## Working with 'Simple' Bound Constraints Using PortfolioMAD Object

'Simple' bound constraints are optional linear constraints that maintain upper and lower bounds on portfolio weights (see 'Simple' Bound Constraints). Although every portfolio set must be bounded, it is not necessary to specify a portfolio set with explicit bound constraints. For example, you can create a portfolio set with an implicit upper bound constraint or a portfolio set with average turnover constraints. The bound constraints have properties LowerBound for the lower-bound constraint and UpperBound for the upper-bound constraint. Set default values for these constraints using the setDefaultConstraints function (see Setting Default Constraints for Portfolio Weights Using Portfolio Object).

### Setting 'Simple' Bounds Using the PortfolioMAD Function

The properties for bound constraints are set through the PortfolioMAD object. Suppose that you have a balanced fund with stocks that can range from 50% to 75% of your portfolio and bonds that can range from 25% to 50% of your portfolio. The bound constraints for a balanced fund are set with:

lb = [ 0.5; 0.25 ];
ub = [ 0.75; 0.5 ];
p = PortfolioMAD('LowerBound', lb, 'UpperBound', ub, 'BoundType', 'Simple');
disp(p.NumAssets)
disp(p.LowerBound)
disp(p.UpperBound)
2

0.5000
0.2500

0.7500
0.5000

To continue with this example, you must set up a budget constraint. For details, see Working with Budget Constraints Using Portfolio Object.

### Setting 'Simple' Bounds Using the setBounds Function

You can also set the properties for bound constraints using setBounds. Suppose that you have a balanced fund with stocks that can range from 50% to 75% of your portfolio and bonds that can range from 25% to 50% of your portfolio. Given a PortfolioMAD object p, use setBounds to set the bound constraints:

lb = [ 0.5; 0.25 ];
ub = [ 0.75; 0.5 ];
p = setBounds(p, lb, ub,'BoundType', 'Simple');
disp(p.NumAssets)
disp(p.LowerBound)
disp(p.UpperBound)
2

0.5000
0.2500

0.7500
0.5000

### Setting 'Simple' Bounds Using the PortfolioMAD Function or setBounds Function

Both the PortfolioMAD object and setBounds function implement scalar expansion on either the LowerBound or UpperBound properties. If the NumAssets property is already set in the PortfolioMAD object, scalar arguments for either property expand to have the same value across all dimensions. In addition, setBounds lets you specify NumAssets as an optional argument. Suppose that you have a universe of 500 assets and you want to set common bound constraints on all assets in your universe. Specifically, you are a long-only investor and want to hold no more than 5% of your portfolio in any single asset. You can set these bound constraints in any of these equivalent ways:

p = PortfolioMAD('NumAssets', 500, 'LowerBound', 0, 'UpperBound', 0.05,'BoundType', 'Simple');

or

p = setBounds(p, 0, 0.05,'BoundType','Simple');

or