Documentation

Using Portfolio Objects

Portfolio object for mean-variance portfolio optimization and analysis

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.

Examples

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Construct a Portfolio Object and Determine Efficient Portfolios

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    

Related Examples

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
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 standard deviation of portfolio returns (portfolio risk)
setSolver Choose main solver and specify associated solver options for portfolio optimization

Introduced in R2011a

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