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Abstract This article examines the strong consistency of the conditional value-at-risk (CVaR) estimate for asymptotic negatively associated (ANA or ρ − $\rho ^{-}$ , for short) random samples under mild conditions. It is demonstrated that the optimal rate can achieve nearly O ( n − 1 / 2 ) $O (n^{-1/2})$ under certain appropriate conditions. Furthermore, we present numerical simulations and a real data example to corroborate our theoretical results based on finite samples.