Setting Linear Inequality Constraints Using thePortfolioMADFunction

The properties for linear inequality constraints are set using thePortfolioMADobject. Suppose that you have a portfolio of five assets and you want to ensure that the first three assets are no more than 50% of your portfolio. To set up these constraints:

A = [ 1 1 1 0 0 ]; b = 0.5; p = PortfolioMAD('AInequality', A,'bInequality', b); disp(p.NumAssets) disp(p.AInequality) disp(p.bInequality)

5 1 1 1 0 0 0.5000

Setting Linear Inequality Constraints Using thesetInequalityandaddInequalityFunctions

You can also set the properties for linear inequality constraints usingsetInequality. Suppose that you have a portfolio of five assets and you want to ensure that the first three assets constitute no more than 50% of your portfolio. Given aPortfolioMADobjectp, usesetInequalityto set the linear inequality constraints:

A = [ 1 1 1 0 0 ]; b = 0.5; p = PortfolioMAD; p = setInequality(p, A, b); disp(p.NumAssets) disp(p.AInequality) disp(p.bInequality)

5 1 1 1 0 0 0.5000

Suppose that you want to add another linear inequality constraint to ensure that the last three assets constitute at least 50% of your portfolio. You can set up an augmented system of linear inequalities or use theaddInequalityfunction to build up linear inequality constraints. For this example, create another system of inequalities:

p = PortfolioMAD; A = [ 1 1 1 0 0 ];% first inequality constraintb = 0.5; p = setInequality(p, A, b); A = [ 0 0 -1 -1 -1 ];% second inequality constraintb = -0.5; p = addInequality(p, A, b); disp(p.NumAssets) disp(p.AInequality) disp(p.bInequality)

5 1 1 1 0 0 0 0 -1 -1 -1 0.5000 -0.5000

ThePortfolioMADobject,setInequality, andaddInequalityimplement scalar expansion on thebInequalityproperty based on the dimension of the matrix in theAInequalityproperty.