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The Markowitz Category

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  • John Armstrong

Abstract

We give an algebraic definition of a Markowitz market and classify markets up to isomorphism. Given this classification, the theory of portfolio optimization in Markowitz markets without short selling constraints becomes trivial. Conversely, this classification shows that, up to isomorphism, there is little that can be said about a Markowitz market that is not already detected by the theory of portfolio optimization. In particular, if one seeks to develop a simplified low-dimensional model of a large financial market using mean--variance analysis alone, the resulting model can be at most two-dimensional.

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  • John Armstrong, 2016. "The Markowitz Category," Papers 1611.07741, arXiv.org, revised Jun 2018.
    • Handle: RePEc:arx:papers:1611.07741
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    References listed on IDEAS

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    1. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    2. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
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    Cited by:

    1. John Armstrong & Damiano Brigo, 2019. "The ineffectiveness of coherent risk measures," Papers 1902.10015, arXiv.org, revised Oct 2020.
    2. Armstrong, John & Brigo, Damiano, 2022. "Coherent risk measures alone are ineffective in constraining portfolio losses," Journal of Banking & Finance, Elsevier, vol. 140(C).
    3. Armstrong, John & Ionescu, Andrei, 2024. "Itô stochastic differentials," Stochastic Processes and their Applications, Elsevier, vol. 171(C).

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