities are assumed to be linear and zigzag uncertain variables. Furthermore, we propose an improved butterfly optimization algorithm (IBOA) to solve the two single-objective models. Finally, numerical simulations are presented to analyze the practicability and effectiveness of the models with different mental accounts and the IBOA algorithm. The results indicate that the IBOA algorithm is effective and putting money into more mental accounts may gain higher returns.
•The mental accounts are considered in uncertain random portfolio optimization.•We establish a mean-absolute semi-deviation-entropy bi-objective optimization model.•An improved butterfly optimization algorithm is proposed to solve the models.
The portfolio optimization model has limited impact in practice because of estimation issues when applied to real data. To address this, we adapt two machine learning methods, regularization and ...cross-validation, for portfolio optimization. First, we introduce
performance-based regularization
(PBR), where the idea is to constrain the sample variances of the estimated portfolio risk and return, which steers the solution toward one associated with less estimation error in the performance. We consider PBR for both mean-variance and mean-conditional value-at-risk (CVaR) problems. For the mean-variance problem, PBR introduces a quartic polynomial constraint, for which we make two convex approximations: one based on rank-1 approximation and another based on a convex quadratic approximation. The rank-1 approximation PBR adds a bias to the optimal allocation, and the convex quadratic approximation PBR shrinks the sample covariance matrix. For the mean-CVaR problem, the PBR model is a combinatorial optimization problem, but we prove its convex relaxation, a quadratically constrained quadratic program, is essentially tight. We show that the PBR models can be cast as robust optimization problems with novel uncertainty sets and establish asymptotic optimality of both sample average approximation (SAA) and PBR solutions and the corresponding efficient frontiers. To calibrate the right-hand sides of the PBR constraints, we develop new, performance-based
k
-fold cross-validation algorithms. Using these algorithms, we carry out an extensive empirical investigation of PBR against SAA, as well as L1 and L2 regularizations and the equally weighted portfolio. We find that PBR dominates all other benchmarks for two out of three Fama–French data sets.
This paper was accepted by Yinyu Ye, optimization
.
This study investigates the impact of the choice of optimization technique when constructing Socially Responsible Investment (SRI) portfolios. Corporate Social Performance (CSP) scores are price ...sensitive information that is subject to considerable estimation risk. Therefore, uncertainty in the input parameters is greater for SRI portfolios than conventional portfolios, and this affects the selection of the appropriate optimization method. We form SRI portfolios based on six different approaches and compare their performance along the dimensions of risk, risk-return trade-off, diversification and stability. Our results for SRI portfolios contradict those of the conventional portfolio optimization literature. We find that the more “formal” optimization approaches (Black-Litterman, Markowitz and robust estimation) lead to SRI portfolios that are both less risky and have superior risk-return trade-offs than do more simplistic approaches; although they also have more unstable asset allocations and lower diversification. Our conclusions are robust to a series of tests, including the use of different estimation windows and stricter screening criteria.
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