Hi Jeremy,
I understand that you need to perform portfolio optimization without using "estimateCustomObjectivePortfolio" function. This can be achieved using `fmincon` function where,
- The Objective Function is defined inline within the fmincon call as, which minimizes the portfolio variance.
- The Nonlinear Constraint is also defined inline within the fmincon call which ensures that the difference between the portfolio's duration and the target duration is zero (an equality constraint).
Below is the MATLAB Code that helps in achieving the requirement:
% Example Data
numAssets = 3; % Adjust based on your actual number of assets
covMatrix = rand(numAssets)*0.01; % Replace with your actual covariance matrix
covMatrix = covMatrix + covMatrix' - diag(diag(covMatrix)); % Making symmetric
assetDurations = [7; 3; 10]; % Example durations for each asset
targetDuration = 5; % Target portfolio duration
% Initial guess for the weights
initialWeights = ones(numAssets, 1) / numAssets;
% Bounds for the weights
lb = zeros(numAssets, 1); % Lower bound of 0
ub = ones(numAssets, 1); % Upper bound of 1
% Equality constraint for the sum of weights
Aeq = ones(1, numAssets);
beq = 1;
% Optimization options
options = optimoptions('fmincon', 'Display', 'iter', 'Algorithm', 'sqp');
% Solve the optimization problem
[optimalWeights, optimalValue] = fmincon(@(weights) weights' * covMatrix * weights, ...
initialWeights, [], [], Aeq, beq, lb, ub, ...
@(weights) deal([], sum(weights .* assetDurations) - targetDuration), options);
% Display the optimal weights
disp('Optimal Weights:');
disp(optimalWeights);
You may refer to this documentation link for more information related to “fmincon” function.
Hope this answers your query!
