## Working with Group Ratio Constraints Using PortfolioCVaR Object

Group ratio constraints are optional linear constraints that maintain bounds on proportional relationships among groups of assets (see Group Ratio Constraints). Although the constraints are implemented as general constraints, the usual convention is to specify a pair of group matrices that identify membership of each asset within specific groups with Boolean indicators (either `true` or `false` or with `1` or `0`) for each element in each of the group matrices. The goal is to ensure that the ratio of a base group compared to a comparison group fall within specified bounds. Group ratio constraints have properties:

• `GroupA` for the base membership matrix

• `GroupB` for the comparison membership matrix

• `LowerRatio` for the lower-bound constraint on the ratio of groups

• `UpperRatio` for the upper-bound constraint on the ratio of groups

### Setting Group Ratio Constraints Using the ` PortfolioCVaR` Function

The properties for group ratio constraints are set using `PortfolioCVaR` object. For example, assume that you want the ratio of financial to nonfinancial companies in your portfolios to never go above 50%. Suppose that you have six assets with three financial companies (assets 1–3) and three nonfinancial companies (assets 4–6). To set group ratio constraints:

```GA = [ 1 1 1 0 0 0 ]; % financial companies GB = [ 0 0 0 1 1 1 ]; % nonfinancial companies p = PortfolioCVaR('GroupA', GA, 'GroupB', GB, 'UpperRatio', 0.5); disp(p.NumAssets) disp(p.GroupA) disp(p.GroupB) disp(p.UpperRatio)```
```6 1 1 1 0 0 0 0 0 0 1 1 1 0.5000```

Group matrices `GA` and `GB` in this example can be logical matrices with `true` and `false` elements that yield the same result:

```GA = [ true true true false false false ]; % financial companies GB = [ false false false true true true ]; % nonfinancial companies p = PortfolioCVaR('GroupA', GA, 'GroupB', GB, 'UpperRatio', 0.5); disp(p.NumAssets) disp(p.GroupA) disp(p.GroupB) disp(p.UpperRatio)```
```6 1 1 1 0 0 0 0 0 0 1 1 1 0.5000```

### Setting Group Ratio Constraints Using the `setGroupRatio` and `addGroupRatio` Functions

You can also set the properties for group ratio constraints using `setGroupRatio`. For example, assume that you want the ratio of financial to nonfinancial companies in your portfolios to never go above 50%. Suppose that you have six assets with three financial companies (assets 1–3) and three nonfinancial companies (assets 4–6). Given a `PortfolioCVaR` object `p`, use `setGroupRatio` to set the group constraints:

```GA = [ true true true false false false ]; % financial companies GB = [ false false false true true true ]; % nonfinancial companies p = PortfolioCVaR; p = setGroupRatio(p, GA, GB, [], 0.5); disp(p.NumAssets) disp(p.GroupA) disp(p.GroupB) disp(p.UpperRatio)```
```6 1 1 1 0 0 0 0 0 0 1 1 1 0.5000```
In this example, you would set the `LowerRatio` property to be empty (`[]`).

Suppose that you want to add another group ratio constraint to ensure that the weights in odd-numbered assets constitute at least 20% of the weights in nonfinancial assets your portfolio. You can set up augmented group ratio matrices and introduce infinite bounds for unconstrained group ratio bounds, or you can use the `addGroupRatio` function to build up group ratio constraints. For this example, create another group matrix for the second group constraint:

```p = PortfolioCVaR; GA = [ true true true false false false ]; % financial companies GB = [ false false false true true true ]; % nonfinancial companies p = setGroupRatio(p, GA, GB, [], 0.5); GA = [ true false true false true false ]; % odd-numbered companies GB = [ false false false true true true ]; % nonfinancial companies p = addGroupRatio(p, GA, GB, 0.2); disp(p.NumAssets) disp(p.GroupA) disp(p.GroupB) disp(p.LowerRatio) disp(p.UpperRatio)```
``` 6 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 -Inf 0.2000 0.5000 Inf```
Notice that `addGroupRatio` determines which bounds are unbounded so you only need to focus on the constraints you want to set.

The `PortfolioCVaR` object, `setGroupRatio`, and `addGroupRatio` implement scalar expansion on either the `LowerRatio` or `UpperRatio` properties based on the dimension of the group matrices in `GroupA` and `GroupB` properties.