Portfolio Optimization for 5 Securities Using Lagrange Multipliers, No Short-Selling, Weights Sum to 1
Portfolio Optimization for 5 Securities Using Lagrange Multipliers, No Short-Selling, Weights Sum to 1
Problem:
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
Method:
Since constraints are equalities => We can use Method Lagrange
Supports up to 5 securities.
Able to do more if requested. Please contact us.
Constraints:
No short-selling (ie. No negative weights)
Solution 00:
Basic MPT with only budget constraint that weights sum to 1
Solution 01:
Tweaked solution where no negative weights are allowed,
but budget contraint fails, as sum of weights exceed 1.
Solution 02:
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.
