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# Portfolio

Portfolio object for mean-variance portfolio optimization and analysis

## Description

The Portfolio object implements mean-variance portfolio optimization. Portfolio objects support functions that are specific to mean-variance portfolio optimization.

The main workflow for portfolio optimization is to create an instance of a `Portfolio` object that completely specifies a portfolio optimization problem and to operate on the `Portfolio` object using supported functions to obtain and analyze efficient portfolios. A mean-variance optimization problem is completely specified with the following three elements:

• A universe of assets with estimates for the prospective mean and covariance of asset total returns for a period of interest.

• A portfolio set that specifies the set of portfolio choices in terms of a collection of constraints.

• A model for portfolio return and risk, which, for mean-variance optimization, is either the gross or net mean of portfolio returns and the standard deviation of portfolio returns.

After you specify these three elements in an unambiguous way, you can solve and analyze portfolio optimization problems. The simplest mean-variance portfolio optimization problem has:

• A mean and covariance of asset total returns

• Nonnegative weights for all portfolios that sum to `1` (the summation constraint is known as a budget constraint)

• Built-in models for portfolio return and risk that use the mean and covariance of asset total returns

Given mean and covariance of asset returns in the variables `AssetMean` and `AssetCovar`, this problem is completely specified by:

```p = Portfolio('AssetMean', AssetMean, 'AssetCovar', AssetCovar,... 'LowerBound', 0, 'UpperBudget',1, 'LowerBudget',1)```
or equivalently by:
```p = Portfolio; p = setAssetMoments(p, AssetMean, AssetCovar); p = setDefaultConstraints(p);```

For more information on the workflow when using Portfolio objects, see Portfolio Object Workflow and for more detailed information on the theoretical basis for mean-variance optimization, see Portfolio Optimization Theory.

## Create Object

To create a `Portfolio` object, use the `Portfolio` function. For more details on working with a Portfolio object, see:

## Properties

 Portfolio Properties Manage Portfolio object for mean-variance portfolio optimization and analysis

## Object Functions

 `setAssetList` Set up list of identifiers for assets `setInitPort` Set up initial or current portfolio `setDefaultConstraints` Set up portfolio constraints with nonnegative weights that sum to 1 `getAssetMoments` Obtain mean and covariance of asset returns from Portfolio object `setAssetMoments` Set moments (mean and covariance) of asset returns for Portfolio object `estimateAssetMoments` Estimate mean and covariance of asset returns from data `setCosts` Set up proportional transaction costs `addEquality` Add linear equality constraints for portfolio weights to existing constraints `addGroupRatio` Add group ratio constraints for portfolio weights to existing group ratio constraints `addGroups` Add group constraints for portfolio weights to existing group constraints `addInequality` Add linear inequality constraints for portfolio weights to existing constraints `getBounds` Obtain bounds for portfolio weights from portfolio object `getBudget` Obtain budget constraint bounds from portfolio object `getCosts` Obtain buy and sell transaction costs from portfolio object `getEquality` Obtain equality constraint arrays from portfolio object `getGroupRatio` Obtain group ratio constraint arrays from portfolio object `getGroups` Obtain group constraint arrays from portfolio object `getInequality` Obtain inequality constraint arrays from portfolio object `getOneWayTurnover` Obtain one-way turnover constraints from portfolio object `setGroups` Set up group constraints for portfolio weights `setInequality` Set up linear inequality constraints for portfolio weights `setBounds` Set up bounds for portfolio weights `setBudget` Set up budget constraints `setCosts` Set up proportional transaction costs `setDefaultConstraints` Set up portfolio constraints with nonnegative weights that sum to 1 `setEquality` Set up linear equality constraints for portfolio weights `setGroupRatio` Set up group ratio constraints for portfolio weights `setInitPort` Set up initial or current portfolio `setOneWayTurnover` Set up one-way portfolio turnover constraints `setTurnover` Set up maximum portfolio turnover constraint `setTrackingPort` Set up benchmark portfolio for tracking error constraint `setTrackingError` Set up maximum portfolio tracking error constraint `checkFeasibility` Check feasibility of input portfolios against portfolio object `estimateBounds` Estimate global lower and upper bounds for set of portfolios `estimateFrontier` Estimate specified number of optimal portfolios on the efficient frontier `estimateFrontierByReturn` Estimate optimal portfolios with targeted portfolio returns `estimateFrontierByRisk` Estimate optimal portfolios with targeted portfolio risks `estimateFrontierLimits` Estimate optimal portfolios at endpoints of efficient frontier `plotFrontier` Plot efficient frontier `estimateMaxSharpeRatio` Estimate efficient portfolio to maximize Sharpe ratio for Portfolio object `estimatePortMoments` Estimate moments of portfolio returns for Portfolio object `estimatePortReturn` Estimate mean of portfolio returns `estimatePortRisk` Estimate portfolio risk according to risk proxy associated with corresponding object `setSolver` Choose main solver and specify associated solver options for portfolio optimization

## Examples

expand all

Create efficient portfolios:

```load CAPMuniverse p = Portfolio('AssetList',Assets(1:12)); p = estimateAssetMoments(p, Data(:,1:12),'missingdata',true); p = setDefaultConstraints(p); plotFrontier(p); pwgt = estimateFrontier(p, 5); pnames = cell(1,5); for i = 1:5 pnames{i} = sprintf('Port%d',i); end Blotter = dataset([{pwgt},pnames],'obsnames',p.AssetList); disp(Blotter); ```
``` Port1 Port2 Port3 Port4 Port5 AAPL 0.017926 0.058247 0.097816 0.12955 0 AMZN 0 0 0 0 0 CSCO 0 0 0 0 0 DELL 0.0041906 0 0 0 0 EBAY 0 0 0 0 0 GOOG 0.16144 0.35678 0.55228 0.75116 1 HPQ 0.052566 0.032302 0.011186 0 0 IBM 0.46422 0.36045 0.25577 0.11928 0 INTC 0 0 0 0 0 MSFT 0.29966 0.19222 0.082949 0 0 ORCL 0 0 0 0 0 YHOO 0 0 0 0 0 ```

## References

For a complete list of references for the Portfolio object, see Portfolio Optimization.