Linear inequalities for asset group comparison constraints

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.

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

| Number of groups ( |

| Scalar or |

`[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]`

.

| INTC | XOM | RD |

| North America | North America | Europe |

| 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 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 = 0.2000 -0.8000 0 -0.2000 0.8000 0 b = 0 0

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

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