active2abs

Convert constraints from active to absolute format

Syntax

AbsConSet = active2abs(ActiveConSet,Index)

Description

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

$A w_{a c t i v e} = A (w_{a b s o l u t e} - w_{i n d e x}) \leq b_{a c t i v e} .$

Therefore

$A w_{a b s o l u t e} \leq b_{a c t i v e} + A w_{i n d e x} = b_{a b s o l u t e} .$

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.

Input Arguments

collapse all

`ActiveConSet` — Portfolio linear inequality constraint matrix expressed in active weight format
matrix

Portfolio linear inequality constraint matrix expressed in active weight format, 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.

Data Types: double

`Index` — Index of portfolio weights
vector

Index of portfolio weights, specified as an ASSETS-by-1 vector. The sum of the index weights must equal the total portfolio value. For example, a standard portfolio optimization imposes a sum to 1 budget constraint.

Data Types: double

Output Arguments

collapse all

`AbsConSet` — Transformed portfolio linear inequality constraint
matrix

Transformed portfolio linear inequality constraint, returned as a matrix and 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.