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Estimation of Optimal Portfolio Compositions for Small Sample and Singular Covariance Matrix

In: Advanced Statistical Methods in Process Monitoring, Finance, and Environmental Science

Author

Listed:
  • Taras Bodnar

    (Linköping University, Department of Management and Engineering)

  • Stepan Mazur

    (Örebro University, Unit of Statistics, School of Business
    Linnaeus University, Department of Economics and Statistics, School of Business and Economics)

  • Hoang Nguyen

    (Linköping University, Department of Management and Engineering)

Abstract

In the chapter we consider the optimal portfolio choice problem under parameter uncertainty when the covariance matrix of asset returns is singular. Very useful stochastic representations are deduced for the characteristics of the expected utility optimal portfolio. Using these stochastic representations, we derive the moments of higher order of the estimated expected return and the estimated variance of the expected utility optimal portfolio. Another line of applications leads to their asymptotic distributions obtained in the high-dimensional setting. Via a simulation study, it is shown that the derived high-dimensional asymptotic distributions provide good approximations of the exact ones even for moderate sample sizes.

Suggested Citation

  • Taras Bodnar & Stepan Mazur & Hoang Nguyen, 2024. "Estimation of Optimal Portfolio Compositions for Small Sample and Singular Covariance Matrix," Springer Books, in: Sven Knoth & Yarema Okhrin & Philipp Otto (ed.), Advanced Statistical Methods in Process Monitoring, Finance, and Environmental Science, pages 259-278, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-69111-9_13
    DOI: 10.1007/978-3-031-69111-9_13
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    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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