medium · Quantitative Finance

What is the economic interpretation of the Lagrange multiplier λ in the portfolio optimization problem where we minimize variance subject to a budget constraint?

1. It is the expected return earned specifically by the global minimum-variance portfolio under budget.
2. It measures how sensitive the optimal portfolio weights are to small changes in the prevailing risk-free rate.
3. It represents the Sharpe ratio, meaning the risk-adjusted excess return per unit of volatility, of the optimal portfolio.
4. It represents the marginal change in the minimum variance for a one-unit relaxation of the budget constraint.

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