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estimateFrontierByRisk

Estimate optimal portfolios with targeted portfolio risks

Use the estimateFrontierByRisk function with a Portfolio, PortfolioCVaR, or PortfolioMAD object to estimate optimal portfolios with targeted portfolio risks.

For details on the respective workflows when using these different objects, see Portfolio Object Workflow, PortfolioCVaR Object Workflow, and PortfolioMAD Object Workflow.

Syntax

[pwgt,pbuy,psell] = estimateFrontierByRisk(obj,TargetRisk)

Description

example

[pwgt,pbuy,psell] = estimateFrontierByRisk(obj,TargetRisk) estimates optimal portfolios with targeted portfolio risks.

Examples

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To obtain efficient portfolios that have targeted portfolio risks, the estimateFrontierByRisk function accepts one or more target portfolio risks and obtains efficient portfolios with the specified risks. Assume you have a universe of four assets where you want to obtain efficient portfolios with target portfolio risks of 12%, 14%, and 16%.

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 = estimateFrontierByRisk(p, [0.12, 0.14, 0.16]);

 display(pwgt);
pwgt = 

    0.3984    0.2659    0.1416
    0.3064    0.3791    0.4474
    0.0882    0.1010    0.1131
    0.2071    0.2540    0.2979

To obtain efficient portfolios that have targeted portfolio risks, the estimateFrontierByRisk function accepts one or more target portfolio risks and obtains efficient portfolios with the specified risks. Assume you have a universe of four assets where you want to obtain efficient portfolios with target portfolio risks of 12%, 20%, and 30%.

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 ];

rng(11);

p = PortfolioCVaR;
p = simulateNormalScenariosByMoments(p, m, C, 2000);
p = setDefaultConstraints(p);
p = setProbabilityLevel(p, 0.95);

pwgt = estimateFrontierByRisk(p, [0.12, 0.20, 0.30]);

display(pwgt);
pwgt = 

    0.5363    0.1388    0.0000
    0.2655    0.4990    0.3830
    0.0568    0.1239    0.1461
    0.1413    0.2383    0.4709

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

To obtain efficient portfolios that have targeted portfolio risks, the estimateFrontierByRisk function accepts one or more target portfolio risks and obtains efficient portfolios with the specified risks. Assume you have a universe of four assets where you want to obtain efficient portfolios with target portfolio risks of 12%, 20%, and 25%.

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 ];

rng(11);

p = PortfolioMAD;
p = simulateNormalScenariosByMoments(p, m, C, 2000);
p = setDefaultConstraints(p);

pwgt = estimateFrontierByRisk(p, [0.12, 0.20, 0.25]);

display(pwgt);
pwgt = 

    0.1613    0.0000    0.0000
    0.4777    0.2139    0.0037
    0.1118    0.1381    0.1214
    0.2492    0.6480    0.8749

The function rng() 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

Target values for portfolio risk, specified as a NumPorts vector.

Note

If any TargetRisk values are outside the range of risks for efficient portfolios, the target risk is replaced with the minimum or maximum efficient portfolio risk, depending on whether the target risk is below or above the range of efficient portfolio risks.

Data Types: double

Output Arguments

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Optimal portfolios on the efficient frontier with specified target returns from TargetRisk, returned as a NumAssets-by-NumPorts matrix. pwgt is returned for a Portfolio, PortfolioCVaR, or PortfolioMAD input object (obj).

Purchases relative to an initial portfolio for optimal portfolios on the efficient frontier, returned as NumAssets-by-NumPorts matrix.

Note

If no initial portfolio is specified in obj.InitPort, that value is assumed to be 0 such that pbuy = max(0, pwgt) and psell = max(0, -pwgt).

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

Sales relative to an initial portfolio for optimal portfolios on the efficient frontier, returned as a NumAssets-by-NumPorts matrix.

Note

If no initial portfolio is specified in obj.InitPort, that value is assumed to be 0 such that pbuy = max(0, pwgt) and psell = max(0, -pwgt).

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

Tips

You can also use dot notation to estimate optimal portfolios with targeted portfolio risks.

[pwgt, pbuy, psell] = obj.estimateFrontierByRisk(TargetRisk);

Introduced in R2011a

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