The `Portfolio`

object implements mean-variance portfolio optimization. Every
property and function of the `Portfolio`

object is public, although
some properties and functions are hidden. See `Portfolio`

for the properties and
functions of the `Portfolio`

object. The
`Portfolio`

object is a value object where every instance of
the object is a distinct version of the object. Since the
`Portfolio`

object is also a MATLAB^{®} object, it inherits the default functions associated with MATLAB objects.

The `Portfolio`

object and its functions are an interface for mean-variance
portfolio optimization. So, almost everything you do with the
`Portfolio`

object can be done using the associated functions.
The basic workflow is:

Design your portfolio problem.

Use

`Portfolio`

to create the`Portfolio`

object or use the various`set`

functions to set up your portfolio problem.Use estimate functions to solve your portfolio problem.

In addition, functions are available to help you view intermediate
results and to diagnose your computations. Since MATLAB features are part of a `Portfolio`

object, you can
save and load objects from your workspace and create and manipulate arrays of
objects. After settling on a problem, which, in the case of mean-variance portfolio
optimization, means that you have either data or moments for asset returns and a
collection of constraints on your portfolios, use `Portfolio`

to set the properties for
the `Portfolio`

object. `Portfolio`

lets you create an object
from scratch or update an existing object. Since the `Portfolio`

object is a value object, it is easy to create a basic object, then use functions to
build upon the basic object to create new versions of the basic object. This is
useful to compare a basic problem with alternatives derived from the basic problem.
For details, see Creating the Portfolio Object.

You can set properties of a `Portfolio`

object using either `Portfolio`

or various
`set`

functions.

Although you can also set properties directly, it is not recommended since error-checking is not performed when you set a property directly.

The `Portfolio`

object supports setting
properties with name-value pair arguments such that each argument name is a property
and each value is the value to assign to that property. For example, to set the
`AssetMean`

and `AssetCovar`

properties in an
existing `Portfolio`

object `p`

with the values
`m`

and `C`

, use the
syntax:

p = Portfolio(p, 'AssetMean', m, 'AssetCovar', C);

In addition to `Portfolio`

, which lets you set
individual properties one at a time, groups of properties are set in a
`Portfolio`

object with various “set” and
“add” functions. For example, to set up an average turnover
constraint, use the `setTurnover`

function to specify the
bound on portfolio average turnover and the initial portfolio. To get individual
properties from a Portfolio object, obtain properties directly or use an assortment
of “get” functions that obtain groups of properties from a
`Portfolio`

object. The `Portfolio`

object and the
`set`

functions have several useful features:

`Portfolio`

and the`set`

functions try to determine the dimensions of your problem with either explicit or implicit inputs.`Portfolio`

and the`set`

functions try to resolve ambiguities with default choices.`Portfolio`

and the`set`

functions perform scalar expansion on arrays when possible.The associated

`Portfolio`

object functions try to diagnose and warn about problems.

The `Portfolio`

object uses the default display functions provided by
MATLAB, where `display`

and `disp`

display
a Portfolio object and its properties with or without the object variable
name.

Save and load `Portfolio`

objects using the MATLAB
`save`

and `load`

commands.

Estimating efficient portfolios and efficient frontiers is the primary purpose of the
portfolio optimization tools. An*efficient portfolio* is the
portfolios that satisfy the criteria of minimum risk for a given level of return and
maximum return for a given level of risk. A collection of “estimate”
and “plot” functions provide ways to explore the efficient frontier.
The “estimate” functions obtain either efficient portfolios or risk
and return proxies to form efficient frontiers. At the portfolio level, a collection
of functions estimates efficient portfolios on the efficient frontier with functions
to obtain efficient portfolios:

At the endpoints of the efficient frontier

That attains targeted values for return proxies

That attains targeted values for risk proxies

Along the entire efficient frontier

These functions also provide purchases and sales needed to shift from an initial or current portfolio to each efficient portfolio. At the efficient frontier level, a collection of functions plot the efficient frontier and estimate either risk or return proxies for efficient portfolios on the efficient frontier. You can use the resultant efficient portfolios or risk and return proxies in subsequent analyses.

Although all functions associated with a `Portfolio`

object are designed to
work on a scalar `Portfolio`

object, the array capabilities of
MATLAB enable you to set up and work with arrays of
`Portfolio`

objects. The easiest way to do this is with the
`repmat`

function. For example, to
create a 3-by-2 array of `Portfolio`

objects:

p = repmat(Portfolio, 3, 2); disp(p)

`Portfolio`

objects, you can work on
individual `Portfolio`

objects in the array by indexing. For
example:p(i,j) = Portfolio(p(i,j), ... );

`Portfolio`

for the
(`i`

,`j`

) element of a matrix of
`Portfolio`

objects in the variable
`p`

.If you set up an array of `Portfolio`

objects, you can access properties of a
particular `Portfolio`

object in the array by indexing so that you
can set the lower and upper bounds `lb`

and `ub`

for the (`i`

,`j`

,`k`

) element of
a 3-D array of `Portfolio`

objects
with

p(i,j,k) = setBounds(p(i,j,k),lb, ub);

[lb, ub] = getBounds(p(i,j,k));

`Portfolio`

object functions work on only one `Portfolio`

object at a
time.You can subclass the `Portfolio`

object to override existing functions or to
add new properties or functions. To do so, create a derived class from the `Portfolio`

class. This gives you all
the properties and functions of the `Portfolio`

class along with
any new features that you choose to add to your subclassed object. The
`Portfolio`

class is derived from an abstract class called
`AbstractPortfolio`

. Because of this, you can also create a
derived class from `AbstractPortfolio`

that implements an entirely
different form of portfolio optimization using properties and functions of the
`AbstractPortfolio`

class.

The portfolio optimization tools follow these conventions regarding the representation of different quantities associated with portfolio optimization:

Asset returns or prices are in matrix form with samples for a given asset going down the rows and assets going across the columns. In the case of prices, the earliest dates must be at the top of the matrix, with increasing dates going down.

The mean and covariance of asset returns are stored in a vector and a matrix and the tools have no requirement that the mean must be either a column or row vector.

Portfolios are in vector or matrix form with weights for a given portfolio going down the rows and distinct portfolios going across the columns.

Constraints on portfolios are formed in such a way that a portfolio is a column vector.

Portfolio risks and returns are either scalars or column vectors (for multiple portfolio risks and returns).

- Creating the Portfolio Object
- Working with Portfolio Constraints Using Defaults
- Asset Allocation Case Study
- Portfolio Optimization Examples
- Portfolio Optimization with Semicontinuous and Cardinality Constraints
- Black-Litterman Portfolio Optimization
- Portfolio Optimization Using Factor Models