The portfolio

In nineteen fifty-two, a young American economist published a short paper: Portfolio Selection. His name was Harry Markowitz.

Until then, shares were chosen one by one, the best ones. Markowitz said: what matters is how they move together.

He measured risk by volatility, and turned diversification into a calculation. This work earned him the Nobel prize in nineteen ninety.

Take two investments. Each returns six per cent a year on average, with a volatility of twenty per cent. Numbers for the example.

Put half in each. If they always move exactly together, nothing changes: six per cent, and twenty of volatility.

If they move with no link at all between them, the return stays at six. But volatility falls to about fourteen.

And if they always move in opposite directions, the risk disappears completely. A textbook case, almost impossible to find in reality.

Same return, less risk. It is called the only free lunch in finance. And the key is correlation.

By combining every possible investment, in every proportion, you get a cloud of portfolios.

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The top edge of the cloud is called the efficient frontier. For each level of risk, the best possible return.

A portfolio below the frontier is a bad choice. You could earn as much for less risk, or earn more for the same risk.

The theory does not say where to sit on the frontier. That depends on you, and the risk you can bear.

In the sixties, William Sharpe and others drew a consequence from it: the CAPM, the capital asset pricing model.

Its idea: risk you can eliminate by diversifying earns nothing. Only market risk is rewarded. It is measured by beta.

The formula fits in one line: expected return equals the risk-free rate, plus beta times the market premium.

Say a risk-free rate of two per cent, a market returning seven, and a share with a beta of one point two.

Two, plus one point two times five: eight per cent. That is what this share should return, according to the model.

It is simple and elegant. But in the data, beta alone explains real returns poorly.

In nineteen seventy-six, Stephen Ross proposed the APT, arbitrage pricing theory. Instead of a single factor, several.

The market, but also rates, inflation, growth. Each share has its own sensitivity to each.

In the early nineties, Fama and French added company size and price compared with book value.

These ideas still shape investing today: asset allocation, index funds, factor funds.

What to remember: the risk of a whole is not the sum of the risks. It all depends on how the pieces move together.

And diversification remains the only known way to reduce risk without reducing expected return.