Exploring entropy-based portfolio strategies: empirical analysis and cryptocurrency impact

Relative entropy, a distance measure, has recently found broad application in portfolio selection. An intriguing and newly proposed risk measure, Entropic Value-at-Risk (EVaR), possesses a dual representation that underscores its connection to relative entropy. EVaR boasts several advantages: it is coherent, strongly monotone, and convex, serving as an upper bound to Conditional Value-at-Risk (CVaR), which, in turn, is an upper bound to Value-at-Risk (VaR). Additionally, a generalization of EVaR has emerged in the form of Relativistic Value-at-Risk (RLVaR), a coherent risk measure rooted in Kaniadakis entropy. Cryptocurrency is of particular importance for diversification purposes since the stock market is currently witnessing an unprecedented level of dominance by giant corporations, particularly those in the technology sector. However, this concentration of power among a few key companies has raised concerns among analysts, who warn of potential risks associated with such dominance. In this study, we undertake an extensive empirical analysis, assessing various minimum-risk models using real-world datasets, which consist of stock indexes from both developed and emerging markets, as well as Bitcoin time series. The objectives of our work are threefold: to determine whether entropy-based criteria outperform other models, to study how the models considered behave in developed markets compared to emerging ones, and to analyze the effect of the introduction of cryptocurrency on the performances of the portfolios.