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Solve Problem for Minimum Tracking Error with Net Return Constraint

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This example shows how to use estimateCustomObjectivePortfolio to solve a portfolio problem for minimum tracking error with a net return constraint using a custom objective.

Create Portfolio Object

Create a Portfolio object.

% Create a Portfolio object
load('SixStocks.mat')
p = Portfolio(AssetMean=AssetMean,AssetCovar=AssetCovar);

Define Problem

The portfolio problem for a minimum tracking error problem with a net return constraint is defined as

minx  (x-x0)TΣ(x-x0)s.t.μTx-cBTmax(0,x-x0)-cSTmax(0,x0-x)≥μ0        ∑ixi=1        x≥0

Define Problem Parameters

Define the problem parameters for the Portfolio object.

% Initial portfolio
initPort = 1/p.NumAssets*ones(p.NumAssets,1);
% Buy cost
buyCost = 0.001*ones(p.NumAssets,1);
% Sell cost
sellCost = 0.002*ones(p.NumAssets,1);
% Net return target
ret0 = 0.03;

Solve Portfolio Problem

Use estimateCustomObjectivePortfolio to solve this portfolio problem for a minimum tracking error with a net return constraint. When using the estimateCustomObjectivePortfolio function with a Portfolio object, you add return constraints by using the estimateCustomObjectivePortfolio name-value argument TargetReturn with a return target value.

% Long-only, fully invested portfolio
p = setDefaultConstraints(p);
% Set the buy and sell costs
p = setCosts(p,buyCost,sellCost,initPort);

% Set the objective
fun = @(x) (x-initPort)'*p.AssetCovar*(x-initPort);

% Solve the portfolio problem
wFinTbx = estimateCustomObjectivePortfolio(p,fun,TargetReturn=ret0)
wFinTbx = 6×1

    0.1633
    0.0648
    0.1950
    0.2618
    0.0625
    0.2525

See Also

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