medium · Quantitative Finance
According to the Lagrangian derivation for the minimum variance portfolio with a target return μ^*, the resulting weight vector w is a linear combination of Σ^-1μ and Σ^-1mathbf1.
If μ is a scalar multiple of 1, what happens to the efficient frontier?
- The Sharpe ratio becomes infinite for every single feasible portfolio located along the frontier.
- The frontier degenerates into a single vertical line plotted against the mean-variance risk-return plane.
- The covariance matrix Sigma must reduce to a purely diagonal form for any feasible solution to exist at all.
- The efficient frontier collapses to a single point, which is the Global Minimum Variance portfolio.
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