# Specify Portfolio Constraints

Define 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

## Examples and How To

### 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 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**

The following sequence of examples highlights features of the`Portfolio`

object in the Financial Toolbox™.**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**

This example shows the workflow to implement the Black-Litterman model with the`Portfolio`

class.**Portfolio Optimization Using a Social Performance Measure**

This example shows how to use a`Portfolio`

object for portfolio optimization that includes a social performance measure for the percentage of women on a company's board.**Diversification of Portfolios**

This example shows three techniques of asset diversification in a portfolio.

## Concepts

**Portfolio Set for 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.