Setting Linear Equality Constraints Using thePortfolioCVaRFunction

The properties for linear equality constraints are set using thePortfolioCVaRobject. Suppose that you have a portfolio of five assets and want to ensure that the first three assets are 50% of your portfolio. To set this constraint:

一个= (1 1 1 0 0);b = 0.5;p = PortfolioCVaR('AEquality', A,'bEquality', b); disp(p.NumAssets) disp(p.AEquality) disp(p.bEquality)

5 1 1 1 0 0 0.5000

Setting Linear Equality Constraints Using thesetEqualityandaddEqualityFunctions

You can also set the properties for linear equality constraints usingsetEquality. Suppose that you have a portfolio of five assets and want to ensure that the first three assets are 50% of your portfolio. Given aPortfolioCVaRobjectp, usesetEqualityto set the linear equality constraints:

一个= (1 1 1 0 0);b = 0.5;p = PortfolioCVaR; p = setEquality(p, A, b); disp(p.NumAssets) disp(p.AEquality) disp(p.bEquality)

5 1 1 1 0 0 0.5000

Suppose that you want to add another linear equality constraint to ensure that the last three assets also constitute 50% of your portfolio. You can set up an augmented system of linear equalities or useaddEqualityto build up linear equality constraints. For this example, create another system of equalities:

p = PortfolioCVaR; A = [ 1 1 1 0 0 ];% first equality constraintb = 0.5;p = setEquality(p, A, b); A = [ 0 0 1 1 1 ];% second equality constraintb = 0.5;p = addEquality(p, A, b); disp(p.NumAssets) disp(p.AEquality) disp(p.bEquality)

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

ThePortfolioCVaRobject,setEquality, andaddEqualityimplement scalar expansion on thebEqualityproperty based on the dimension of the matrix in theAEqualityproperty.