Creating the Portfolio Object
To create a fully specified mean-variance portfolio optimization problem, instantiate
the Portfolio object using Portfolio. For information on the workflow when using
Portfolio objects, see Portfolio Object Workflow.
Syntax
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 name-value 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 name-value 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 case-sensitive, 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, ...)
Portfolio Problem Sufficiency
A mean-variance 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
AssetMeancontains a valid finite mean vector of asset returns and the propertyAssetCovarcontains a valid symmetric positive-semidefinite 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 mean-variance
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 mean-variance portfolio optimization, see
Portfolio Optimization.
Portfolio Function Examples
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: []
ConditionalBudgetThreshold: []
ConditionalUpperBudget: []
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.
Using the Portfolio Function for a Single-Step Setup
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: []
ConditionalBudgetThreshold: []
ConditionalUpperBudget: []
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
Using the Portfolio Function with a Sequence of Steps
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 case-sensitive):
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 single-asset problem and produces an error at the call to set
asset moments with four assets.
Shortcuts for Property Names
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
case-insensitive 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
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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)
Direct Setting of Portfolio Object Properties
Although not recommended, you can set properties directly, however no error-checking 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)See Also
Topics
- Common Operations on the Portfolio Object
- Working with Portfolio Constraints Using Defaults
- Asset Allocation Case Study
- Portfolio Optimization Examples Using Financial Toolbox
- Portfolio Optimization with Semicontinuous and Cardinality Constraints
- Black-Litterman Portfolio Optimization Using Financial Toolbox
- Portfolio Optimization Using Factor Models
- Diversify Portfolios Using Custom Objective
- Portfolio Optimization Using Social Performance Measure
- Portfolio Object
- Portfolio Optimization Theory
- Portfolio Object Workflow
