Documentation

# 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.