# Documentation

### This is machine translation

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

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

# active2abs

Convert constraints from active to absolute format

## Syntax

```AbsConSet = active2abs(ActiveConSet,Index)
```

## Arguments

 `ActiveConSet` Portfolio linear inequality constraint matrix expressed in active weight format. `ActiveConSet` is formatted as `[A b]` such that `A*w <= b`, where `A` is a number of constraints (`NCONSTRAINTS`) by number of assets (`NASSETS`) weight coefficient matrix, and `b` and `w` are column vectors of length `NASSETS`. The value `w` represents a vector of active asset weights (relative to the index portfolio) whose elements sum to 0. See the output `ConSet` from `portcons` for additional details about constraint matrices. `Index` `NASSETS`-by-`1` vector of index portfolio weights. The sum of the index weights must equal the total portfolio value (for example, a standard portfolio optimization imposes a sum-to-one budget constraint).

## Description

`AbsConSet = active2abs(ActiveConSet,Index)` transforms a constraint matrix to an equivalent matrix expressed in absolute weight format. The transformation equation is

`$A{w}_{active}=A\left({w}_{absolute}-{w}_{index}\right)\le {b}_{active}.$`

Therefore

`$A{w}_{absolute}\le {b}_{active}+A{w}_{index}={b}_{absolute}.$`

The initial constraint matrix consists of `NCONSTRAINTS` portfolio linear inequality constraints expressed in active weight format (relative to the index portfolio). The index portfolio vector contains `NASSETS` assets.

`AbsConSet` is the transformed portfolio linear inequality constraint matrix expressed in absolute weight format, also of the form `[A b]` such that `A*w <= b`. The value `w` represents a vector of active asset weights (relative to the index portfolio) whose elements sum to the total portfolio value.