Modern portfolio theory
mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk, defined as variance
Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of financial 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 principle 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. Often, the historical variance and covariance of returns is used as a proxy for the forward-looking versions of these quantities, but other, more sophisticated methods are available.
Economist Harry Markowitz introduced MPT in a 1952 paper, for which he was later awarded a Nobel Memorial Prize in Economic Sciences; see Markowitz model.
In 1940, Bruno de Finetti published 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.
Mathematical model
Risk and expected return
MPT assumes that investors are risk averse, meaning that given two portfolios that offer the same expected return, investors will prefer the less risky one. Thus, an investor will take on increased risk only if compensated by higher expected returns.
Begin with the source’s own compact description: “Modern portfolio theory” is mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk, defined as variance. The dossier treats that line as a proposition to test through Modern, portfolio and theory, not as a finished interpretation.
Why this record matters
The phrase “mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk, defined as variance” supplies a clear boundary for inquiry. It also exposes the unanswered questions: who defined that boundary, when it became stable and which sources sit outside it.
Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Sep 22, 2026. The linked authority identifier is Q1072885. None of the 0 selected statements returned an explicit reference. The first chronological checks are 1952, 1940 and 2006.
The absence of detail may reflect summary conventions rather than a lack of surviving documentation. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “Modern portfolio theory”, its source revision and the description used here.
- Expand the search: follow Modern portfolio theory primary sources, Modern portfolio theory archive and Modern research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “Modern portfolio theory”?
- Which institution is responsible for the underlying evidence?
- Which cited source is closest to the event, object or claim?
Search terms from this dossier
This entry incorporates text from “Modern portfolio theory” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.