# estimatePortRisk

Estimate portfolio risk according to risk proxy associated with corresponding object

## Description

example

prsk = estimatePortRisk(obj,pwgt) estimates portfolio risk according to the risk proxy associated with the corresponding object (obj) for Portfolio, PortfolioCVaR, or PortfolioMAD objects. For details on the respective workflows when using these different objects, see Portfolio Object Workflow, PortfolioCVaR Object Workflow, and PortfolioMAD Object Workflow.

## Examples

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Given portfolio p, use the estimatePortRisk function to show the standard deviation of portfolio returns for each portfolio in pwgt.

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 = setAssetMoments(p, m, C);
p = setDefaultConstraints(p);
pwgt = estimateFrontierLimits(p);
prsk = estimatePortRisk(p, pwgt);
disp(prsk)
0.0769
0.3500

Create a Portfolio object for three assets.

AssetMean = [ 0.0101110; 0.0043532; 0.0137058 ];
AssetCovar = [ 0.00324625 0.00022983 0.00420395;
0.00022983 0.00049937 0.00019247;
0.00420395 0.00019247 0.00764097 ];
p = Portfolio('AssetMean', AssetMean, 'AssetCovar', AssetCovar);
p = setDefaultConstraints(p);

Use setBounds with semi-continuous constraints to set xi=0 or 0.02<=xi<=0.5 for all i=1,...NumAssets.

p = setBounds(p, 0.02, 0.5,'BoundType', 'Conditional', 'NumAssets', 3);

When working with a Portfolio object, the setMinMaxNumAssets function enables you to set up cardinality constraints for a long-only portfolio. This sets the cardinality constraints for the Portfolio object, where the total number of allocated assets satisfying the nonzero semi-continuous constraints are between MinNumAssets and MaxNumAssets. By setting MinNumAssets=MaxNumAssets=2, only two of the three assets are invested in the portfolio.

p = setMinMaxNumAssets(p, 2, 2);

Use estimatePortRisk to estimate the portfolio risk according to a risk proxy associated with a Portfolio object.

pwgt = estimateFrontierLimits(p);
prsk = estimatePortRisk(p, pwgt)
prsk = 2×1

0.0324
0.0695

The estimatePortRisk function uses the MINLP solver to solve this problem. Use the setSolverMINLP function to configure the SolverType and options.

p.solverOptionsMINLP
ans = struct with fields:
MaxIterations: 1000
AbsoluteGapTolerance: 1.0000e-07
RelativeGapTolerance: 1.0000e-05
NonlinearScalingFactor: 1000
ObjectiveScalingFactor: 1000
Display: 'off'
CutGeneration: 'basic'
MaxIterationsInactiveCut: 30
ActiveCutTolerance: 1.0000e-07
IntMasterSolverOptions: [1x1 optim.options.Intlinprog]
NumIterationsEarlyIntegerConvergence: 30

Given a portfolio pwgt, use the estimatePortRisk function to show the conditional value-at-risk (CVaR) of portfolio returns for each portfolio.

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);

pwgt = estimateFrontierLimits(p);
prsk = estimatePortRisk(p, pwgt);
disp(prsk)
0.0407
0.1911

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.

Given a portfolio pwgt, use the estimatePortRisk function to show the mean-absolute deviation of portfolio returns for each portfolio.

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

pwgt = estimateFrontierLimits(p);
prsk = estimatePortRisk(p, pwgt);
disp(prsk)
0.0177
0.0809

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

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Object for portfolio, specified using Portfolio, PortfolioCVaR, or PortfolioMAD object. For more information on creating a portfolio object, see

Data Types: object

Collection of portfolios, specified as a NumAssets-by-NumPorts matrix, where NumAssets is the number of assets in the universe and NumPorts is the number of portfolios in the collection of portfolios.

Data Types: double

## Output Arguments

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Estimates for portfolio risk according to the risk proxy associated with the corresponding object (obj) for each portfolio in pwgt, returned as a NumPorts vector.

prsk is returned for a Portfolio, PortfolioCVaR, or PortfolioMAD input object (obj).

## Tips

You can also use dot notation to estimate portfolio risk according to the risk proxy associated with the corresponding object (obj).

prsk = obj.estimatePortRisk(pwgt);

## Version History

Introduced in R2011a