pcgcomp (Financial Toolbox)

Linear inequalities for asset group comparison constraints.

Syntax

[A,b] = pcgcomp(GroupA, AtoBmin, AtoBmax, GroupB)

Arguments


`GroupA GroupB`	Number of groups `(NGROUPS)` by number of assets (`NASSETS)` specifications of groups to compare. Each row specifies which assets are in a group: `Group(i,j) = 1` if group i contains asset `j`; otherwise, `Group(i,j) = 0`.
`AtoBmin AtoBmax`	Scalar or `NGROUPS`-long vectors of minimum and maximum ratios of allocations in group `A` to allocations in group `B`. `NaN` indicates no constraint between the two groups. Scalar bounds are applied to all group pairs. For each of the group pairs: `GroupA` total `>= GroupB` total `* AtoBmin` `GroupA` total `<= GroupB` total `* AtoBmax`

Description

[A,b] = pcgcomp(GroupA, AtoBmin, AtoBmax, GroupB)

Specifies that the ratio of allocations in one group to allocations in another group is at least AtoBmin to 1 and at most AtoBmax to 1. Comparisons can be made between an arbitrary number of group pairs NGROUPS comprising subsets of NASSETS available investments.

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

Example


Asset	INTC	XON	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	0.20	0.80

Make the North American energy sector compose exactly 20% of the North American investment.

           INTC  XON  RD       
GroupA = [   0    1   0  ];  % North American Energy
GroupB = [   1    1   0  ];  % North America
AtoBmin = 0.20;
AtoBmax = 0.20;
[A,b] = pcgcomp(GroupA, AtoBmin, AtoBmax, GroupB)
A =

    0.2000    -0.8000     0
   -0.2000     0.8000     0
b =

   0
   0

Portfolio weights of 40% for INTC, 10% for XON, and 50% for RD satisfy the constraints.