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Mean–variance optimal portfolios in the presence of a benchmark with applications to fraud detection

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  • Bernard, C.
  • Vanduffel, S.

Abstract

We first study mean–variance efficient portfolios when there are no trading constraints and show that optimal strategies perform poorly in bear markets. We then assume that investors use a stochastic benchmark (linked to the market) as a reference portfolio. We derive mean–variance efficient portfolios when investors aim to achieve a given correlation (or a given dependence structure) with this benchmark. We also provide upper bounds on Sharpe ratios and show how these bounds can be useful for fraud detection. For example, it is shown that under some conditions it is not possible for investment funds to display a negative correlation with the financial market and to have a positive Sharpe ratio. All the results are illustrated in a Black–Scholes market.

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  • Bernard, C. & Vanduffel, S., 2014. "Mean–variance optimal portfolios in the presence of a benchmark with applications to fraud detection," European Journal of Operational Research, Elsevier, vol. 234(2), pages 469-480.
    • Handle: RePEc:eee:ejores:v:234:y:2014:i:2:p:469-480
    DOI: 10.1016/j.ejor.2013.06.023
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    1. Farzad Pourbabaee & Minsuk Kwak & Traian A. Pirvu, 2014. "Risk minimization and portfolio diversification," Papers 1411.6657, arXiv.org, revised Dec 2014.
    2. Philippe Bernard & Najat El Mekkaoui De Freitas & Bertrand B. Maillet, 2022. "A financial fraud detection indicator for investors: an IDeA," Annals of Operations Research, Springer, vol. 313(2), pages 809-832, June.
    3. Carole Bernard & Franck Moraux & Ludger R�schendorf & Steven Vanduffel, 2015. "Optimal payoffs under state-dependent preferences," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1157-1173, July.
    4. Farzad Pourbabaee & Minsuk Kwak & Traian A. Pirvu, 2016. "Risk minimization and portfolio diversification," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1325-1332, September.
    5. Bernardo D'Auria & Jos'e Antonio Salmer'on, 2017. "Valuing the anticipative information on the stochastic short interest rates," Papers 1711.03642, arXiv.org, revised Nov 2021.
    6. Aditya Maheshwari & Traian A. Pirvu, 2020. "Portfolio Optimization under Correlation Constraint," Risks, MDPI, vol. 8(1), pages 1-18, February.
    7. Shuzhen Yang, 2020. "Bellman type strategy for the continuous time mean-variance model," Papers 2005.01904, arXiv.org, revised Jul 2020.
    8. L. Rüschendorf & Steven Vanduffel, 2020. "On the construction of optimal payoffs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 129-153, June.
    9. Giuzio, Margherita & Ferrari, Davide & Paterlini, Sandra, 2016. "Sparse and robust normal and t- portfolios by penalized Lq-likelihood minimization," European Journal of Operational Research, Elsevier, vol. 250(1), pages 251-261.
    10. Galeotti, Marcello & Rabitti, Giovanni & Vannucci, Emanuele, 2020. "An evolutionary approach to fraud management," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1167-1177.
    11. Shuzhen Yang, 2020. "Discrete time multi-period mean-variance model: Bellman type strategy and Empirical analysis," Papers 2011.10966, arXiv.org.
    12. Bernard, Carole & Vanduffel, Steven & Ye, Jiang, 2019. "Optimal strategies under Omega ratio," European Journal of Operational Research, Elsevier, vol. 275(2), pages 755-767.
    13. Frank Schuhmacher & Hendrik Kohrs & Benjamin R. Auer, 2021. "Justifying Mean-Variance Portfolio Selection when Asset Returns Are Skewed," Management Science, INFORMS, vol. 67(12), pages 7812-7824, December.
    14. Aditya Maheshwari & Traian Pirvu, 2019. "Portfolio Optimization under Correlation Constraint," Papers 1912.12521, arXiv.org.
    15. Bodnar, Taras & Mazur, Stepan & Okhrin, Yarema, 2017. "Bayesian estimation of the global minimum variance portfolio," European Journal of Operational Research, Elsevier, vol. 256(1), pages 292-307.
    16. Pieter M. van Staden & Peter A. Forsyth & Yuying Li, 2023. "A parsimonious neural network approach to solve portfolio optimization problems without using dynamic programming," Papers 2303.08968, arXiv.org.

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