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Risk-adjusted geometric diversified portfolios

Author

Listed:
  • Maria-Laura Torrente

    (University of Genova)

  • Pierpaolo Uberti

    (University of Milan-Bicocca)

Abstract

In this paper, exploiting a geometric argument, a novel and intuitive approach to portfolio diversification is proposed. The risk-adjusted geometric diversified portfolio is obtained as the point that is equally distant, for a given distance, from the vertices of the simplex, as they represent the single asset portfolios, the worst portfolios in terms of diversification. The definition of risk-adjusted distance as a special case of weighted Euclidean distance permits to introduce the information on the risks of the assets composing the portfolio in a very general way. The closed form solution for the allocation problem is provided and interesting theoretical properties are proved. Further, a direct comparison with Rao’s Quadratic Entropy maximization problem is outlined, thus yielding a different perspective to the use of such entropy as a diversification measure. Finally, the effectiveness of our proposal is emphasized through a comprehensive empirical out-of-sample exercise on real financial data.

Suggested Citation

  • Maria-Laura Torrente & Pierpaolo Uberti, 2024. "Risk-adjusted geometric diversified portfolios," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(1), pages 35-55, February.
    • Handle: RePEc:spr:qualqt:v:58:y:2024:i:1:d:10.1007_s11135-023-01631-w
    DOI: 10.1007/s11135-023-01631-w
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Portfolio diversification; Risk-adjusted distance; Weighted Euclidean distance; Asset allocation; Rao’s quadratic entropy;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G1 - Financial Economics - - General Financial Markets
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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