Abstract: The $\ell_0$-constrained mean-CVaR model is an NP-hard problem, and the existing methods mainly lie in combinatorial approaches with a high computational cost. From a very different perspective, we propose an autonomous sparse mean-CVaR portfolio model that can approximate the $\ell_0$-constrained mean-CVaR model to arbitrary accuracy. The core idea is to transform the $\ell_0$ constraint into an indicator function and handle it with a tailed approximation. Then we propose a proximal alternating linearized minimization algorithm with a nested fixed-point proximity algorithm (both convergent) to iteratively solve this model. Autonomous sparsity means that a large proportion of assets can remain in the selected asset pool when adjusting the pool size. Hence our approach approximates the $\ell_0$-constrained mean-CVaR model with a theoretical guarantee, improves computational efficiency, and provides a robust asset selection scheme.