# Estimate Efficient Portfolios and Frontiers

Analyze efficient portfolios and efficient frontiers for portfolio

## Objects

 `Portfolio` Create Portfolio object for mean-variance portfolio optimization and analysis

## Functions

expand all

 `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 `estimatePortSharpeRatio` Estimate Sharpe ratio of given portfolio weights 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 `setSolverMINLP` Choose mixed integer nonlinear programming (MINLP) solver 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 several 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.

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.

Mixed-Integer Quadratic Programming Portfolio Optimization: Problem-Based

This example shows how to solve a Mixed-Integer Quadratic Programming (MIQP) portfolio optimization problem using the problem-based approach.

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.

## Concepts

Portfolio Object Workflow

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

Choosing and Controlling the Solver for Mean-Variance Portfolio Optimization

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