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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

` PortfolioCVaR`

FunctionThe 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

`setGroupRatio`

and `addGroupRatio`

FunctionsYou 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

`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

`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.

`PortfolioCVaR`

| `setBounds`

| `setBudget`

| `setDefaultConstraints`

| `setEquality`

| `setGroupRatio`

| `setGroups`

| `setInequality`

| `setOneWayTurnover`

| `setTurnover`

- Creating the PortfolioCVaR Object
- Working with CVaR Portfolio Constraints Using Defaults
- Validate the CVaR Portfolio Problem
- Estimate Efficient Portfolios for Entire Frontier for PortfolioCVaR Object
- Estimate Efficient Frontiers for PortfolioCVaR Object
- Asset Returns and Scenarios Using PortfolioCVaR Object