Portfolio Selection

Source: Markowitz, H. (1952) · Journal of Finance 7(1), 77–91 · doi:10.2307/2975974

TL;DR

Founds modern portfolio theory. Markowitz rejects "maximize expected (discounted) return" — which

never favors diversification — and replaces it with the expected return–variance of return (E–V)

rule. What matters for a portfolio is not each asset's risk in isolation but its covariance with

the rest; combining imperfectly correlated assets reduces variance for a given return. The set of

portfolios with maximum return at each variance is the efficient frontier.

Problem it solves

How should an investor choose among securities when the future is uncertain? Markowitz shows the

"maximize discounted anticipated return" rule implies putting all funds in the single highest-value

security and "never implies that there is a diversified portfolio which is preferable" — contradicting

observed, sensible diversification. He therefore casts portfolio choice as a trade-off between a

desirable thing (expected return) and an undesirable thing (variance).

The method

the covariance of returns i and j (σᵢⱼ = ρᵢⱼ σᵢ σⱼ).

for its return). Tracing these out yields the efficient frontier; the rational mean-variance

investor holds a frontier portfolio. Markowitz illustrates the relations geometrically.

Assumptions & inputs

Requires the vector of expected returns and the full covariance matrix as "relevant beliefs about

future performances" (Markowitz's stage one, observation/experience, supplies these; the paper treats

stage two, the choice given beliefs).

How to use it

The conceptual and mathematical basis for the CAPM, risk budgeting, and essentially all quantitative

portfolio construction; establishes covariance/diversification as the heart of risk management.

Limitations & pitfalls

covariances (DeMiguel et al. show naive 1/N often beats it out of sample).

estimate; the no-short-sale form is a special case.

Key references

Provenance: verified/generated from the paper's full text.