Coherent measure of portfolio risk

This study introduces a multivariate entropic Value at Risk (mEVaR) risk measure, broadening the conventional Value at Risk scope to a multi-asset scenario. The mEVaR is coherent and encapsulates the integrated risk of various assets in a portfolio. In addition, a new theoretical result incorporates mutual information into the mEVaR to capture tail dependence during extreme market events. The findings suggest that greater mutual dependence among assets increases risk as the benefit of diversification decreases. Examples, simulations, and empirical studies illustrate the applicability of these risk measures as tools for managing and optimizing investment portfolios. •The mEVaR and MI-mEVaR are introduced to capture integrated portfolio risk.•It is shown that these risk measures are theoretically coherent.•MI-mEVaR incorporates mutual information as weight in mEVaR.•These risk measures effectively captures tail risks.•Simulations illustrate how mEVaR and MI-mEVaR help manage and optimize portfolios.