Risk-adjusted geometric diversified portfolios

Maria-Laura Torrente () and Pierpaolo Uberti ()
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Maria-Laura Torrente: University of Genova
Pierpaolo Uberti: University of Milan-Bicocca

Quality & Quantity: International Journal of Methodology, 2024, vol. 58, issue 1, No 2, 35-55

Abstract: 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.

Keywords: Portfolio diversification; Risk-adjusted distance; Weighted Euclidean distance; Asset allocation; Rao’s quadratic entropy; 91G10; 52B99 (search for similar items in EconPapers)
JEL-codes: C02 G1 G11 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11135-023-01631-w

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