# Documentation

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# Estimate Efficient Portfolios and Frontiers

Analyze efficient portfolios and efficient frontiers for portfolio

## Using Objects

 Portfolio Portfolio object for mean-variance portfolio optimization and analysis

## Functions

 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 and How To

Estimate Efficient Portfolios for Entire Efficient Frontier for Portfolio Object

The most basic way to obtain optimal portfolios is to obtain points over the entire range of the efficient frontier.

Obtaining Endpoints of the Efficient Frontier

Determine the range of returns from minimum to maximum to refine a search for a portfolio with a specific target return.

Obtaining Efficient Portfolios for Target Returns

To obtain efficient portfolios that have targeted portfolio returns, use the estimateFrontierByReturn function.

Obtaining Efficient Portfolios for Target Risks

To obtain efficient portfolios that have targeted portfolio risks, use the estimateFrontierByRisk function.

Efficient Portfolio That Maximizes Sharpe Ratio

Portfolios that maximize the Sharpe ratio are portfolios on the efficient frontier that satisfy a number of theoretical conditions in finance.

Estimate Efficient Frontiers for Portfolio Object

Given any portfolio, the functions estimatePortReturn, estimatePortRisk, and estimatePortMoments provide estimates for the return and risk.

Plotting the Efficient Frontier for a Portfolio Object

The plotFrontier function creates a plot of the efficient frontier for a given portfolio optimization problem.

Choosing and Controlling the Solver for Mean-Variance Portfolio Optimization

The default solver for mean-variance portfolio optimization is lcprog.

Asset Allocation Case Study

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

Portfolio Optimization Examples

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

## Concepts

Portfolio Object Workflow

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