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 Portfolio 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

Portfolio Create Portfolio object for mean-variance 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
`setTrackingPort`	Set up benchmark portfolio for tracking error constraint
`setTrackingError`	Set up maximum portfolio tracking error constraint
`setMinMaxNumAssets`	Set cardinality constraints on the number of assets invested in a portfolio

Topics

Specifying Constraints

Working with 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 Portfolio Object
'Simple' bound constraints are optional linear constraints that maintain upper and lower bounds on portfolio weights.
Working with Budget Constraints Using Portfolio 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 Portfolio Object
The conditional budget constraint supports the Undertakings for Collective Investment in Transferable Securities (UCITS) directive for a Portfolio object.
Working with Group Constraints Using Portfolio Object
Group constraints are optional linear constraints that group assets together and enforce bounds on the group weights.
Working with Group Ratio Constraints Using Portfolio Object
Group ratio constraints are optional linear constraints that maintain bounds on proportional relationships among groups of assets.
Working with Linear Equality Constraints Using Portfolio Object
Linear equality constraints are optional linear constraints that impose systems of equalities on portfolio weights.
Working with Linear Inequality Constraints Using Portfolio Object
Linear inequality constraints are optional linear constraints that impose systems of inequalities on portfolio weights.
Working with Average Turnover Constraints Using Portfolio 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 Portfolio Object
One-way turnover constraints are optional constraints that enforce upper bounds on net purchases or net sales.
Working with Tracking Error Constraints Using Portfolio Object
Tracking error constraints are optional constraints that measure the risk relative to a portfolio called a tracking portfolio.
Working with 'Conditional' BoundType, MinNumAssets, and MaxNumAssets Constraints Using Portfolio Objects
Using 'Conditional' BoundType, MinNumAssets, and MaxNumAssets constraints with portfolio objects.

Using Constraints

Constraint Specification Using a Portfolio Object
This example computes the efficient frontier of portfolios consisting of three different assets, INTC, XON, and RD, given a list of constraints.
Asset Allocation Case Study
This example shows how to set up a basic asset allocation problem that uses mean-variance portfolio optimization with a Portfolio object to estimate efficient portfolios.
Portfolio Optimization Examples Using Financial Toolbox
Follow a sequence of examples that highlight features of the Portfolio object.
Portfolio Analysis with Turnover Constraints
This example shows how to analyze the characteristics of a portfolio of equities, and then compare them with the efficient frontier.
Leverage in Portfolio Optimization with a Risk-Free Asset
This example shows how to use the setBudget function for the Portfolio class to define the limits on the sum(AssetWeight_i) in risky assets.
Portfolio Optimization with Semicontinuous and Cardinality Constraints
This example shows how to use a Portfolio object to directly handle semicontinuous and cardinality constraints.
Black-Litterman Portfolio Optimization Using Financial Toolbox
This example shows the workflow to implement the Black-Litterman model with the Portfolio class in Financial Toolbox™.
Portfolio Optimization Using Social Performance Measure
Use a Portfolio object to minimize the variance, maximize return, and maximize the average percentage of women on a company's board.
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 Portfolio Objects
The complete specification of a portfolio optimization problem is the set of feasible portfolios, which is called a portfolio set.
Portfolio Object Workflow
Portfolio object workflow for creating and modeling a mean-variance portfolio.
Setting Up a Tracking Portfolio
The Portfolio object property TrackingPort lets you identify a tracking 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.

Related Information

Getting Started with Portfolio Optimization (4 min 13 sec)