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# estimateScenarioMoments

Estimate mean and covariance of asset return scenarios

## Syntax

``````[ScenarioMean,ScenarioCovar] = estimateScenarioMoments(obj)``````

## Description

example

``````[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

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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.

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

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

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

Data Types: `object`

## Output Arguments

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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 `[]`.

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`