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Tensors Associated with Mean Quadratic Differences Explaining the Riskiness of Portfolios of Financial Assets

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  • Pierpaolo Angelini

    (Dipartimento di Scienze Statistiche, Università La Sapienza, 00185 Rome, Italy)

  • Fabrizio Maturo

    (Faculty of Economics, Universitas Mercatorum, 00186 Rome, Italy)

Abstract

Bound choices such as portfolio choices are studied in an aggregate fashion using an extension of the notion of barycenter of masses. This paper answers the question of whether such an extension is a natural fashion of studying bound choices or not. Given n risky assets, the question of why it is appropriate to treat only two risky assets at a time inside the budget set of the decision-maker is handled in this paper. Two risky assets are two goods. They are two marginal goods. The question of why they always give rise to a joint good inside the budget set of the decision-maker is addressed by this research work. A single risky asset is viewed as a double one using four nonparametric joint distributions of probability. The variability of a joint distribution of probability always depends on the state of information and knowledge associated with a given decision-maker. For this reason, two variability tensors are defined to identify the riskiness of the same risky asset. A multilinear version of the Sharpe ratio is shown. It is based on tensors. After computing the expected return on an n -risky asset portfolio, its riskiness is obtained using mean quadratic differences developed through tensors.

Suggested Citation

  • Pierpaolo Angelini & Fabrizio Maturo, 2023. "Tensors Associated with Mean Quadratic Differences Explaining the Riskiness of Portfolios of Financial Assets," JRFM, MDPI, vol. 16(8), pages 1-25, August.
  • Handle: RePEc:gam:jjrfmx:v:16:y:2023:i:8:p:369-:d:1215353
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    References listed on IDEAS

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    Cited by:

    1. Pierpaolo Angelini, 2023. "Probability Spaces Identifying Ordinal and Cardinal Utilities in Problems of an Economic Nature: New Issues and Perspectives," Mathematics, MDPI, vol. 11(20), pages 1-22, October.

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