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Annals of Operations Research

, Volume 282, Issue 1–2, pp 315–329 | Cite as

Managing portfolio diversity within the mean variance theory

  • Anatoly B. SchmidtEmail author
S.I.: Application of O. R. to Financial Markets
First Online:

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.

Keywords

Mean variance portfolio Portfolio diversity Performance analysis 
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Notes

Acknowledgements

I am grateful to anonymous reviewers for constructive comments to my work.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Kensho Technologies, Inc, One World Trade CenterNew YorkUSA
  2. 2.Department of Finance and Risk EngineeringNYU School of EngineeringBrooklynUSA

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