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

`PortfolioMAD`

FunctionThe properties for group ratio constraints are set using `PortfolioMAD`

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 = PortfolioMAD('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 = PortfolioMAD('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
`PortfolioMAD`

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 = PortfolioMAD; 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 = PortfolioMAD; 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`PortfolioMAD`

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.

`PortfolioMAD`

| `setBounds`

| `setBudget`

| `setDefaultConstraints`

| `setEquality`

| `setGroupRatio`

| `setGroups`

| `setInequality`

| `setOneWayTurnover`

| `setTurnover`

- Setting Default Constraints for Portfolio Weights Using PortfolioMAD Object
- Creating the PortfolioMAD Object
- Validate the MAD Portfolio Problem
- Estimate Efficient Portfolios Along the Entire Frontier for PortfolioMAD Object
- Estimate Efficient Frontiers for PortfolioMAD Object
- Asset Returns and Scenarios Using PortfolioMAD Object