estimateScenarioMoments

Estimate mean and covariance of asset return scenarios

Syntax

[ScenarioMean,ScenarioCovar] = estimateScenarioMoments(obj)

Description

[ScenarioMean,ScenarioCovar] = estimateScenarioMoments(obj) estimates mean and covariance of asset return scenarios for PortfolioCVaR or PortfolioMAD objects. For details on the workflows, see PortfolioCVaR Object Workflow, and PortfolioMAD Object Workflow.

Examples

Estimate Mean and Covariance of Asset Return Scenarios for a PortfolioCVaR Object

Given PortfolioCVaR object p, use the estimatePortRisk function to estimate mean and covariance of asset return scenarios.

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;

rng(11);

AssetScenarios = mvnrnd(m, C, 20000);

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

[ScenarioMean, ScenarioCovar] = estimateScenarioMoments(p)

ScenarioMean = 4×1

    0.0039
    0.0082
    0.0102
    0.0154

ScenarioCovar = 4×4

    0.0005    0.0003    0.0001   -0.0001
    0.0003    0.0024    0.0017    0.0010
    0.0001    0.0017    0.0048    0.0028
   -0.0001    0.0010    0.0028    0.0102

The function rng($$seed$$) resets the random number generator to produce the documented results. It is not necessary to reset the random number generator to simulate scenarios.

Estimate Mean and Covariance of Asset Return Scenarios for a PortfolioMAD Object

Given PortfolioMAD object p, use the estimatePortRisk function to estimate mean and covariance of asset return scenarios.

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;

rng(11);

AssetScenarios = mvnrnd(m, C, 20000);

p = PortfolioMAD;
p = setScenarios(p, AssetScenarios);
p = setDefaultConstraints(p);

[ScenarioMean, ScenarioCovar] = estimateScenarioMoments(p)

ScenarioMean = 4×1

    0.0039
    0.0082
    0.0102
    0.0154

ScenarioCovar = 4×4

    0.0005    0.0003    0.0001   -0.0001
    0.0003    0.0024    0.0017    0.0010
    0.0001    0.0017    0.0048    0.0028
   -0.0001    0.0010    0.0028    0.0102

The function rng($$seed$$) resets the random number generator to produce the documented results. It is not necessary to reset the random number generator to simulate scenarios.

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

Output Arguments

ScenarioMean — Estimate for mean of scenarios

[] (default) | vector

Estimate for mean of scenarios, returned as a NumPorts vector or [].

Note

If no scenarios are associated with the specified object, both ScenarioMean and ScenarioCovar are set to empty [].

ScenarioCovar — Estimate for covariance of scenarios

[] (default) | matrix

Estimate for covariance of scenarios, returned as a NumAssets-by-NumAssets matrix or [].

Note

If no scenarios are associated with the specified object, both ScenarioMean and ScenarioCovar are set to empty [].

Tips

You can also use dot notation to estimate the mean and covariance of asset return scenarios for a portfolio.

[ScenarioMean, ScenarioCovar] = obj.estimateScenarioMoments