pcglims

Linear inequalities for asset group minimum and maximum allocation

Syntax

[A,b] = pcglims(Groups,GroupMin,GroupMax)

Description

As an alternative to pcglims, use the Portfolio object (Portfolio) for mean-variance portfolio optimization. This object supports gross or net portfolio returns as the return proxy, the variance of portfolio returns as the risk proxy, and a portfolio set that is any combination of the specified constraints to form a portfolio set. For information on the workflow when using Portfolio objects, see Portfolio Object Workflow.

[A,b] = pcglims(Groups,GroupMin,GroupMax) specifies minimum and maximum allocations to groups of assets. Bounds can be specified for an arbitrary number of groups NGROUPS,made up as subsets of the NASSETS investments.

If pcglims is called with fewer than two output arguments, the function returns A concatenated with b [A,b].

Examples

Linear Inequalities for Asset Group Minimum and Maximum Allocation

Use the following assets and groupings.

Set the minimum and maximum investment in various groups.

%          INTC  XOM  RD       
Groups = [   1    1   0  ;  % North America
             0    0   1  ;  % Europe
             1    0   0  ;  % Technology
             0    1   1  ]; % Energy

GroupMin = [0.30
            0.10
            0.20
            0.50];

GroupMax = [0.75
            0.55
            0.50
            0.50];

[A,b] = pcglims(Groups, GroupMin, GroupMax)

A = 8×3

    -1    -1     0
     0     0    -1
    -1     0     0
     0    -1    -1
     1     1     0
     0     0     1
     1     0     0
     0     1     1

b = 8×1

   -0.3000
   -0.1000
   -0.2000
   -0.5000
    0.7500
    0.5500
    0.5000
    0.5000

Portfolio weights of 50% in INTC, 25% in XOM, and 25% in RD satisfy the constraints.

Input Arguments

Groups — Grouping

vector

Grouping, specified as a number of groups (NGROUPS) by number of assets (NASSETS) vector of which assets belong to which group. Each row specifies a group. For a specific group, Group(i,j) = 1 if the group contains asset j; otherwise, Group(i,j) = 0.

Data Types: double

GroupMin — Minimum allocations

scalar | vector

Minimum allocations, specified as a scalar or NGROUPS-long vectors of minimum combined allocations in each group. NaN indicates no constraint. Scalar bounds are applied to all groups.

Data Types: double

GroupMax — Maximum allocations

scalar | vector

Maximum allocations, specified as a scalar or NGROUPS-long vectors maximum combined allocations in each group. NaN indicates no constraint. Scalar bounds are applied to all groups.

Data Types: double

Output Arguments

A — Lower bound

matrix

Lower bound, returned as a matrix such that A*PortWts' <= b, where PortWts is a 1-by-NASSETS vector of asset allocations.

b — Upper bound

vector

Upper bound, returned as a vector such that A*PortWts' <= b, where PortWts is a 1-by-NASSETS vector of asset allocations.

Version History

Introduced before R2006a