To create a fully specified meanvariance portfolio optimization problem, instantiate
the Portfolio
object using Portfolio
. For information on the workflow when using
Portfolio
objects, see Portfolio Object Workflow.
Use Portfolio
to create an instance of an
object of the Portfolio
class. You can use Portfolio
in several ways. To set up
a portfolio optimization problem in a Portfolio
object, the
simplest syntax
is:
p = Portfolio;
Portfolio
object, p
, such
that all object properties are empty. The Portfolio
object also accepts
collections of argument namevalue pair arguments for properties and their values.
The Portfolio
object accepts inputs for
public properties with the general
syntax:
p = Portfolio('property1', value1, 'property2', value2, ... );
If a Portfolio
object already exists, the syntax permits the
first (and only the first argument) of Portfolio
to be an existing object
with subsequent argument namevalue pair arguments for properties to be added or
modified. For example, given an existing Portfolio
object in
p
, the general syntax
is:
p = Portfolio(p, 'property1', value1, 'property2', value2, ... );
Input argument names are not casesensitive, but must be completely specified. In
addition, several properties can be specified with alternative argument names (see
Shortcuts for Property Names). The Portfolio
object detects problem
dimensions from the inputs and, once set, subsequent inputs can undergo various
scalar or matrix expansion operations that simplify the overall process to formulate
a problem. In addition, a Portfolio
object is a value object so
that, given portfolio p
, the following code creates two objects,
p
and q
, that are
distinct:
q = Portfolio(p, ...)
A meanvariance portfolio optimization is completely specified with the
Portfolio
object if these two conditions are met:
The moments of asset returns must be specified such that the property
AssetMean
contains a valid finite mean vector of
asset returns and the property AssetCovar
contains a
valid symmetric positivesemidefinite matrix for the covariance of asset
returns.
The first condition is satisfied by setting the properties associated with the moments of asset returns.
The set of feasible portfolios must be a nonempty compact set, where a compact set is closed and bounded.
The second condition is satisfied by an extensive collection of
properties that define different types of constraints to form a set of
feasible portfolios. Since such sets must be bounded, either explicit or
implicit constraints can be imposed, and several functions, such as
estimateBounds
, provide
ways to ensure that your problem is properly formulated.
Although the general sufficiency conditions for meanvariance
portfolio optimization go beyond these two conditions, the
Portfolio
object implemented in Financial Toolbox™ implicitly handles all these additional conditions. For more
information on the Markowitz model for meanvariance portfolio optimization, see
Portfolio Optimization.
If you create a Portfolio
object, p
, with no
input arguments, you can display it using
disp
:
p = Portfolio; disp(p)
Portfolio with properties: BuyCost: [] SellCost: [] RiskFreeRate: [] AssetMean: [] AssetCovar: [] TrackingError: [] TrackingPort: [] Turnover: [] BuyTurnover: [] SellTurnover: [] Name: [] NumAssets: [] AssetList: [] InitPort: [] AInequality: [] bInequality: [] AEquality: [] bEquality: [] LowerBound: [] UpperBound: [] LowerBudget: [] UpperBudget: [] GroupMatrix: [] LowerGroup: [] UpperGroup: [] GroupA: [] GroupB: [] LowerRatio: [] UpperRatio: [] MinNumAssets: [] MaxNumAssets: [] BoundType: []
The approaches listed provide a way to set up a portfolio optimization problem
with the Portfolio
object. The
set
functions offer additional ways to set and modify
collections of properties in the Portfolio
object.
You can use the Portfolio
object to directly set
up a “standard” portfolio optimization problem, given a mean and
covariance of asset returns in the variables m
and
C
:
m = [ 0.05; 0.1; 0.12; 0.18 ]; C = [ 0.0064 0.00408 0.00192 0; 0.00408 0.0289 0.0204 0.0119; 0.00192 0.0204 0.0576 0.0336; 0 0.0119 0.0336 0.1225 ]; p = Portfolio('assetmean', m, 'assetcovar', C, ... 'lowerbudget', 1, 'upperbudget', 1, 'lowerbound', 0)
p = Portfolio with properties: BuyCost: [] SellCost: [] RiskFreeRate: [] AssetMean: [4×1 double] AssetCovar: [4×4 double] TrackingError: [] TrackingPort: [] Turnover: [] BuyTurnover: [] SellTurnover: [] Name: [] NumAssets: 4 AssetList: [] InitPort: [] AInequality: [] bInequality: [] AEquality: [] bEquality: [] LowerBound: [4×1 double] UpperBound: [] LowerBudget: 1 UpperBudget: 1 GroupMatrix: [] LowerGroup: [] UpperGroup: [] GroupA: [] GroupB: [] LowerRatio: [] UpperRatio: [] MinNumAssets: [] MaxNumAssets: [] BoundType: []
LowerBound
property value undergoes scalar expansion
since AssetMean
and AssetCovar
provide the
dimensions of the problem.You can use dot notation with the function plotFrontier
.
p.plotFrontier
An alternative way to accomplish the same task of setting up a
“standard” portfolio optimization problem, given a mean and
covariance of asset returns in the variables m
and
C
(which also illustrates that argument names are not casesensitive):
m = [ 0.05; 0.1; 0.12; 0.18 ]; C = [ 0.0064 0.00408 0.00192 0; 0.00408 0.0289 0.0204 0.0119; 0.00192 0.0204 0.0576 0.0336; 0 0.0119 0.0336 0.1225 ]; p = Portfolio; p = Portfolio(p, 'assetmean', m, 'assetcovar', C); p = Portfolio(p, 'lowerbudget', 1, 'upperbudget', 1); p = Portfolio(p, 'lowerbound', 0); plotFrontier(p)
This way works because the calls to Portfolio
are in this particular
order. In this case, the call to initialize AssetMean
and
AssetCovar
provides the dimensions for the problem. If
you were to do this step last, you would have to explicitly dimension the
LowerBound
property as follows:
m = [ 0.05; 0.1; 0.12; 0.18 ]; C = [ 0.0064 0.00408 0.00192 0; 0.00408 0.0289 0.0204 0.0119; 0.00192 0.0204 0.0576 0.0336; 0 0.0119 0.0336 0.1225 ]; p = Portfolio; p = Portfolio(p, 'LowerBound', zeros(size(m))); p = Portfolio(p, 'LowerBudget', 1, 'UpperBudget', 1); p = Portfolio(p, 'AssetMean', m, 'AssetCovar', C); plotFrontier(p)
If you did not specify the size of
LowerBound
but, instead, input a scalar argument, the
Portfolio
object assumes that you
are defining a singleasset problem and produces an error at the call to set
asset moments with four assets.
The Portfolio
object has shorter
argument names that replace longer argument names associated with specific
properties of the Portfolio
object. For example, rather than
enter 'assetcovar'
, the Portfolio
object accepts the
caseinsensitive name 'covar'
to set the
AssetCovar
property in a Portfolio
object. Every shorter argument name corresponds with a single property in the
Portfolio
object. The one
exception is the alternative argument name 'budget'
, which
signifies both the LowerBudget
and
UpperBudget
properties. When 'budget'
is used, then the LowerBudget
and
UpperBudget
properties are set to the same value to form
an equality budget constraint.
Shortcuts for Property Names
Shortcut Argument Name  Equivalent Argument / Property Name 



























For example, this call Portfolio
uses these shortcuts
for properties and is equivalent to the previous
examples:
m = [ 0.05; 0.1; 0.12; 0.18 ]; C = [ 0.0064 0.00408 0.00192 0; 0.00408 0.0289 0.0204 0.0119; 0.00192 0.0204 0.0576 0.0336; 0 0.0119 0.0336 0.1225 ]; p = Portfolio('mean', m, 'covar', C, 'budget', 1, 'lb', 0); plotFrontier(p)
Although not recommended, you can set properties directly, however no errorchecking is done on your inputs:
m = [ 0.05; 0.1; 0.12; 0.18 ]; C = [ 0.0064 0.00408 0.00192 0; 0.00408 0.0289 0.0204 0.0119; 0.00192 0.0204 0.0576 0.0336; 0 0.0119 0.0336 0.1225 ]; p = Portfolio; p.NumAssets = numel(m); p.AssetMean = m; p.AssetCovar = C; p.LowerBudget = 1; p.UpperBudget = 1; p.LowerBound = zeros(size(m)); plotFrontier(p)