The paper investigates the concept of sparse second-order stochastic dominance (SSD) spanning and its implications for portfolio construction. It proposes a new estimation method for sparse SSD spanning using a greedy algorithm and linear programming. The study shows that expanding a sparse portfolio beyond 45 assets does not improve investment opportunities for risk-averse investors. The optimal sparse portfolio, consisting of 10 industry sectors, reduces tail risk compared to a sparse mean-variance portfolio. On a rolling-window basis, the number of assets in the portfolio shrinks to 25 during crisis periods, while standard factor models fail to explain the performance of sparse portfolios. The paper provides a theoretical framework for sparse SSD spanning, establishes statistical guarantees for the greedy algorithm, and demonstrates its effectiveness in empirical applications. The results suggest that sparse SSD spanning is achievable with a limited number of assets, and that the greedy algorithm offers a computationally efficient and statistically robust method for portfolio optimization. The study contributes to the literature on sparse portfolio construction and stochastic dominance, offering practical insights for risk-averse investors.The paper investigates the concept of sparse second-order stochastic dominance (SSD) spanning and its implications for portfolio construction. It proposes a new estimation method for sparse SSD spanning using a greedy algorithm and linear programming. The study shows that expanding a sparse portfolio beyond 45 assets does not improve investment opportunities for risk-averse investors. The optimal sparse portfolio, consisting of 10 industry sectors, reduces tail risk compared to a sparse mean-variance portfolio. On a rolling-window basis, the number of assets in the portfolio shrinks to 25 during crisis periods, while standard factor models fail to explain the performance of sparse portfolios. The paper provides a theoretical framework for sparse SSD spanning, establishes statistical guarantees for the greedy algorithm, and demonstrates its effectiveness in empirical applications. The results suggest that sparse SSD spanning is achievable with a limited number of assets, and that the greedy algorithm offers a computationally efficient and statistically robust method for portfolio optimization. The study contributes to the literature on sparse portfolio construction and stochastic dominance, offering practical insights for risk-averse investors.