# Documentation

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# pcalims

Linear inequalities for individual asset allocation

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.

## Syntax

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

## Arguments

 `AssetMin` Scalar or `NASSETS` vector of minimum allocations in each asset. `NaN` indicates no constraint. `AssetMax` Scalar or `NASSETS` vector of maximum allocations in each asset. `NaN` indicates no constraint. `NumAssets` (Optional) Number of assets. Default = length of `AssetMin` or `AssetMax`.

## Description

`[A,b] = pcalims(AssetMin,AssetMax,NumAssets)` specifies the lower and upper bounds of portfolio allocations in each of `NumAssets` available asset investments.

`A` is a matrix and `b` is a vector such that `A*PortWts' <= b`, where `PortWts` is a `1`-by-`NASSETS` vector of asset allocations.

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

## Examples

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.

Asset

IBM

INTC

CSCO

Minimum Weight

0

0

0

Maximum Weight

0.5

0.8

```AssetMin = 0 AssetMax = [0.5 NaN 0.8] [A,b] = pcalims(AssetMin, AssetMax)```
```A = 1 0 0 0 0 1 -1 0 0 0 -1 0 0 0 -1 b = 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.

Asset

IBM

INTC

CSCO

Minimum Weight

0

0

0

Maximum Weight

1

1

1

```AssetMin = 0 AssetMax = 1 NumAssets = 3 [A,b] = pcalims(AssetMin, AssetMax, NumAssets)```
```A = 1 0 0 0 1 0 0 0 1 -1 0 0 0 -1 0 0 0 -1 b = 1 1 1 0 0 0 ```

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