1952 · The Journal of Finance

Portfolio Selection

What it says

Markowitz shows that a portfolio's expected return alone is not a sufficient criterion. The investor cares about two quantities at once: expected return and variance. Taken together, the set of choosable portfolios collapses to a curve.

A portfolio's return is the weighted sum of the asset returns:

E [R_{p}] = i = 1 \sum n w_{i} μ_{i}

Variance, however, depends not only on the variance of the individual assets but also on the covariance between them:

σ_{p}^{2} = i = 1 \sum n j = 1 \sum n w_{i} w_{j} σ_{ij}

The cross terms in the second expression are the paper's real contribution. When assets that are not perfectly correlated are combined, the portfolio's variance falls below the weighted average of the individual variances.

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Why it matters

This framing turns the question of a "good portfolio" into an optimisation problem. For a given level of expected return, one looks for the weights that minimise variance; the collection of those points forms the efficient set.

Much of the next fifty years of the literature is a set of answers to the weak points of this setup: estimation error in the inputs, the instability of the covariance matrix, and the single-period assumption.