Sparse portfolio optimization, which significantly boosts the out-of-sample performance of traditional mean–variance methods, is widely studied in the fields of optimization and financial economics. ...In this paper, we explore the ℓ1/ℓ2 fractional regularization constructed by the ratio of the ℓ1 and ℓ2 norms on the mean–variance model to promote sparse portfolio selection. We present an ℓ1/ℓ2 regularized sparse portfolio optimization model and provide financial insights regarding short positions and estimation errors. Then, we develop an efficient alternating direction method of multipliers (ADMM) method to solve it numerically. Due to the nonconvexity and noncoercivity of the ℓ1/ℓ2 term, we give the convergence analysis for the proposed ADMM based on the nonconvex optimization framework. Furthermore, we discuss an extension of the model to incorporate a more general ℓ1/ℓq regularization, where q>1. Moreover, we conduct numerical experiments on four stock datasets to demonstrate the effectiveness and superiority of the proposed model in promoting sparse portfolios while achieving the desired level of expected return.
•An ℓ1 over ℓ2 regularization was introduced to promote sparse portfolio selection.•Financial insights regarding short positions and estimation errors were explored.•An ADMM-based solving method with convergence analysis was proposed.•An extension of the model with a more general regularization was discussed.•The in-sample and out-of-sample numerical experiments were conducted.
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.
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