Group constraints are optional linear constraints that group assets together and
enforce bounds on the group weights (see Group Constraints). Although the constraints are implemented as general
constraints, the usual convention is to form a group matrix that identifies membership
of each asset within a specific group with Boolean indicators (either
true or false or with 1 or
0) for each element in the group matrix. Group constraints have
properties GroupMatrix for the group membership matrix,
LowerGroup for the lower-bound constraint on groups, and
UpperGroup for the upper-bound constraint on groups.
PortfolioCVaR FunctionThe properties for group constraints are set through the PortfolioCVaR object. Suppose that
you have a portfolio of five assets and want to ensure that the first three assets
constitute no more than 30% of your portfolio, then you can set group
constraints:
G = [ 1 1 1 0 0 ]; p = PortfolioCVaR('GroupMatrix', G, 'UpperGroup', 0.3); disp(p.NumAssets) disp(p.GroupMatrix) disp(p.UpperGroup)
5 1 1 1 0 0 0.3000
The group matrix G can also be a logical matrix so that the
following code achieves the same
result.
G = [ true true true false false ]; p = PortfolioCVaR('GroupMatrix', G, 'UpperGroup', 0.3); disp(p.NumAssets) disp(p.GroupMatrix) disp(p.UpperGroup)
5 1 1 1 0 0 0.3000
setGroups and addGroups FunctionsYou can also set the properties for group constraints using setGroups. Suppose that you have a
portfolio of five assets and want to ensure that the first three assets constitute
no more than 30% of your portfolio. Given a PortfolioCVaR object
p, use setGroups to set the group
constraints:
G = [ true true true false false ]; p = PortfolioCVaR; p = setGroups(p, G, [], 0.3); disp(p.NumAssets) disp(p.GroupMatrix) disp(p.UpperGroup)
5 1 1 1 0 0 0.3000
In this example, you would set the LowerGroup property to be
empty ([]).
Suppose that you want to add another group constraint to make odd-numbered assets
constitute at least 20% of your portfolio. Set up an augmented group matrix and
introduce infinite bounds for unconstrained group bounds or use the addGroups function to build up
group constraints. For this example, create another group matrix for the second
group
constraint:
p = PortfolioCVaR; G = [ true true true false false ]; % group matrix for first group constraint p = setGroups(p, G, [], 0.3); G = [ true false true false true ]; % group matrix for second group constraint p = addGroups(p, G, 0.2); disp(p.NumAssets) disp(p.GroupMatrix) disp(p.LowerGroup) disp(p.UpperGroup)
5 1 1 1 0 0 1 0 1 0 1 -Inf 0.2000 0.3000 Inf
addGroups determines which bounds
are unbounded so you only need to focus on the constraints that you want to
set.The PortfolioCVaR object, setGroups, and addGroups implement scalar
expansion on either the LowerGroup or
UpperGroup properties based on the dimension of the group
matrix in the property GroupMatrix. Suppose that you have a
universe of 30 assets with 6 asset classes such that assets 1–5, assets 6–12, assets
13–18, assets 19–22, assets 23–27, and assets 28–30 constitute each of your asset
classes and you want each asset class to fall from 0% to 25% of your portfolio. Let
the following group matrix define your groups and scalar expansion define the common
bounds on each group:
p = PortfolioCVaR; G = blkdiag(true(1,5), true(1,7), true(1,6), true(1,4), true(1,5), true(1,3)); p = setGroups(p, G, 0, 0.25); disp(p.NumAssets) disp(p.GroupMatrix) disp(p.LowerGroup) disp(p.UpperGroup)
30
Columns 1 through 16
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Columns 17 through 30
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 1 1 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 1 1 1 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 1 1
0
0
0
0
0
0
0.2500
0.2500
0.2500
0.2500
0.2500
0.2500PortfolioCVaR | setBounds | setBudget | setDefaultConstraints | setEquality | setGroupRatio | setGroups | setInequality | setOneWayTurnover | setTurnover