Specify Portfolio Constraints

Define constraints for portfolio assets such as linear equality and inequality, bound, budget, group, group ratio, and turnover constraints

Working with a PortfolioMAD object, use functions to define the constraints for portfolio assets such as linear equality and inequality, bound, budget, group, group ratio, and turnover constraints.

Objects

PortfolioMAD Create PortfolioMAD object for mean-absolute deviation portfolio optimization and analysis

Functions

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Add Portfolio Parameters

`addEquality`	Add linear equality constraints for portfolio weights to existing constraints
`addGroupRatio`	Add group ratio constraints for portfolio weights to existing group ratio constraints
`addGroups`	Add group constraints for portfolio weights to existing group constraints
`addInequality`	Add linear inequality constraints for portfolio weights to existing constraints

Display Portfolio Parameters

`getBounds`	Obtain bounds for portfolio weights from portfolio object
`getBudget`	Obtain budget constraint bounds from portfolio object
`getCosts`	Obtain buy and sell transaction costs from portfolio object
`getEquality`	Obtain equality constraint arrays from portfolio object
`getGroupRatio`	Obtain group ratio constraint arrays from portfolio object
`getGroups`	Obtain group constraint arrays from portfolio object
`getInequality`	Obtain inequality constraint arrays from portfolio object
`getOneWayTurnover`	Obtain one-way turnover constraints from portfolio object

Set Portfolio Parameters

`setGroups`	Set up group constraints for portfolio weights
`setInequality`	Set up linear inequality constraints for portfolio weights
`setBounds`	Set up bounds for portfolio weights for portfolio
`setBudget`	Set up budget constraints for portfolio
`setConditionalBudget`	Set up conditional budget constraints for portfolio (Since R2024b)
`setCosts`	Set up proportional transaction costs for portfolio
`setDefaultConstraints`	Set up portfolio constraints with nonnegative weights that sum to 1
`setEquality`	Set up linear equality constraints for portfolio weights
`setGroupRatio`	Set up group ratio constraints for portfolio weights
`setInitPort`	Set up initial or current portfolio
`setOneWayTurnover`	Set up one-way portfolio turnover constraints
`setTurnover`	Set up maximum portfolio turnover constraint
`setMinMaxNumAssets`	Set cardinality constraints on the number of assets invested in a portfolio

Topics

Portfolio Optimizations

Working with MAD Portfolio Constraints Using Defaults
The most basic or “default” portfolio set requires portfolio weights to be nonnegative and to sum to 1.
Working with 'Simple' Bound Constraints Using PortfolioMAD Object
'Simple' bound constraints are optional linear constraints that maintain upper and lower bounds on portfolio weights.
Working with Budget Constraints Using PortfolioMAD Object
The budget constraint is an optional linear constraint that maintains upper and lower bounds on the sum of portfolio weights.
Working with Conditional Budget Constraints Using PortfolioMAD Object
The conditional budget constraint supports the Undertakings for Collective Investment in Transferable Securities (UCITS) directive for a PortfolioMAD object.
Working with Group Constraints Using PortfolioMAD Object
Group constraints are optional linear constraints that group assets together and enforce bounds on the group weights.
Working with Group Ratio Constraints Using PortfolioMAD Object
Group ratio constraints are optional linear constraints that maintain bounds on proportional relationships among groups of assets.
Working with Linear Equality Constraints Using PortfolioMAD Object
Linear equality constraints are optional linear constraints that impose systems of equalities on portfolio weights.
Working with Linear Inequality Constraints Using PortfolioMAD Object
Linear inequality constraints are optional linear constraints that impose systems of inequalities on portfolio weights.
Working with Average Turnover Constraints Using PortfolioMAD Object
The turnover constraint is an optional linear absolute value constraint that enforces an upper bound on the average of purchases and sales.
Working with One-Way Turnover Constraints Using PortfolioMAD Object
One-way turnover constraints are optional constraints that enforce upper bounds on net purchases or net sales.
Working with 'Conditional' BoundType, MinNumAssets, and MaxNumAssets Constraints Using PortfolioMAD Objects
Using 'Conditional' BoundType, MinNumAssets, and MaxNumAssets constraints with PortfolioMAD objects.
Adding Constraints to Satisfy UCITS Directive
This example shows how to set up and solve a portfolio optimization problem that satisfies the Undertakings for Collective Investment in Transferable Securities (UCITS) Directive.

Portfolio Theory

Portfolio Optimization Theory
Portfolios are points from a feasible set of assets that constitute an asset universe.
Supported Constraints for Portfolio Optimization Using PortfolioMAD Object
The complete specification of a portfolio optimization problem is the set of feasible portfolios, which is called a portfolio set.
Default Portfolio Problem
The default portfolio optimization problem has a risk and return proxy associated with a given problem, and a portfolio set that specifies portfolio weights to be nonnegative and to sum to 1.
PortfolioMAD Object Workflow
PortfolioMAD object workflow for creating and modeling a mean-absolute deviation (MAD) portfolio.
When to Use Portfolio Objects Over Optimization Toolbox
The three cases for using Portfolio, PortfolioCVaR, PortfolioMAD object are: always use, preferred use, and use Optimization Toolbox.