Editing Modern portfolio theory (section)

{{Short description|Mathematical framework for investment risk}}
{{redirect|Portfolio analysis|the text book|Portfolio Analysis|theorems about the mean-variance efficient frontier|Mutual fund separation theorem|non-mean-variance portfolio analysis|Marginal conditional stochastic dominance}}
[[File:Asset Allocation.pdf|thumb|right|250px|Modern portfolio theory suggests a diversified portfolio of [[shares]] and other [[asset classes]] (such as debt in [[corporate bonds]], [[treasury bond]]s, or [[money market funds]]) will realise more predictable returns if there is prudent market regulation.]]
'''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 (finance)|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.<ref name="markowitz1952"/> Often, the historical variance and covariance of returns is used as a proxy for the forward-looking versions of these quantities,<ref name=":0">{{Cite news|url=https://www.ft.com/content/be68aac6-3d13-11e8-b9f9-de94fa33a81e|title=How a volatility virus infected Wall Street|last=Wigglesworth|first=Robin|date=11 April 2018|work=The Financial Times}}</ref> but other, more sophisticated methods are available.<ref name=":bauwensetal2006">{{cite journal |author=Luc Bauwens, Sébastien Laurent, Jeroen V. K. Rombouts|title=Multivariate GARCH models: a survey |journal=Journal of Applied Econometrics |date=February 2006 |volume=21|issue=1 |pages=79–109 |doi=10.1002/jae.842 |url=https://doi.org/10.1002/jae.842}}</ref>

Economist [[Harry Markowitz]] introduced MPT in a 1952 paper,<ref name="markowitz1952">{{cite journal |author=Markowitz, H.M. |title=Portfolio Selection |journal=The Journal of Finance |date=March 1952 |volume=7 |issue=1 |pages=77–91 |doi=10.2307/2975974 |jstor=2975974|url=http://onlinelibrary.wiley.com/doi/10.1111/j.1540-6261.1952.tb01525.x/full|url-access=subscription }}</ref> for which he was later awarded a [[Nobel Memorial Prize in Economic Sciences]]; see [[Markowitz model]].

In 1940, [[Bruno de Finetti]] published<ref>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</ref> 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.<ref>{{Cite journal |last1=Pressacco |first1=Flavio |last2=Serafini |first2=Paolo |date=May 2007 |title=The origins of the mean-variance approach in finance: revisiting de Finetti 65 years later |journal=Decisions in Economics and Finance |language=en |volume=30 |issue=1 |pages=19–49 |doi=10.1007/s10203-007-0067-7 |issn=1593-8883|doi-access=free }}</ref>