simulateNormalScenariosByData

Simulate multivariate normal asset return scenarios from data

Using a fints object for the AssetReturns argument of simulateNormalScenariosByData is not recommended. Use timetable instead for financial time series. For more information, see Convert Financial Time Series Objects fints to Timetables.

Syntax

obj = simulateNormalScenariosByData(obj,AssetReturns)

obj = simulateNormalScenariosByData(obj,AssetReturns,NumScenarios,Name,Value)

Description

obj = simulateNormalScenariosByData(obj,AssetReturns) simulates multivariate normal asset return scenarios from data for portfolio object for PortfolioCVaR or PortfolioMAD objects. For details on the workflows, see PortfolioCVaR Object Workflow, and PortfolioMAD Object Workflow.

obj = simulateNormalScenariosByData(obj,AssetReturns,NumScenarios,Name,Value) simulates multivariate normal asset return scenarios from data for portfolio object for PortfolioCVaR or PortfolioMAD objects using additional options specified by one or more Name,Value pair arguments.

This function estimates the mean and covariance of asset returns from either price or return data and then uses these estimates to generate the specified number of scenarios with the function mvnrnd.

Data can be in a NumSamples-by-NumAssets matrix of NumSamples prices or returns at a given periodicity for a collection of NumAssets assets, a table or a timetable.

Note

If you want to use the method 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.

Examples

Simulate Multivariate Normal Asset Return Scenarios from Data for a PortfolioCVaR Object

Given a PortfolioCVaR object p, use the simulateNormalScenariosByData function to simulate multivariate normal asset return scenarios from data.

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;

RawData = mvnrnd(m, C, 240);
NumScenarios = 2000;

p = PortfolioCVaR;
p = simulateNormalScenariosByData(p, RawData, NumScenarios)

p = 
  PortfolioCVaR with properties:

             BuyCost: []
            SellCost: []
        RiskFreeRate: []
    ProbabilityLevel: []
            Turnover: []
         BuyTurnover: []
        SellTurnover: []
        NumScenarios: 2000
                Name: []
           NumAssets: 4
           AssetList: []
            InitPort: []
         AInequality: []
         bInequality: []
           AEquality: []
           bEquality: []
          LowerBound: []
          UpperBound: []
         LowerBudget: []
         UpperBudget: []
         GroupMatrix: []
          LowerGroup: []
          UpperGroup: []
              GroupA: []
              GroupB: []
          LowerRatio: []
          UpperRatio: []
        MinNumAssets: []
        MaxNumAssets: []
           BoundType: []

p = setDefaultConstraints(p);
p = setProbabilityLevel(p, 0.9);

disp(p);

  PortfolioCVaR with properties:

             BuyCost: []
            SellCost: []
        RiskFreeRate: []
    ProbabilityLevel: 0.9000
            Turnover: []
         BuyTurnover: []
        SellTurnover: []
        NumScenarios: 2000
                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: [4x1 categorical]

Estimate Mean and Covariance of Asset Returns from Market Data for a PortfolioCVaR Object

Create a PortfolioCVaR object p and use the simulateNormalScenariosByData function with market data loaded from CAPMuniverse.mat to simulate multivariate normal asset return scenarios. The market data, AssetsTimeTable, is a timetable of asset returns.

load CAPMuniverse

p = PortfolioCVaR('AssetList',Assets);
disp(p);

  PortfolioCVaR with properties:

             BuyCost: []
            SellCost: []
        RiskFreeRate: []
    ProbabilityLevel: []
            Turnover: []
         BuyTurnover: []
        SellTurnover: []
        NumScenarios: []
                Name: []
           NumAssets: 14
           AssetList: {1x14 cell}
            InitPort: []
         AInequality: []
         bInequality: []
           AEquality: []
           bEquality: []
          LowerBound: []
          UpperBound: []
         LowerBudget: []
         UpperBudget: []
         GroupMatrix: []
          LowerGroup: []
          UpperGroup: []
              GroupA: []
              GroupB: []
          LowerRatio: []
          UpperRatio: []
        MinNumAssets: []
        MaxNumAssets: []
           BoundType: []

Simulate the scenarios from the timetable data for each of the assets from CAPMuniverse.mat and plot the efficient frontier.

p = simulateNormalScenariosByData(p,AssetsTimeTable,10000,'missingdata',true);
p = setDefaultConstraints(p);
p = setProbabilityLevel(p, 0.9);
plotFrontier(p);

Estimate Mean and Covariance of Asset Returns from Data for a PortfolioMAD Object

Given a PortfolioMAD object p, use the simulateNormalScenariosByData function to simulate multivariate normal asset return scenarios from data.

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;

RawData = mvnrnd(m, C, 240);
NumScenarios = 2000;

p = PortfolioMAD;
p = simulateNormalScenariosByData(p, RawData, NumScenarios);
p = setDefaultConstraints(p);

disp(p);

  PortfolioMAD with properties:

         BuyCost: []
        SellCost: []
    RiskFreeRate: []
        Turnover: []
     BuyTurnover: []
    SellTurnover: []
    NumScenarios: 2000
            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: [4x1 categorical]

Estimate Mean and Covariance of Asset Returns from Market Data for a PortfolioMAD Object

Create a PortfolioMAD object p and use the simulateNormalScenariosByData function with market data loaded from CAPMuniverse.mat to simulate multivariate normal asset return scenarios. The market data, AssetsTimeTable, is a timetable of asset returns.

load CAPMuniverse

p = PortfolioMAD('AssetList',Assets);
disp(p.AssetList');

    {'AAPL'  }
    {'AMZN'  }
    {'CSCO'  }
    {'DELL'  }
    {'EBAY'  }
    {'GOOG'  }
    {'HPQ'   }
    {'IBM'   }
    {'INTC'  }
    {'MSFT'  }
    {'ORCL'  }
    {'YHOO'  }
    {'MARKET'}
    {'CASH'  }

Simulate the scenarios from the timetable data for each of the assets from CAPMuniverse.mat and plot the efficient frontier.

p = simulateNormalScenariosByData(p,AssetsTimeTable,10000,'missingdata',true);
p = setDefaultConstraints(p);
plotFrontier(p);

Input Arguments

obj — Object for portfolio

object

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

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

• PortfolioCVaR

• PortfolioMAD

Data Types: object

AssetReturns — Asset data that can be converted into asset returns

matrix | table | timetable

Asset data that can be converted into asset returns ([NumSamples-by-NumAssets] matrix), specified as a matrix, table, or timetable.

AssetReturns data can be:

• NumSamples-by-NumAssets matrix.

• Table of NumSamples prices or returns at a given periodicity for a collection of NumAssets assets

• Timetable object with NumSamples observations and NumAssets time series

Data Types: double | table | timetable

NumScenarios — Number of scenarios to simulate

positive integer

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

Data Types: double

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: p = simulateNormalScenariosByData(p,RawData,NumScenarios,'DataFormat','Returns','MissingData',true,'GetAssetList',true)

'DataFormat' — Flag to convert input data as prices into returns

'Returns' (default) | character vector with values 'Returns' or 'Prices'

Flag to convert input data as prices into returns, specified as the comma-separated pair consisting of 'DataFormat' and a character vector with the values:

• 'Returns' — Data in AssetReturns contains asset total returns.

• 'Prices' — Data in AssetReturns contains asset total return prices.

Data Types: char

'MissingData' — Flag to use ECM algorithm to handle NaN values

false (default) | logical with values true or false

Flag to use ECM algorithm to handle NaN values, specified as the comma-separated pair consisting of 'MissingData' and a logical with a value of true or false.

• false — Do not use ECM algorithm to handle NaN values (exclude NaN values).

• true — Use ECM algorithm to handle NaN values.

Data Types: logical

'GetAssetList' — Flag indicating which asset names to use for the asset list

false (default) | logical with values true or false

Flag indicating which asset names to use for the asset list, specified as the comma-separated pair consisting of 'GetAssetList' and a logical with a value of true or false.

• false — Do not extract or create asset names.

• true — Extract or create asset names from the table or timetable.

If a table or timetable is passed into this function using the AssetReturns argument and the GetAssetList flag is true, the column names from the table or timetable are used as asset names in obj.AssetList.

If a matrix is passed and the GetAssetList flag is true, default asset names are created based on the AbstractPortfolio property defaultforAssetList, which is 'Asset'.

If the GetAssetList flag is false, no action occurs, which is the default behavior.

Data Types: logical

Output Arguments

obj — Updated portfolio object

object for portfolio

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

• PortfolioCVaR

• PortfolioMAD

Tips

You can also use dot notation to simulate multivariate normal asset return scenarios from data for a PortfolioCVaR or PortfolioMAD object.

obj = obj.simulateNormalScenariosByData(AssetReturns,NumScenarios,Name,Value);