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Managing portfolio diversity within the mean variance theory

Author

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  • Anatoly B. Schmidt

    (Kensho Technologies, Inc, One World Trade Center
    NYU School of Engineering)

Abstract

It is well documented that the classical mean variance theory (MVT) may yield portfolios (MVTP) that are highly concentrated and/or are outperformed by equal weight portfolios (EWP). In this work, it is proposed to expand the MVT minimizing objective function with an additional term that explicitly controls portfolio diversity (diversity booster DB). DB decreases with growing number of non-zero portfolio weights and has a minimum when all weights are equal. As a result, high values of DB yield EWP. For performance analysis, portfolio constructed with 12 major US equity ETFs is considered. Out-of-sample performance of maximum Sharpe portfolios is tested using statistics of bootstrapped Sharpe ratios for monthly rebalancing periods. It is found that for the 3-year calibrating window, the diversified MVT portfolio (DMVTP) outperformed both MVTP and EWP in 2012–2015. While the MVTP weights were highly concentrated and had sharp jumps between rebalancing periods, the DMVTP weights slowly changed with time.

Suggested Citation

  • Anatoly B. Schmidt, 2019. "Managing portfolio diversity within the mean variance theory," Annals of Operations Research, Springer, vol. 282(1), pages 315-329, November.
    • Handle: RePEc:spr:annopr:v:282:y:2019:i:1:d:10.1007_s10479-018-2896-x
    DOI: 10.1007/s10479-018-2896-x
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    References listed on IDEAS

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    3. Syed Kumail Abbas Rizvi & Bushra Naqvi & Nawazish Mirza, 2022. "Is green investment different from grey? Return and volatility spillovers between green and grey energy ETFs," Annals of Operations Research, Springer, vol. 313(1), pages 495-524, June.
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    5. Sergey Kovalev & Isabelle Chalamon & Fabio J. Petani, 2023. "Maximizing single attribute diversity in group selection," Annals of Operations Research, Springer, vol. 320(1), pages 535-540, January.
    6. Naqvi, Bushra & Mirza, Nawazish & Rizvi, Syed Kumail Abbas & Porada-Rochoń, Małgorzata & Itani, Rania, 2021. "Is there a green fund premium? Evidence from twenty seven emerging markets," Global Finance Journal, Elsevier, vol. 50(C).

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