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simulateNormalScenariosByMoments

Simulate multivariate normal asset return scenarios from mean and covariance of asset returns

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Syntax

obj = simulateNormalScenariosByMoments(obj,AssetMean,AssetCovar,NumScenarios)
obj = simulateNormalScenariosByMoments(obj,AssetMean,AssetCovarNumScenarios,NumAssets)

Description

obj = simulateNormalScenariosByMoments(obj,AssetMean,AssetCovar,NumScenarios) simulates multivariate normal asset return scenarios from mean and covariance of asset returns for PortfolioCVaR or PortfolioMAD objects. For details on the workflows, see PortfolioCVaR Object Workflow, and PortfolioMAD Object Workflow.

example

obj = simulateNormalScenariosByMoments(obj,AssetMean,AssetCovarNumScenarios,NumAssets) simulates multivariate normal asset return scenarios from mean and covariance of asset returns for PortfolioCVaR or PortfolioMAD objects using the optional input NumScenarios.

Note

This function overwrites existing scenarios associated with PortfolioCVaR or PortfolioMAD objects, and also, possibly, NumScenarios.

If you want to use the function multiple times and you want to simulate identical scenarios each time the function is called, precede each function call with rng(seed) using a specified integer seed.

example

Examples

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Open Live Script

Given PortfolioCVaR object p, use the simulateNormalScenariosByMoments function to simulate multivariate normal asset return scenarios from moments. 

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 = PortfolioCVaR;
p = setScenarios(p, AssetScenarios);
p = setDefaultConstraints(p);
p = setProbabilityLevel(p, 0.95);

AssetMean = [.5]
AssetMean = 
0.5000

AssetCovar = [.5]
AssetCovar = 
0.5000

NumScenarios = 100
NumScenarios = 
100

p = simulateNormalScenariosByMoments(p, AssetMean, AssetCovar, NumScenarios)
p = 
  PortfolioCVaR with properties:

                       BuyCost: []
                      SellCost: []
                  RiskFreeRate: []
              ProbabilityLevel: 0.9500
                      Turnover: []
                   BuyTurnover: []
                  SellTurnover: []
                  NumScenarios: 100
                          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: []
    ConditionalBudgetThreshold: []
        ConditionalUpperBudget: []
                     BoundType: [4x1 categorical]
Open Live Script

Given PortfolioMAD object p, use the simulateNormalScenariosByMoments function to simulate multivariate normal asset return scenarios from moments. 

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 = setDefaultConstraints(p);

AssetMean = [.5]
AssetMean = 
0.5000

AssetCovar = [.5]
AssetCovar = 
0.5000

NumScenarios = 100
NumScenarios = 
100

p = simulateNormalScenariosByMoments(p, AssetMean, AssetCovar, NumScenarios)
p = 
  PortfolioMAD with properties:

                       BuyCost: []
                      SellCost: []
                  RiskFreeRate: []
                      Turnover: []
                   BuyTurnover: []
                  SellTurnover: []
                  NumScenarios: 100
                          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: []
    ConditionalBudgetThreshold: []
        ConditionalUpperBudget: []
                     BoundType: [4x1 categorical]

Input Arguments

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Object for portfolio, specified using a PortfolioCVaR or PortfolioMAD object.

For more information on creating a PortfolioCVaR or PortfolioMAD object, see

Data Types: object

Mean of asset returns, specified as a vector.

Note

If AssetMean is a scalar and the number of assets is known, scalar expansion occurs. If the number of assets cannot be determined, this function assumes that NumAssets = 1.

Data Types: double

Covariance of asset returns, specified as a symmetric positive semidefinite matrix.

Note

  • If AssetCovar is a scalar and the number of assets is known, a diagonal matrix is formed with the scalar value along the diagonals. If it is not possible to determine the number of assets, this method assumes that NumAssets = 1.

  • If AssetCovar is a vector, a diagonal matrix is formed with the vector along the diagonal.

  • If AssetCovar is not a symmetric positive semidefinite matrix, use nearcorr to create a positive semidefinite matrix for a correlation matrix.

Data Types: double

Number of scenarios to simulate, specified as a positive integer.

Data Types: double

Number of assets, specified as a scalar.

Data Types: double

Output Arguments

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Updated portfolio object, returned as a PortfolioCVaR or PortfolioMAD object. For more information on creating a portfolio object, see

Tips

You can also use dot notation to simulate multivariate normal asset return scenarios from a mean and covariance of asset returns for a PortfolioCVaR or PortfolioMAD object.

obj = obj.simulateNormalScenariosByMoments(AssetMean, AssetCovar, NumScenarios, NumAssets);

Version History

Introduced in R2012b

See Also

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Topics

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