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

Author

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  • Stelios Arvanitis

    (Department of Economics, AUEB)

Abstract

We develop and implement methods for determining whether relaxing sparsity constraints on portfolios improves the investment opportunity set for risk-averse investors.We formulate a new estimation procedure for sparse second-order stochastic spanning based on a greedy algorithm and Linear Programming. We show the optimal recovery of the sparse solution asymptotically whether spanning holds or not. From large equity datasets, we estimate the expected utility loss due to possible under-diversification, and find that there is no benefit from expanding a sparse opportunity set beyond 45 assets. The optimal sparse portfolio invests in 10 industry sectors and cuts tail risk when compared to a sparse mean-variance portfolio. On a rolling-window basis, the number of assets shrinks to 25 assets in crisis periods, while standard factor models cannot explain the performance of the sparse portfolios.

Suggested Citation

  • Stelios Arvanitis, 2025. "Sparse spanning portfolios and under-diversification with second-order stochastic dominance," Working Paper 1532, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1532
    as

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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/wpaper/qed_wp_1532.pdf
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    References listed on IDEAS

    as
    1. Samuelson, Paul A., 1967. "General Proof that Diversification Pays*," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(1), pages 1-13, March.
    2. Stelios Arvanitis & Thierry Post & Nikolas Topaloglou, 2021. "Stochastic Bounds for Reference Sets in Portfolio Analysis," Management Science, INFORMS, vol. 67(12), pages 7737-7754, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Nonparametric estimation; stochastic dominance; spanning; under-diversification; greedy algorithm; Linear Programming;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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