Modern Portfolio Theory

In 1952, a 25-year-old graduate student named Harry Markowitz published a paper with the plain title “Portfolio Selection”. It fundamentally changed how people think about investing and earned him the Nobel Prize in 1990. His core idea: don’t judge investments in isolation – look at how they work together in a portfolio.

Looking at return and risk together#

Markowitz described each investment by two numbers: its expected return and its risk, measured as volatility. A portfolio’s expected return is simply the weighted average of the individual returns. Its risk isn’t – because it depends on the correlation between the assets.

As long as correlation is below 1, portfolio risk is lower than the weighted average of the individual risks. That’s the mathematical heart of diversification.

The efficient frontier#

Combine two assets in every possible proportion and you get a curved line in the return-risk chart. Try it: change the stock weight and the correlation and watch the curve bend.

A few insights:

• The lower the correlation, the more the curve bends to the left – the more risk can be mixed away.
• There’s a minimum-variance portfolio. It often isn’t 100% the least risky asset but includes some of the riskier one.
• The upper branch of the curve is the efficient frontier: for each level of risk it offers the highest expected return. Portfolios below it are inefficient – you could expect more for the same risk.

With many assets the logic is the same, just more computation. The result is always a frontier of efficient portfolios.

The Sharpe ratio#

Which efficient portfolio is best? William Sharpe developed a simple measure in 1966:

The Sharpe ratio measures how much excess return an investment delivers per unit of risk. Broad stock markets have historically had Sharpe ratios of roughly 0.3 to 0.5. Values well above 1 over long periods are rare – and products advertising them deserve scepticism.

A key idea behind it: with a high-Sharpe portfolio, you can dial risk to your liking by mixing in risk-free assets (or a little borrowing). The question “how much risk do I want?” becomes separate from “what’s the best mix of risky assets?”

CAPM and beta#

Building on Markowitz, William Sharpe and others developed the capital asset pricing model (CAPM) in the 1960s. Its claim: in equilibrium everyone holds the market portfolio, and a stock’s expected return depends only on how much it moves with the market – its beta.

• Beta 1: moves like the market on average.
• Beta above 1: moves more (many tech and cyclical stocks).
• Beta below 1: moves less (utilities, consumer staples).

CAPM explains why only systematic risk is rewarded: company-specific risk can be diversified away, so nobody pays a premium for bearing it.

Theory meets practice#

Elegant as portfolio theory is, applying it is tricky:

• Estimation error: optimisation needs expected returns, volatilities and correlations. Expected returns can barely be estimated reliably. Small errors produce extreme, unstable portfolios – critics call mean-variance optimisers “error maximisers”.
• Unstable correlations: in crises, correlations rise – exactly when diversification is needed most.
• Volatility isn’t everything: investors mainly fear large losses and lasting loss of purchasing power, which volatility captures only partly.

Studies show that simple rules – equal weighting or a fixed stock-bond mix – often do no worse in practice than elaborately “optimised” portfolios. Other approaches such as risk parity spread risk rather than capital evenly across asset classes.

Summary#

Markowitz showed that a portfolio’s risk depends on the correlation of its parts. The efficient frontier connects the best possible mixes, the Sharpe ratio measures return per unit of risk, and CAPM explains expected returns through beta. In practice, estimation error makes precise optimisation difficult – robust, simple portfolios are often the smarter choice.