PortfolioMAD

Create PortfolioMAD object for mean-absolute deviation portfolio optimization and analysis

Description

The PortfolioMAD object implements mean-absolute deviation portfolio optimization, where MAD stands for “mean-absolute deviation.” PortfolioMAD objects support functions that are specific to MAD portfolio optimization.

The main workflow for MAD portfolio optimization is to create an instance of a PortfolioMAD object that completely specifies a portfolio optimization problem and to operate on the PortfolioMAD object to obtain and analyze efficient portfolios. For more information on the workflow when using PortfolioMAD objects, see PortfolioMAD Object Workflow.

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

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

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

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

If a PortfolioMAD object exists, the syntax permits the first (and only the first argument) of the PortfolioMAD object to be an existing object with subsequent name-value pair arguments for properties to be added or modified. For example, given an existing PortfolioMAD object in p, the general syntax is:

p = PortfolioMAD(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 PortfolioMAD 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 PortfolioMAD object is a value object so that, given portfolio p, the following code creates two objects, p and q, that are distinct:

q = PortfolioMAD(p, ...)

After creating a PortfolioMAD 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 conditional value-at-risk portfolio optimization, see Portfolio Optimization Theory.

Creation

Description

example

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

example

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

example

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

Input Arguments

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Previously constructed PortfolioMAD object, specified using PortfolioMAD.

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 PortfolioMAD object, specified as a character vector.

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 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

Type of bounds for each asset weight, specified as a scalar character vector or string, or a cell array of character vectors or a string array. For more information, see setBounds.

Data Types: char | cell | string

Minimum number of assets allocated in portfolio, specified as a scalar numeric value. For more information, see setMinMaxNumAssets.

Data Types: double

Maximum number of assets allocated in portfolio, specified as a scalar numeric value. For more information, see setMinMaxNumAssets.

Data Types: double

Turnover constraint on purchases, specified as a scalar.

Data Types: double

Turnover constraint on sales, specified as a scalar.

Data Types: double

Turnover constraint, specified as a scalar.

Data Types: double

Portfolio Object Modeling

Proportional purchase costs, specified as a vector.

Data Types: double

Risk-free rate, specified as a scalar.

Data Types: double

Value-at-risk probability level which is 1 − (loss probability), specified as a scalar.

Data Types: double

Number of scenarios, specified as an integer scalar.

Data Types: double

Proportional sales costs, specified as a vector.

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
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 for a portfolio object
setMinMaxNumAssetsSet cardinality constraints on the number of assets invested in a portfolio object
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
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
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
setProbabilityLevelSet probability level for VaR and CVaR calculations
setScenariosSet asset returns scenarios by direct matrix
getScenariosObtain scenarios from portfolio object
simulateNormalScenariosByDataSimulate multivariate normal asset return scenarios from data
simulateNormalScenariosByMomentsSimulate multivariate normal asset return scenarios from mean and covariance of asset returns
estimateScenarioMomentsEstimate mean and covariance of asset return scenarios
estimatePortStdEstimate standard deviation of portfolio returns

Examples

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You can create a PortfolioMAD object, p, with no input arguments and display it using disp.

p = PortfolioMAD;
disp(p);
  PortfolioMAD with properties:

         BuyCost: []
        SellCost: []
    RiskFreeRate: []
        Turnover: []
     BuyTurnover: []
    SellTurnover: []
    NumScenarios: []
            Name: []
       NumAssets: []
       AssetList: []
        InitPort: []
     AInequality: []
     bInequality: []
       AEquality: []
       bEquality: []
      LowerBound: []
      UpperBound: []
     LowerBudget: []
     UpperBudget: []
     GroupMatrix: []
      LowerGroup: []
      UpperGroup: []
          GroupA: []
          GroupB: []
      LowerRatio: []
      UpperRatio: []
    MinNumAssets: []
    MaxNumAssets: []
       BoundType: []

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

You can use the PortfolioMAD object directly to set up a “standard” portfolio optimization problem. Given scenarios of asset returns in the variable AssetScenarios, this problem is completely specified 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 ];
m = m/12;
C = C/12;

AssetScenarios = mvnrnd(m, C, 20000);

p = PortfolioMAD('Scenarios', AssetScenarios, ...
'LowerBound', 0, 'LowerBudget', 1, 'UpperBudget', 1)
p = 
  PortfolioMAD with properties:

         BuyCost: []
        SellCost: []
    RiskFreeRate: []
        Turnover: []
     BuyTurnover: []
    SellTurnover: []
    NumScenarios: 20000
            Name: []
       NumAssets: 4
       AssetList: []
        InitPort: []
     AInequality: []
     bInequality: []
       AEquality: []
       bEquality: []
      LowerBound: [4x1 double]
      UpperBound: []
     LowerBudget: 1
     UpperBudget: 1
     GroupMatrix: []
      LowerGroup: []
      UpperGroup: []
          GroupA: []
          GroupB: []
      LowerRatio: []
      UpperRatio: []
    MinNumAssets: []
    MaxNumAssets: []
       BoundType: []

Note that the LowerBound property value undergoes scalar expansion since AssetScenarios provides the dimensions of the problem.

Using a sequence of steps is an alternative way to accomplish the same task of setting up a “standard” MAD portfolio optimization problem, given AssetScenarios variable is:

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 ];

m = m/12;
C = C/12;

AssetScenarios = mvnrnd(m, C, 20000);

p = PortfolioMAD;
p = setScenarios(p, AssetScenarios);
p = PortfolioMAD(p, 'LowerBound', 0);
p = PortfolioMAD(p, 'LowerBudget', 1, 'UpperBudget', 1);

plotFrontier(p);

This way works because the calls to PortfolioMAD are in this particular order. In this case, the call to initialize AssetScenarios 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 ];

m = m/12;
C = C/12;

AssetScenarios = mvnrnd(m, C, 20000);

p = PortfolioMAD;
p = PortfolioMAD(p, 'LowerBound', zeros(size(m)));
p = PortfolioMAD(p, 'LowerBudget', 1, 'UpperBudget', 1);
p = setScenarios(p, AssetScenarios);

plotFrontier(p);

If you did not specify the size of LowerBound but, instead, input a scalar argument, the PortfolioMAD object assumes that you are defining a single-asset problem and produces an error at the call to set asset scenarios with four assets.

You can create a PortfolioMAD object, p with the PortfolioMAD object 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 ];

m = m/12;
C = C/12;

AssetScenarios = mvnrnd(m, C, 20000);

p = PortfolioMAD('scenario', AssetScenarios, 'lb', 0, 'budget', 1)
p = 
  PortfolioMAD with properties:

         BuyCost: []
        SellCost: []
    RiskFreeRate: []
        Turnover: []
     BuyTurnover: []
    SellTurnover: []
    NumScenarios: 20000
            Name: []
       NumAssets: 4
       AssetList: []
        InitPort: []
     AInequality: []
     bInequality: []
       AEquality: []
       bEquality: []
      LowerBound: [4x1 double]
      UpperBound: []
     LowerBudget: 1
     UpperBudget: 1
     GroupMatrix: []
      LowerGroup: []
      UpperGroup: []
          GroupA: []
          GroupB: []
      LowerRatio: []
      UpperRatio: []
    MinNumAssets: []
    MaxNumAssets: []
       BoundType: []

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 ];
m = m/12;
C = C/12;

AssetScenarios = mvnrnd(m, C, 20000);

p = PortfolioMAD;

p = setScenarios(p, AssetScenarios);

p.LowerBudget = 1;
p.UpperBudget = 1;
p.LowerBound = zeros(size(m));
disp(p);
  PortfolioMAD with properties:

         BuyCost: []
        SellCost: []
    RiskFreeRate: []
        Turnover: []
     BuyTurnover: []
    SellTurnover: []
    NumScenarios: 20000
            Name: []
       NumAssets: 4
       AssetList: []
        InitPort: []
     AInequality: []
     bInequality: []
       AEquality: []
       bEquality: []
      LowerBound: [4x1 double]
      UpperBound: []
     LowerBudget: 1
     UpperBudget: 1
     GroupMatrix: []
      LowerGroup: []
      UpperGroup: []
          GroupA: []
          GroupB: []
      LowerRatio: []
      UpperRatio: []
    MinNumAssets: []
    MaxNumAssets: []
       BoundType: []

Scenarios cannot be assigned directly to a PortfolioMAD object. Scenarios must always be set through either the PortfolioMAD function, the setScenarios function, or any of the scenario simulation functions.

Create efficient portfolios:

load CAPMuniverse

p = PortfolioMAD('AssetList',Assets(1:12));
p = simulateNormalScenariosByData(p, Data(:,1:12), 20000 ,'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     0.029787    0.076199     0.11265    0.13397    0    
    AMZN            0           0           0          0    0    
    CSCO            0           0           0          0    0    
    DELL    0.0089177           0           0          0    0    
    EBAY            0           0           0          0    0    
    GOOG      0.16094      0.3516     0.54479    0.74898    1    
    HPQ      0.056856    0.023073           0          0    0    
    IBM       0.46074     0.37919     0.29379    0.11705    0    
    INTC            0           0           0          0    0    
    MSFT      0.28277     0.16994    0.048762          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 PortfolioMAD object, see Portfolio Optimization.

Introduced in R2013b