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Markowitz Portfolio Variance

σp2=wTΣw\sigma_p^2 = \mathbf{w}^T \Sigma \mathbf{w}

Portfolio risk depends on asset weights and their covariance matrix.

By Harry Markowitz

Social Sciences
Markowitz Portfolio Variance
1952 · Harry Markowitz
Why it matters: Showed diversification reduces risk without sacrificing expected return.

Discoverers: Harry Markowitz (1952)

What does it mean?

Portfolio risk depends on asset weights and their covariance matrix.

Why should I care?

Showed diversification reduces risk without sacrificing expected return.

Variables & Units

SymbolNameUnitMeaning
σp2σ_p²Portfolio variance—Risk
wwWeights—Asset fractions
ΣΣCovariance matrix—Asset covariances

Worked Example

Negatively correlated assets lower σ_p² at same expected return.

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Sources & further reading

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Equation Universe

Markowitz Portfolio Variance

σp2=wTΣw\sigma_p^2 = \mathbf{w}^T \Sigma \mathbf{w}

Real-world impact

Global economy

Quantitative models shape markets and policy.

Photo: Unsplash — financial markets

Portfolio risk depends on asset weights and their covariance matrix.

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