pcalims

Linear inequalities for individual asset allocation

Syntax

[A,b] = pcalims(AssetMin,AssetMax)

[A,b] = pcalims(___,NumAssets)

Description

As an alternative to pcalims, 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] = pcalims(AssetMin,AssetMax) specifies the lower and upper bounds of portfolio allocations in each of NumAssets available asset investments. pcalims specifies the lower and upper bounds of portfolio allocations in each of NASSETS available asset investments.

Note

If pcalims is called with fewer than two output arguments, the function returns A concatenated with b [A,b].

[A,b] = pcalims(___,NumAssets) specifies options using an optional argument in addition to the input arguments in the previous syntax.

Examples

Compute Linear Inequalities for Individual Asset Allocation

Set the minimum weight in every asset to 0 (no short-selling), and set the maximum weight of IBM stock to 0.5 and CSCO to 0.8, while letting the maximum weight in INTC float.

Minimum weight:

• IBM — 0

• INTC — 0

• CSCO — 0

Maximum weight:

• IBM — 0.5

• INTC —

• CSCO — 0.8

AssetMin = 0

AssetMin = 0

AssetMax = [0.5 NaN 0.8]

AssetMax = 1×3

    0.5000       NaN    0.8000

[A,b] = pcalims(AssetMin, AssetMax)

A = 5×3

     1     0     0
     0     0     1
    -1     0     0
     0    -1     0
     0     0    -1

b = 5×1

    0.5000
    0.8000
         0
         0
         0

Portfolio weights of 50% in IBM and 50% in INTC satisfy the constraints

Set the minimum weight in every asset to 0 and the maximum weight to 1.

Minimum weight:

• IBM — 0

• INTC — 0

• CSCO — 0

Maximum weight:

• IBM — 1

• INTC — 1

• CSCO — 1

AssetMin = 0

AssetMin = 0

AssetMax = 1

AssetMax = 1

NumAssets = 3

NumAssets = 3

[A,b] = pcalims(AssetMin, AssetMax, NumAssets)

A = 6×3

     1     0     0
     0     1     0
     0     0     1
    -1     0     0
     0    -1     0
     0     0    -1

b = 6×1

     1
     1
     1
     0
     0
     0

Portfolio weights of 50% in IBM and 50% in INTC satisfy the constraints.

Input Arguments

AssetMin — Minimum allocations in each asset

scalar numeric | vector

Minimum allocations in each asset, specified as a scalar numeric or NASSETS vector. NaN indicates no constraint.

Data Types: double

AssetMax — Maximum allocations in each asset

scalar numeric | vector

Maximum allocations in each asset, specified as a scalar numeric or NASSETS vector. NaN indicates no constraint.

Data Types: double

NumAssets — Number of assets

length of AssetMin or AssetMax (default) | scalar numeric

(Optional) Number of assets, specified as a scalar numeric.

Data Types: double

Output Arguments

A — Lower bound

matrix

Lower bound, returned as a matrix such that A*PortWts' <= b, where PortWts is a 1-by-NASSETS vector of asset allocations.

b — Upper bound

vector

Upper bound, returned as a vector such that A*PortWts' <= b, where PortWts is a 1-by-NASSETS vector of asset allocations.