A new multivariate performance measure Average-Value-at-Risk, mAVaR αevaluating the sum of N risky assets composing the portfolio of an investor with respect to riskN-dimensional risk level vectorαis proposed. We show that the proposed operator satisfies the four axioms of a coherent risk measure, while reducing to the one variableAverage-Value-at-RiskAVaR, in caseN= 1. In that respect, mAVaRα is the natural extension of AVaR to N dimensional case, while maintaining its axiomatic properties.mAVaRαis flexible by giving the investor the choice of choosing the risk level α i of each risky asset differently.