## Working with Linear Equality Constraints Using PortfolioCVaR Object

Linear equality constraints are optional linear constraints that impose systems of
equalities on portfolio weights (see Linear Equality Constraints). Linear equality constraints have properties
`AEquality`

, for the equality constraint matrix, and
`bEquality`

, for the equality constraint vector.

### Setting Linear Equality Constraints Using the ` PortfolioCVaR`

Function

The properties for linear equality constraints are set using the `PortfolioCVaR`

object. 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:

A = [ 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 the `setEquality`

and `addEquality`

Functions

You can also set the properties for linear equality constraints using `setEquality`

. Suppose that you have
a portfolio of five assets and want to ensure that the first three assets are 50% of
your portfolio. Given a `PortfolioCVaR`

object
`p`

, use `setEquality`

to set the linear
equality constraints:

A = [ 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 use `addEquality`

to build up linear
equality constraints. For this example, create another system of
equalities:

p = PortfolioCVaR; A = [ 1 1 1 0 0 ]; % first equality constraint b = 0.5; p = setEquality(p, A, b); A = [ 0 0 1 1 1 ]; % second equality constraint b = 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

The `PortfolioCVaR`

object, `setEquality`

, and `addEquality`

implement scalar
expansion on the `bEquality`

property based on the dimension of the
matrix in the `AEquality`

property.

## See Also

`PortfolioCVaR`

| `setDefaultConstraints`

| `setBounds`

| `setBudget`

| `setGroups`

| `setGroupRatio`

| `setEquality`

| `setInequality`

| `setTurnover`

| `setOneWayTurnover`

## Related Examples

- Creating the PortfolioCVaR Object
- Working with CVaR Portfolio Constraints Using Defaults
- Validate the CVaR Portfolio Problem
- Estimate Efficient Portfolios for Entire Frontier for PortfolioCVaR Object
- Estimate Efficient Frontiers for PortfolioCVaR Object
- Asset Returns and Scenarios Using PortfolioCVaR Object
- Hedging Using CVaR Portfolio Optimization
- Compute Maximum Reward-to-Risk Ratio for CVaR Portfolio