Overview
Modern portfolio theory (MPT) was introduced by the American economist Harry Markowitz in "Portfolio Selection", published in the Journal of Finance in 1952, and expanded in his 1959 book of the same title. It turned the intuition "don't put all your eggs in one basket" into mathematics and became a starting point of modern finance; Markowitz shared the 1990 Nobel Memorial Prize with Merton Miller and William Sharpe.
The mean–variance model
Markowitz assumed that investors prefer higher expected return and lower risk, and measured risk as the variance (or standard deviation) of returns. A portfolio's expected return is the weighted average of its assets' expected returns, but its variance depends not only on each asset's variance but also on the covariances (correlations) between assets.
The diversification effect
If two assets have a correlation of +1, combining them does not reduce risk. If the correlation is below +1, the portfolio's standard deviation is lower than the weighted average of the assets' standard deviations, and at −1 risk could in theory be eliminated. What matters is therefore not only each asset's return but how assets move together.
The efficient frontier
Collecting the portfolios with the highest expected return for each level of risk, or the lowest risk for each expected return, traces a curve in risk–return space called the efficient frontier. Each investor then picks the point on it that fits their risk preference (indifference curve).
Systematic and unsystematic risk
- Unsystematic risk: risk specific to individual assets, such as one firm's accident or earnings miss, which can be reduced by holding more securities.
- Systematic risk: market-wide risk from the business cycle, interest rates or war, which diversification cannot remove.
Tobin's separation theorem and CAPM
Tobin (1958) showed that once a risk-free asset is added, all investors hold the same portfolio of risky assets and differ only in how much they put into the risk-free asset, according to their risk preference. Sharpe (1964) and others extended this to market equilibrium, producing the capital asset pricing model (CAPM), in which only systematic risk (beta) is rewarded.
Limitations
Expected returns and covariances are hard to estimate, and small changes in inputs can shift the optimal portfolio a lot. The assumption of normally distributed returns understates extreme losses such as those in financial crises, and correlations between assets tend to rise in a crisis, weakening diversification. The critique that investors are not always rational belongs to behavioral finance, and whether prices reflect information is the subject of the efficient market hypothesis.
Sources reviewed: 2026-10-16
References
- Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77–91.
- Markowitz, H. M. (1959). Portfolio Selection: Efficient Diversification of Investments. New York: Wiley.
- Tobin, J. (1958). Liquidity preference as behavior towards risk. Review of Economic Studies, 25(2), 65–86.
- Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19(3), 425–442.