Modern portfolio theory

Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning only one type. Its key insight is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return. The variance of return (or its transformation, the standard deviation) is used as a measure of risk, because it is tractable when assets are combined into portfolios.^[1] Often, the historical variance and covariance of returns is used as a proxy for the forward-looking versions of these quantities,^[2] but other, more sophisticated methods are available.^[3]

Economist Harry Markowitz introduced MPT in a 1952 essay,^[1] for which he was later awarded a Nobel Memorial Prize in Economic Sciences; see Markowitz model.

In 1940, Bruno de Finetti published^[4] the mean-variance analysis method, in the context of proportional reinsurance, under a stronger assumption. The paper was obscure and only became known to economists of the English-speaking world in 2006.^[5]

^ ^a ^b Markowitz, H.M. (March 1952). "Portfolio Selection". The Journal of Finance. 7 (1): 77–91. doi:10.2307/2975974. JSTOR 2975974.
^ Wigglesworth, Robin (11 April 2018). "How a volatility virus infected Wall Street". The Financial Times.
^ Luc Bauwens, Sébastien Laurent, Jeroen V. K. Rombouts (February 2006). "Multivariate GARCH models: a survey". Journal of Applied Econometrics. 21 (1).{{cite journal}}: CS1 maint: multiple names: authors list (link)
^ de Finetti, B. (1940): Il problema dei “Pieni”. Giornale dell’ Istituto Italiano degli Attuari 11, 1–88; translation (Barone, L. (2006)): The problem of full-risk insurances. Chapter I. The risk within a single accounting period. Journal of Investment Management 4(3), 19–43
^ Pressacco, Flavio; Serafini, Paolo (May 2007). "The origins of the mean-variance approach in finance: revisiting de Finetti 65 years later". Decisions in Economics and Finance. 30 (1): 19–49. doi:10.1007/s10203-007-0067-7. ISSN 1593-8883.

[markowitz1952-1] Markowitz, H.M. (March 1952). "Portfolio Selection". The Journal of Finance. 7 (1): 77–91. doi:10.2307/2975974. JSTOR 2975974.

[:0-2] Wigglesworth, Robin (11 April 2018). "How a volatility virus infected Wall Street". The Financial Times.

[:bauwensetal2006-3] Luc Bauwens, Sébastien Laurent, Jeroen V. K. Rombouts (February 2006). "Multivariate GARCH models: a survey". Journal of Applied Econometrics. 21 (1).{{cite journal}}: CS1 maint: multiple names: authors list (link)

[4] Finetti, B. (1940): Il problema dei “Pieni”. Giornale dell’ Istituto Italiano degli Attuari 11, 1–88; translation (Barone, L. (2006)): The problem of full-risk insurances. Chapter I. The risk within a single accounting period. Journal of Investment Management 4(3), 19–43

[5] Pressacco, Flavio; Serafini, Paolo (May 2007). "The origins of the mean-variance approach in finance: revisiting de Finetti 65 years later". Decisions in Economics and Finance. 30 (1): 19–49. doi:10.1007/s10203-007-0067-7. ISSN 1593-8883.

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