Portfolio Optimization for 5 Securities Using Lagrange Multipliers, No Short-Selling, Weights Sum to 1
Construct the Optimal Portfolio that:
delivers the target return (mu_Target)
with minimum risk
Minimize the risk of the portfolio (in this case, measured as half the variance)
While maintaining an expected return target of (mu_Target)
By adjusting the investment weights on each asset
Subject to the budget constraint that the weights sum to 1
Since constraints are equalities => We can use Method Lagrange
Supports up to 5 securities.
Able to do more if requested. Please contact us.
No short-selling (ie. No negative weights)
Basic MPT with only budget constraint that weights sum to 1
Tweaked solution where no negative weights are allowed,
but budget contraint fails, as sum of weights exceed 1.
Maintain that no negative weights are allowed,
but normalize weights such that they sum to 1.
This yields a practical solution, but usually unable to meet target return.