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estimatePortReturn

Estimate mean of portfolio returns

Description

example

pret = estimatePortReturn(obj,pwgt) estimates the mean of portfolio returns (as the proxy for portfolio return) 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 estimatePortReturn function to estimate the mean of portfolio returns.

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);
pret = estimatePortReturn(p, pwgt);
disp(pret)
    0.0590
    0.1800

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 estimatePortReturn to estimate the mean of portfolio returns for a Portfolio object.

pwgt = estimateFrontierLimits(p);
pret = estimatePortReturn(p, pwgt)
pret = 2×1

    0.0072
    0.0119

The estimatePortReturn 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 portfolio p, use the estimatePortReturn function to estimate the mean of portfolio returns.

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);
pret = estimatePortReturn(p, pwgt);
disp(pret)
    0.0050
    0.0154

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 portfolio p, use the estimatePortReturn function to estimate the mean of portfolio returns.

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);

pwgt = estimateFrontierLimits(p);
pret = estimatePortReturn(p, pwgt);
disp(pret)
    0.0048
    0.0154

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 means of portfolio returns for each portfolio in pwgt, returned as a NumPorts vector.

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

Note

Depending on whether costs have been set, the portfolio return is either gross or net portfolio returns. For information on setting costs, see setCosts.

Tips

You can also use dot notation to estimate the mean of portfolio returns (as the proxy for portfolio return).

pret = obj.estimatePortReturn(pwgt);

Version History

Introduced in R2011a