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 Quad- ratic 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.

Risk-adjusted geometric diversified portfolios

Torrente, Maria-Laura;
2024-01-01

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 Quad- ratic 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/1108994
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