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# setEquality

Set up linear equality constraints for portfolio weights

Use the `setEquality` function with a `Portfolio`, `PortfolioCVaR`, or `PortfolioMAD` object to set up linear equality constraints for portfolio weights for portfolio objects.

For details on the respective workflows when using these different objects, see Portfolio Object Workflow, PortfolioCVaR Object Workflow, and PortfolioMAD Object Workflow.

## Syntax

``obj= setEquality(obj,AEquality,bEquality)``

## Description

example

````obj= setEquality(obj,AEquality,bEquality)` sets up linear equality constraints for portfolio weights for portfolio objects.Given linear equality constraint matrix `AEquality` and vector `bEquality`, every weight in a portfolio `Port` must satisfy the following: AEquality * Port = bEquality ```

## Examples

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Suppose you have a portfolio of five assets, and you want to ensure that the first three assets are 50% of your portfolio. Given a Portfolio object `p`, set the linear equality constraints with the following.

```A = [ 1 1 1 0 0 ]; b = 0.5; p = Portfolio; p = setEquality(p, A, b); disp(p.NumAssets);```
``` 5 ```
`disp(p.AEquality);`
``` 1 1 1 0 0 ```
`disp(p.bEquality);`
``` 0.5000 ```

Suppose you have a portfolio of five assets and you want to ensure that the first three assets are 50% of your portfolio. Given a PortfolioCVaR object `p`, set the linear equality constraints and obtain the values for `AEquality` and `bEquality`:

```A = [ 1 1 1 0 0 ]; b = 0.5; p = PortfolioCVaR; p = setEquality(p, A, b); disp(p.NumAssets);```
``` 5 ```
`disp(p.AEquality);`
``` 1 1 1 0 0 ```
`disp(p.bEquality);`
``` 0.5000 ```

Suppose you have a portfolio of five assets and you want to ensure that the first three assets are 50% of your portfolio. Given a PortfolioMAD object `p`, set the linear equality constraints and obtain the values for `AEquality` and `bEquality`:

```A = [ 1 1 1 0 0 ]; b = 0.5; p = PortfolioMAD; p = setEquality(p, A, b); [AEquality, bEquality] = getEquality(p)```
```AEquality = 1 1 1 0 0 ```
```bEquality = 0.5000 ```

## Input Arguments

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Object for portfolio, specified using `Portfolio`, `PortfolioCVaR`, or `PortfolioMAD` object. For more information on creating a portfolio object, see

Matrix to form linear equality constraints, returned as a matrix for a `Portfolio`, `PortfolioCVaR`, or `PortfolioMAD` input object (`obj`).

### Note

An error results if `AEquality` is empty and `bEquality` is nonempty.

Data Types: `double`

Vector to form linear equality constraints, returned as a vector for a `Portfolio`, `PortfolioCVaR`, or `PortfolioMAD` input object (`obj`).

### Note

An error results if `AEquality` is nonempty and `bEquality` is empty.

Data Types: `double`

## Output Arguments

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Updated portfolio object, returned as a `Portfolio`, `PortfolioCVaR`, or `PortfolioMAD` object. For more information on creating a portfolio object, see

## Tips

• You can also use dot notation to set up linear equality constraints for portfolio weights.

`obj = obj.setEquality(AEquality, bEquality);`

• Linear equality constraints can be removed from a portfolio object by entering `[]` for each property you want to remove.