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.