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Estimate Mean and Covariance for Returns

Evaluate mean and covariance for portfolio asset returns, including assets with missing data and financial time series data


PortfolioCreate Portfolio object for mean-variance portfolio optimization and analysis


getAssetMomentsObtain mean and covariance of asset returns from Portfolio object
setAssetMoments Set moments (mean and covariance) of asset returns for Portfolio object
estimateAssetMomentsEstimate mean and covariance of asset returns from data
setCostsSet up proportional transaction costs

Examples and How To

Asset Returns and Moments of Asset Returns Using Portfolio Object

Mean-variance portfolio optimization problems require estimates for the mean and covariance of asset returns.

Working with a Riskless Asset

The Portfolio object uses a separate RiskFreeRate property that stores the rate of return of a riskless asset.

Working with Transaction Costs

The difference between net and gross portfolio returns is transaction costs.

Asset Allocation Case Study

This example shows how to set up a basic asset allocation problem that uses mean-variance portfolio optimization with a Portfolio object to estimate efficient portfolios.

Portfolio Optimization Examples

The following sequence of examples highlights features of the Portfolio object in the Financial Toolbox™.

Leverage in Portfolio Optimization with a Risk-Free Asset

This example shows how to use the setBudget function for the Portfolio class to define the limits on the sum(AssetWeight_i) in risky assets.

Portfolio Optimization with Semicontinuous and Cardinality Constraints

This example shows how to use a Portfolio object to directly handle semicontinuous and cardinality constraints.

Black-Litterman Portfolio Optimization

This example shows the workflow to implement the Black-Litterman model with the Portfolio class.

Portfolio Optimization Using Factor Models

This example shows two approaches for using a factor model to optimize asset allocation under a mean-variance framework.

Portfolio Optimization Using a Social Performance Measure

This example shows how to use a Portfolio object for portfolio optimization that includes a social performance measure for the percentage of women on a company's board and group constraints.

Diversification of Portfolios

This example shows three techniques of asset diversification in a portfolio.


Portfolio Object Workflow

Portfolio object workflow for creating and modeling a mean-variance portfolio.

When to Use Portfolio Objects Over Optimization Toolbox

The three cases for using Portfolio, PortfolioCVaR, PortfolioMAD object are: always use, preferred use, and use Optimization Toolbox.