 Portfolio opportunity set

The set of attainable return standard deviations and expected returns for budget-feasible risky investment portfolios. Negative weights are allowed when short selling is permitted. With positive definite covariance matrix and nonconstant means, the minimum-risk boundary is a hyperbola in standard-deviation/mean coordinates; its upper branch is the mean-variance efficient frontier. Adding a risk-free asset changes the budget constraint on risky holdings and produces a different attainable set.