# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

# pcglims

Linear inequalities for asset group minimum and maximum allocation

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.

## 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.