Portfolio optimization -- estimateCu​stomObject​ivePortfol​io equivalent in R2021b?

Hello, Matlab community. I am working on a portfolio optimization exercise, and I'm looking for a way to incorporate a user-defined objective function in the usual Portfolio object workflow. The "estimateCustomObjectivePortfolio" function seems to be exactly what I need, but unfortunately it was introduced in R2022b. I am using a corporate R2021b Matlab license, so my IT department may not let me just upgrade to get the new functionality (I'm checking on that as well).

Assuming I have to live with R2021b for now, I'll give you an example of what I'm trying to accomplish. Consider a fixed-income-only universe of asset classes, and durations for each:

- IG corporate duration = 7 years

- high yield corporate duration = 3 years

- treasury duration = 10 years

- etc.

In the portfolio optimization, I'd like to be able to have a stated duration target for the resulting portfolio. But, the duration of any hypothetical portfolio depends on the portfolio weights the optimizer is considering in any given iteration, and I don't see a way (in my version of Matlab) to state that duration target as a constraint or objective.

Thanks in advance for any thoughts you may have.

Answer 1

[MULI]

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.

https://www.mathworks.com/help/releases/R2021b/optim/ug/fmincon.html

Hope this answers your query!

[jeremy gogos]

Muli, thank you so much for the guidance! Your illustration of how to run this problem through the optimizer was exactly what I needed.

Answer 2

[Alejandra Pena-Ordieres]

Hello,

Since target duration can be added as a linear equality constraint, you can still use the Portfolio object. You won't need the estimateCustomObjectivePortfolio function. Here is the code that you'd need to include the target duration constraint:

% Initialize Portfolio object
p = Portfolio;

% Set moments and problem constraints (other than target duration)
% ...

% Set target duration constraint
assetDurations = [7; 3; 10]; % Example durations for each asset 
targetDuration = 5;          % Target portfolio duration
p = setEquality(p,assetDurations',targetDuration);

% Get efficient frontier
plotFrontier(p)

Hope this helps!