The PortfolioCVaR object implements conditional value-at-risk
(CVaR) portfolio optimization. Every property and function of the
PortfolioCVaR object is public, although some properties and
functions are hidden. SeePortfolioCVaR for the properties and
functions of a PortfolioCVaR object. The
PortfolioCVaR object is a value object where every instance
of the object is a distinct version of the object. Since the
PortfolioCVaR object is also a MATLAB® object, it inherits the default functions associated with MATLAB objects.
The PortfolioCVaR object and its functions are an interface for
conditional value-at-risk portfolio optimization. So, almost everything you do with
the PortfolioCVaR object can be done using the functions. The
basic workflow is:
Design your portfolio problem.
Use PortfolioCVaR to create
the PortfolioCVaR 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 PortfolioCVaR 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 CVaR portfolio
optimization, means that you have either scenarios, data, or moments for asset
returns, a probability level, and a collection of constraints on your portfolios,
use PortfolioCVaR to set the properties
for the PortfolioCVaR object.
PortfolioCVaR lets you create an
object from scratch or update an existing object. Since the
PortfolioCVaR 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 PortfolioCVaR Object.
You can set properties of a PortfolioCVaR object using either
the PortfolioCVaR object or various
set functions.
Note
Although you can also set properties directly, it is not recommended since error-checking is not performed when you set a property directly.
The PortfolioCVaR 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
LowerBound, Budget, and
ProbabilityLevel properties in an existing
PortfolioCVaR object p, use the
syntax:
p = PortfolioCVaR(p,'LowerBound', 0, 'Budget', 'ProbabilityLevel', 0.95);
In addition to the PortfolioCVaR object, which lets you
set individual properties one at a time, groups of properties are set in a
PortfolioCVaR 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 turnover and the initial portfolio. To get individual properties
from a PortfolioCVaR object, obtain properties directly or use an
assortment of “get” functions that obtain groups of properties from a
PortfolioCVaR object. The PortfolioCVaR object and
set functions have several useful features:
The PortfolioCVaR object and
set functions try to determine the dimensions of
your problem with either explicit or implicit inputs.
The PortfolioCVaR object and
set functions try to resolve ambiguities with
default choices.
The PortfolioCVaR object and
set functions perform scalar expansion on arrays
when possible.
The CVaR functions try to diagnose and warn about problems.
The PortfolioCVaR object uses the default display functions
provided by MATLAB, where display and disp display
a PortfolioCVaR object and its properties with or without the
object variable name.
Save and load PortfolioCVaR objects using the MATLAB
save and load commands.
Estimating efficient portfolios and efficient frontiers is the primary purpose of the CVaR 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 attain targeted values for return proxies
That attain 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 PortfolioCVaR object
are designed to work on a scalar PortfolioCVaR object, the array
capabilities of MATLAB enables you to set up and work with arrays of
PortfolioCVaR objects. The easiest way to do this is with the
repmat function. For example, to
create a 3-by-2 array of PortfolioCVaR
objects:
p = repmat(PortfolioCVaR, 3, 2); disp(p)
PortfolioCVaR objects, you can work on
individual PortfolioCVaR objects in the array by indexing. For
example:p(i,j) = PortfolioCVaR(p(i,j), ... );
PortfolioCVaR for the
(i,j) element of a matrix of
PortfolioCVaR objects in the variable
p.If you set up an array of PortfolioCVaR objects, you can access
properties of a particular PortfolioCVaR 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 PortfolioCVaR objects
with
p(i,j,k) = setBounds(p(i,j,k), lb, ub);
[lb, ub] = getBounds(p(i,j,k));
PortfolioCVaR
object functions work on only one PortfolioCVaR object at a
time.You can subclass the PortfolioCVaR object to override existing
functions or to add new properties or functions. To do so, create a derived class
from the PortfolioCVaR class. This gives you all the properties
and functions of thePortfolioCVaR class along with any new
features that you choose to add to your subclassed object.
ThePortfolioCVaR 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
theAbstractPortfolio class.
The CVaR portfolio optimization tools follow these conventions regarding the representation of different quantities associated with portfolio optimization:
Asset returns or prices for scenarios 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.
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).