For theorems about the mean-variance efficient frontier, see Mutual fund separation theorem. For non-mean-variance portfolio analysis, see Marginal conditional stochastic dominance. Its key insight is that an asset’s risk and return should not be assessed by itself, but by how it contributes to a portfolio’s overall risk portfolio risk and return pdf return. Economist Harry Markowitz introduced MPT in a 1952 essay, for which he was later awarded a Nobel Prize in economics.

MPT assumes that investors are risk averse, meaning that given two portfolios that offer the same expected return, investors will prefer the less risky one. Thus, an investor will take on increased risk only if compensated by higher expected returns. Conversely, an investor who wants higher expected returns must accept more risk.

The exact trade-off will be the same for all investors, but different investors will evaluate the trade-off differently based on individual risk aversion characteristics. Portfolio return is the proportion-weighted combination of the constituent assets’ returns. In other words, investors can reduce their exposure to individual asset risk by holding a diversified portfolio of assets.

Diversification may allow for the same portfolio expected return with reduced risk. These ideas have been started with Markowitz and then reinforced by other economists and mathematicians such as Andrew Brennan who have expressed ideas in the limitation of variance through portfolio theory. If all the asset pairs have correlations of 1—they are perfectly positively correlated—then the portfolio return’s standard deviation is the sum of the asset returns’ standard deviations weighted by the fractions held in the portfolio. For given portfolio weights and given standard deviations of asset returns, the case of all correlations being 1 gives the highest possible standard deviation of portfolio return.