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Portfolio

Create Portfolio object for mean-variance portfolio optimization and analysis

Description

Use the Portfolio function to create a Portfolio object for mean-variance portfolio optimization.

The main workflow for portfolio optimization is to create an instance of a Portfolio object that completely specifies a portfolio optimization problem and to operate on the Portfolio object using supported functions to obtain and analyze efficient portfolios. For details on this workflow, see Portfolio Object Workflow.

You can use the Portfolio object in several ways. To set up a portfolio optimization problem in a Portfolio object, the simplest syntax is:

p = Portfolio;
This syntax creates a Portfolio object, p, such that all object properties are empty.

The Portfolio object also accepts collections of name-value pair arguments for properties and their values. The Portfolio object accepts inputs for properties with the general syntax:

	p = Portfolio('property1',value1,'property2',value2, ... );

If a Portfolio object exists, the syntax permits the first (and only the first argument) of the Portfolio object to be an existing object with subsequent 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 = PortfolioCVaR(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 tries to detect 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, ...)

After creating a Portfolio object, you can use the associated object functions to set portfolio constraints, analyze the efficient frontier, and validate the portfolio model.

For more detailed information on the theoretical basis for mean-variance optimization, see Portfolio Optimization Theory.

Creation

Syntax

p = Portfolio
p = Portfolio(Name,Value)
p = Portfolio(p,Name,Value)

Description

example

p = Portfolio creates an empty Portfolio object for mean-variance portfolio optimization and analysis. You can then add elements to the Portfolio object using the supported "add" and "set" functions. For more information, see Creating the Portfolio Object.

example

p = Portfolio(Name,Value) creates a Portfolio object (p) and sets Properties using name-value pairs. For example, p = Portfolio('AssetList',Assets(1:12)). You can specify multiple name-value pairs.

example

p = Portfolio(p,Name,Value) creates a Portfolio object (p) using a previously created Portfolio object p and sets Properties using name-value pairs. You can specify multiple name-value pairs.

Input Arguments

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Previously constructed Portfolio object, specified using Portfolio.

Properties

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Setting Up the Object

Names or symbols of assets in the universe, specified as a cell array of character vectors or a string array.

Data Types: cell | string

Initial portfolio, specified as a vector.

Data Types: double

Name for instance of the Portfolio object, specified as a character vector or a string.

Data Types: char | string

Number of assets in the universe, specified as an integer scalar.

Data Types: double

Portfolio Object Constraints

Linear equality constraint matrix, specified as a matrix.

Data Types: double

Linear inequality constraint matrix, specified as a matrix.

Data Types: double

Linear equality constraint vector, specified as a vector.

Data Types: double

Linear inequality constraint vector, specified as a vector.

Data Types: double

Group A weights to be bounded by weights in group B, specified as a matrix.

Data Types: double

Group B weights, specified as a matrix.

Data Types: double

Group membership matrix, specified as a matrix.

Data Types: double

Lower-bound constraint, specified as a vector.

Data Types: double

Lower-bound budget constraint, specified as a scalar.

Data Types: double

Lower-bound group constraint, specified as a vector.

Data Types: double

Minimum ratio of allocations between GroupA and GroupB, specified as a vector.

Data Types: double

Upper bound for tracking error constraint, specified as a scalar.

Data Types: double

Tracking portfolio for tracking error constraint, specified as a vector.

Data Types: double

Upper-bound constraint, specified as a vector.

Data Types: double

Upper-bound budget constraint, specified as a scalar.

Data Types: double

Upper-bound group constraint, specified as a vector.

Data Types: double

Maximum ratio of allocations between GroupA and GroupB, specified as a vector.

Data Types: double

Portfolio Object Modeling

Covariance of asset returns, specified as a square matrix.

Data Types: double

Mean of asset returns, specified as a vector.

Data Types: double

Proportional purchase costs, specified as a vector.

Data Types: double

Turnover constraint on purchases, specified as a scalar.

Data Types: double

Risk-free rate, specified as a scalar.

Data Types: double

Proportional sales costs, specified as a vector.

Data Types: double

Turnover constraint on sales, specified as a scalar.

Data Types: double

Turnover constraint, specified as a scalar.

Data Types: double

Object Functions

setAssetListSet up list of identifiers for assets
setInitPortSet up initial or current portfolio
setDefaultConstraintsSet up portfolio constraints with nonnegative weights that sum to 1
getAssetMomentsObtain mean and covariance of asset returns from Portfolio object
setAssetMoments Set moments (mean and covariance) of asset returns for Portfolio object
estimateAssetMomentsEstimate mean and covariance of asset returns from data
setCostsSet up proportional transaction costs
addEqualityAdd linear equality constraints for portfolio weights to existing constraints
addGroupRatioAdd group ratio constraints for portfolio weights to existing group ratio constraints
addGroupsAdd group constraints for portfolio weights to existing group constraints
addInequalityAdd linear inequality constraints for portfolio weights to existing constraints
getBoundsObtain bounds for portfolio weights from portfolio object
getBudgetObtain budget constraint bounds from portfolio object
getCostsObtain buy and sell transaction costs from portfolio object
getEqualityObtain equality constraint arrays from portfolio object
getGroupRatioObtain group ratio constraint arrays from portfolio object
getGroupsObtain group constraint arrays from portfolio object
getInequalityObtain inequality constraint arrays from portfolio object
getOneWayTurnoverObtain one-way turnover constraints from portfolio object
setGroupsSet up group constraints for portfolio weights
setInequalitySet up linear inequality constraints for portfolio weights
setBoundsSet up bounds for portfolio weights
setBudgetSet up budget constraints
setCostsSet up proportional transaction costs
setDefaultConstraintsSet up portfolio constraints with nonnegative weights that sum to 1
setEqualitySet up linear equality constraints for portfolio weights
setGroupRatioSet up group ratio constraints for portfolio weights
setInitPortSet up initial or current portfolio
setOneWayTurnoverSet up one-way portfolio turnover constraints
setTurnoverSet up maximum portfolio turnover constraint
setTrackingPortSet up benchmark portfolio for tracking error constraint
setTrackingErrorSet up maximum portfolio tracking error constraint
checkFeasibilityCheck feasibility of input portfolios against portfolio object
estimateBoundsEstimate global lower and upper bounds for set of portfolios
estimateFrontierEstimate specified number of optimal portfolios on the efficient frontier
estimateFrontierByReturnEstimate optimal portfolios with targeted portfolio returns
estimateFrontierByRiskEstimate optimal portfolios with targeted portfolio risks
estimateFrontierLimitsEstimate optimal portfolios at endpoints of efficient frontier
plotFrontierPlot efficient frontier
estimateMaxSharpeRatio Estimate efficient portfolio to maximize Sharpe ratio for Portfolio object
estimatePortMoments Estimate moments of portfolio returns for Portfolio object
estimatePortReturnEstimate mean of portfolio returns
estimatePortRiskEstimate portfolio risk according to risk proxy associated with corresponding object
setSolverChoose main solver and specify associated solver options for portfolio optimization

Examples

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You can create a Portfolio object, p, with no input arguments and 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: []

This approach provides a way to set up a portfolio optimization problem with the Portfolio function. You can then use the associated set functions to set and modify collections of properties in the Portfolio object.

You can use the Portfolio object directly to 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: [4x1 double]
       AssetCovar: [4x4 double]
    TrackingError: []
     TrackingPort: []
         Turnover: []
      BuyTurnover: []
     SellTurnover: []
             Name: []
        NumAssets: 4
        AssetList: []
         InitPort: []
      AInequality: []
      bInequality: []
        AEquality: []
        bEquality: []
       LowerBound: [4x1 double]
       UpperBound: []
      LowerBudget: 1
      UpperBudget: 1
      GroupMatrix: []
       LowerGroup: []
       UpperGroup: []
           GroupA: []
           GroupB: []
       LowerRatio: []
       UpperRatio: []

Note that the LowerBound property value undergoes scalar expansion since AssetMean and AssetCovar provide the dimensions of the problem.

Using a sequence of steps is 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.

You can create a Portfolio object, p with Portfolio using shortcuts for property names.

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)
p = 
  Portfolio with properties:

          BuyCost: []
         SellCost: []
     RiskFreeRate: []
        AssetMean: [4x1 double]
       AssetCovar: [4x4 double]
    TrackingError: []
     TrackingPort: []
         Turnover: []
      BuyTurnover: []
     SellTurnover: []
             Name: []
        NumAssets: 4
        AssetList: []
         InitPort: []
      AInequality: []
      bInequality: []
        AEquality: []
        bEquality: []
       LowerBound: [4x1 double]
       UpperBound: []
      LowerBudget: 1
      UpperBudget: 1
      GroupMatrix: []
       LowerGroup: []
       UpperGroup: []
           GroupA: []
           GroupB: []
       LowerRatio: []
       UpperRatio: []

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));
disp(p)
  Portfolio with properties:

          BuyCost: []
         SellCost: []
     RiskFreeRate: []
        AssetMean: [4x1 double]
       AssetCovar: [4x4 double]
    TrackingError: []
     TrackingPort: []
         Turnover: []
      BuyTurnover: []
     SellTurnover: []
             Name: []
        NumAssets: 4
        AssetList: []
         InitPort: []
      AInequality: []
      bInequality: []
        AEquality: []
        bEquality: []
       LowerBound: [4x1 double]
       UpperBound: []
      LowerBudget: 1
      UpperBudget: 1
      GroupMatrix: []
       LowerGroup: []
       UpperGroup: []
           GroupA: []
           GroupB: []
       LowerRatio: []
       UpperRatio: []

Create efficient portfolios:

load CAPMuniverse

p = Portfolio('AssetList',Assets(1:12));
p = estimateAssetMoments(p, Data(:,1:12),'missingdata',true);
p = setDefaultConstraints(p);
plotFrontier(p);

pwgt = estimateFrontier(p, 5);

pnames = cell(1,5);
for i = 1:5
	pnames{i} = sprintf('Port%d',i);
end

Blotter = dataset([{pwgt},pnames],'obsnames',p.AssetList);

disp(Blotter);
            Port1        Port2       Port3       Port4      Port5
    AAPL     0.017926    0.058247    0.097816    0.12955    0    
    AMZN            0           0           0          0    0    
    CSCO            0           0           0          0    0    
    DELL    0.0041906           0           0          0    0    
    EBAY            0           0           0          0    0    
    GOOG      0.16144     0.35678     0.55228    0.75116    1    
    HPQ      0.052566    0.032302    0.011186          0    0    
    IBM       0.46422     0.36045     0.25577    0.11928    0    
    INTC            0           0           0          0    0    
    MSFT      0.29966     0.19222    0.082949          0    0    
    ORCL            0           0           0          0    0    
    YHOO            0           0           0          0    0    

More About

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References

[1] For a complete list of references for the Portfolio object, see Portfolio Optimization.

Introduced in R2011a

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