Efficient frontier

The set of portfolios offering the highest expected return for each level of risk, given a set of assets and their expected returns, volatilities and correlations.

The geometry is elegant and the inputs are the problem. Expected returns cannot be estimated with any precision, and the optimisation is extremely sensitive to them, so small changes in assumptions produce wildly different portfolios.

The practical response is either to constrain the optimiser heavily or to use methods that reduce the reliance on return estimates.

The frontier is a way of thinking, not a portfolio construction tool.