pcgcomp

Linear inequalities for asset group comparison constraints

Description

As an alternative to pcgcomp, 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.

example

[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.

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

Examples

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Use the following assets and groupings.  Make the North American energy sector compose exactly 20% of the North American investment.

%          INTC  XOM  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 = 2×3

0.2000   -0.8000         0
-0.2000    0.8000         0

b = 2×1

0
0

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

Input Arguments

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Grouping A, specified as a number of groups (NGROUPS) by number of assets (NASSETS) vector of groups to compare. 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

Minimum ratios, specified as a scalar or NGROUPS-long vectors of minimum ratios of allocations in GroupA to allocations in GroupB. NaN indicates no constraint between the two groups. Scalar bounds are applied to all group pairs. The total number of assets allocated to GroupA divided by the total number of assets allocated to GroupB is >= AtoBmin and <= AtoBmax.

Data Types: double

Maximum ratios, specified as a scalar or NGROUPS-long vectors of maximum ratios of allocations in GroupA to allocations in GroupB. NaN indicates no constraint between the two groups. Scalar bounds are applied to all group pairs. The total number of assets allocated to GroupA divided by the total number of assets allocated to GroupB is >= AtoBmin and <= AtoBmax.

Data Types: double

Grouping B, specified as a number of groups (NGROUPS) by number of assets (NASSETS) vector of groups to compare. 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

Output Arguments

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

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

Introduced before R2006a