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pcglims - Linear inequalities for asset group minimum and maximum allocation

Syntax

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

Arguments

Groups	Number of groups (NGROUPS) by number of assets (NASSETS) specification 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.
GroupMin GroupMax	Scalar or NGROUPS-long vectors of minimum and maximum combined allocations in each group. NaN indicates no constraint. Scalar bounds are applied to all groups.

Description

[A,b] = pcglims(Groups, GroupMin, GroupMax) specifies minimum and maximum allocations to groups of assets. An arbitrary number of groups, NGROUPS, comprising subsets of NASSETS investments, is allowed.

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

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

Examples

Asset	INTC	XOM	RD
Region	North America	North America	Europe
Sector	Technology	Energy	Energy

Group	Min. Exposure	Max. Exposure
North America	0.30	0.75
Europe	0.10	0.55
Technology	0.20	0.50
Energy	0.50	0.50

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 =

    -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 =

   -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.

See Also

pcalims, pcgcomp, pcpval, portcons, portopt

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