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Economics 1952

Portfolio Selection

Harry Markowitz

A portfolio's risk lives not in each stock alone, but in how they move together.

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In depth · the introduction

Everyone says “don't put all your eggs in one basket.” In 1952 a 25-year-old graduate student turned that proverb into mathematics — and showed that what protects you is not the number of baskets, but whether they tip over together.

The big idea

Before Markowitz, choosing investments meant hunting for the best individual stocks — the ones expected to earn the most. He argued that this misses the point. What matters is not how each holding behaves alone, but how the whole collection behaves together. A portfolio has two numbers: its expected return, and its risk — how much that return is likely to swing. His decisive move was to measure risk by how much the holdings move in step with one another.

If two investments tend to rise and fall together, owning both gives little protection — when one drops, so does the other. But if they move out of step, a bad month for one is often a good month for the other, and the bumps partly cancel. So you can sometimes combine two risky assets and end up with a blend that is less risky than either one alone, without giving up return. That is the surprising, precise heart of diversification.

How it came about

Harry Markowitz was a doctoral student at the University of Chicago, looking for a thesis topic. As the story goes, while waiting outside a professor's office he fell into conversation with a stockbroker, who suggested he study the stock market. Reading the standard theory of investment value, he was struck that it focused only on expected return and said nothing about risk, or about holding more than one thing. Sketching a curve on a page, he saw that if investors care about both return and risk, the sensible choices form a frontier. He published the nine-page result in 1952.

Years later, his own thesis defense nearly went sideways: Milton Friedman reportedly teased that the work was not quite economics. Yet it would reshape the field. In 1990 Markowitz shared the Nobel Memorial Prize in Economics with William Sharpe and Merton Miller, for the theory that grew from those nine pages.

Why it mattered

It changed the question from “which stock will go up?” to “how should I combine things so my whole portfolio behaves the way I want?” That shift built the modern investment industry. It is why your retirement fund holds a spread of stocks and bonds rather than a single hot pick; why “diversify” is the first advice every honest adviser gives; and why index funds — owning a little of everything — became the default way for ordinary people to invest. Risk stopped being a vague worry and became a number you could manage.

A way to picture it

Imagine running an ice-cream stand and an umbrella stand. Each alone is risky: the ice-cream stand dies in the rain, the umbrella stand dies in the sun. But run both, and almost every day one of them is busy. Your combined income is far steadier than either business on its own — even though you didn't choose “safer” businesses, only ones that fail at opposite times. Markowitz's mathematics is exactly this idea, made precise: pair things that don't slump together, and their risks partly cancel.

Interactive risk–return map. One slider splits your money between stocks (high return, high risk) and bonds (low return, low risk); another sets how much the two rise and fall together (the correlation). A curve shows all blends; a dot is your blend — up means more return, right means more risk. Turning the correlation down bows the curve to the left, so the same return becomes reachable at lower risk.

Where it sits

Markowitz built on the older economics of value and risk and on basic probability — in the Library, Bayes sits upstream in the story of reasoning under uncertainty. His frontier became the foundation that Sharpe and others extended into the Capital Asset Pricing Model, and it shares a worldview with the Library's Black–Scholes (1973): price and manage risk by combining assets, not by forecasting their direction. Together they turned finance into a quantitative science — for better, as in the index fund, and for worse, in the crises when everyone's “diversified” portfolios fell together after all.

The original document
Original source text
H. Markowitz · The Journal of Finance 7, no. 1 (Mar. 1952): 77–91
Two stages
The process of selecting a portfolio may be divided into two stages. The first stage starts with observation and experience and ends with beliefs about the future performances of available securities. The second stage starts with the relevant beliefs about future performances and ends with the choice of portfolio. This paper is concerned with the second stage.
Taking the investor's beliefs as given, Markowitz asks which portfolio to hold. He first considers — and rejects — the rule of maximizing the discounted expected value of future returns, on the grounds that it never recommends diversification: it would tell the investor to put everything into the single security with the highest expected yield, which is neither how investors behave nor sound advice.
Return is desirable, variance is not
We next consider the rule that the investor does (or should) consider expected return a desirable thing and variance of return an undesirable thing.
A portfolio's return is the weighted average of its securities' returns, so its expected return is the weighted average of their expected returns. Its variance, however, depends on the covariances between every pair of securities — not just their individual variances. This is why risk is not the simple average of the parts, and why how securities move together becomes the central quantity.
Why diversification works
Diversification is both observed and sensible. A rule of behavior which does not imply the superiority of diversification must be rejected both as a hypothesis and as a maxim.
Among all portfolios yielding a given expected return there is one of minimum variance; the set of portfolios that are not dominated — offering the most expected return for their variance, or the least variance for their return — forms the “efficient” frontier, from which the investor should choose. Securities with low or negative covariance reduce variance far more than merely holding a large number of securities does.
Not only does the E-V (Expected returns – Variance of returns) rule imply diversification, it implies the 'right kind' of diversification for the 'right reason.'
[ … ]
The paper then develops the geometry of the efficient set explicitly for three and four securities, and indicates how the general problem is solved. The full article — including the geometric exposition and a closing discussion of expected utility — is available at the source below.
The Journal of Finance · March 1952