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A Portfolio of Risky Assets and Its Intrinsic Properties

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  • Pierpaolo Angelini

Abstract

We show a canonical expression of a univariate risky asset. We find out a canonical expression of the product of two univariate risky assets when they are jointly considered. We find out a canonical expression of a portfolio of two univariate risky assets when it is viewed as a stand-alone entity. We prove that a univariate risky asset is an isometry. We define different distributions of probability on R inside of metric spaces having di erent dimensions. We use the geometric property of collinearity in order to obtain this thing. We obtain the expected return on a portfolio of two univariate risky assets when it is viewed as a stand-alone entity. We also obtain its variance. We show that it is possible to use two di erent quadratic metrics in order to analyze a portfolio of two univariate risky assets. We consider two intrinsic properties of it. If a portfolio of two univariate risky assets is viewed as a stand-alone entity then it is an antisymmetric tensor of order 2. What we say can be extended to a portfolio of more than two univariate risky assets.

Suggested Citation

  • Pierpaolo Angelini, 2020. "A Portfolio of Risky Assets and Its Intrinsic Properties," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(3), pages 1-61, June.
    • Handle: RePEc:ibn:jmrjnl:v:12:y:2020:i:3:p:61
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    References listed on IDEAS

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    More about this item

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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