Sparse spanning portfolios and under-diversification with second-order stochastic dominance

Sparse spanning portfolios and under-diversification with second-order stochastic dominance

January 2024 | Stelios Arvanitis, Olivier Scaillet, Nikolas Topaloglou
The paper develops methods to determine whether relaxing sparsity constraints on investment portfolios improves the opportunity set for risk-averse investors. It introduces a new estimation procedure based on a greedy algorithm and Linear Programming (LP) for sparse second-order stochastic dominance (SSD). The authors show that the optimal recovery of the sparse solution is asymptotically valid whether SSD holds or not. Using large equity datasets, they estimate the expected utility loss due to under-diversification and find that there is no benefit from expanding the sparse opportunity set beyond 45 assets. The optimal sparse portfolio, investing in 10 industry sectors, reduces tail risk compared to a sparse mean-variance (MV) portfolio. On a rolling-window basis, the number of assets shrinks to 25 in crisis periods, while standard factor models cannot explain the performance of the sparse portfolios. The paper provides theoretical foundations, empirical procedures, and numerical results to support these findings.The paper develops methods to determine whether relaxing sparsity constraints on investment portfolios improves the opportunity set for risk-averse investors. It introduces a new estimation procedure based on a greedy algorithm and Linear Programming (LP) for sparse second-order stochastic dominance (SSD). The authors show that the optimal recovery of the sparse solution is asymptotically valid whether SSD holds or not. Using large equity datasets, they estimate the expected utility loss due to under-diversification and find that there is no benefit from expanding the sparse opportunity set beyond 45 assets. The optimal sparse portfolio, investing in 10 industry sectors, reduces tail risk compared to a sparse mean-variance (MV) portfolio. On a rolling-window basis, the number of assets shrinks to 25 in crisis periods, while standard factor models cannot explain the performance of the sparse portfolios. The paper provides theoretical foundations, empirical procedures, and numerical results to support these findings.
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