Follow a sequence of examples that highlight features of the Portfolio object. Specifically, the examples use the Portfolio object to show how to set up mean-variance portfolio optimization problems that focus on the two-fund theorem, the impact of transaction costs and turnover constraints, how to obtain portfolios that maximize the Sharpe ratio, and how to set up two popular hedge-fund strategies — dollar-neutral and 130-30 portfolios.

Demonstrates optimizing a portfolio to maximize the information ratio relative to a market benchmark.

Perform backtesting of portfolio strategies using a backtesting framework. Backtesting is a useful tool to compare how investment strategies perform over historical or simulated market data. This example develops five different investment strategies and then compares their performance after running over a one-year period of historical stock data. The backtesting framework is implemented in two Financial Toolbox™ classes: backtestStrategy and backtestEngine.

Perform backtesting of portfolio strategies that incorporate investment signals in their trading strategy. The term signals includes any information that a strategy author needs to make with respect to trading decisions outside of the price history of the assets. Such information can include technical indicators, the outputs of machine learning models, sentiment data, macroeconomic data, and so on. This example uses three simple investment strategies based on derivative signal data:

Construct trading strategies using a deep learning model and then backtest the strategies using the Financial Toolbox™ backtesting framework. The example uses Deep Learning Toolbox™ to train a predictive model from a set of time series and demonstrates the steps necessary to convert the model output into trading signals. It builds a variety of trading strategies that backtest the signal data over a 5-year period.

Use a Portfolio object to minimize the variance, maximize return, and maximize the average percentage of women on a company's board. The same workflow can be applied with other Environmental, Social and Governance (ESG) criteria, such as an ESG score, a climate, or a temperature score.

Include qualitative factors for environmental, social, and corporate governance (ESG) in the portfolio selection process. The example extends the traditional mean-variance portfolio using a Portfolio object to include the ESG metric. First, the estimateFrontier function computes the mean-variance efficient frontier for different ESG levels. Then, the example illustrates how to combine the ESG performance measure with portfolio diversification techniques. Specifically, it introduces hybrid models that use the Herfindahl-Hirshman (HH) index and the most diversified portfolio (MDP) approach using the estimateCustomObjectivePortfolio function. Finally, the backtestEngine framework compares the returns and behavior of the different ESG strategies.

Use riskBudgetingPortfolio to create a risk budgeting portfolio and portfolioRiskContribution to compute the risk contribution of the assets in the portfolio.

Use backtesting with a risk parity or equal risk contribution strategy rebalanced approximately every month as a risk-based indexation. In this example, you use the backtesting engine (backtestEngine) to create the risk parity strategy, that all assets in the portfolio contribute equally to the risk of the portfolio at each rebalancing period.

Compute a hierarchical risk parity (HRP) portfolio. You can use HRP as a technique for portfolio diversification where the assets are divided and weighted according to a hierarchical tree structure. The weights of the assets within a cluster and between clusters can be assigned in many ways. A few ideas of the ways to allocate the weights are:

Use a Portfolio object to construct an optimal portfolio of 10, 20, and 30 year treasuries that will be held for a period of one month. The workflow for the overall asset allocation process is:

Prepare data, create a brinsonAttribution object, and then analyze the performance attribution with respect to category (sector) weights and returns. In this example, you use the categoryAttribution, categoryReturns, categoryWeights, totalAttribution, and summary functions for the anlaysis.

Include qualitative factors for environmental, social, and corporate governance (ESG) in the portfolio selection process. The example extends the traditional mean-variance portfolio using a Portfolio object to include the ESG metric. First, the estimateFrontier function computes the mean-variance efficient frontier for different ESG levels. Then, the example illustrates how to combine the ESG performance measure with portfolio diversification techniques. Specifically, it introduces hybrid models that use the Herfindahl-Hirshman (HH) index and the most diversified portfolio (MDP) approach using the estimateCustomObjectivePortfolio function. Finally, the backtestEngine framework compares the returns and behavior of the different ESG strategies.

Three techniques of asset diversification in a portfolio using the estimateCustomObjectivePortfolio function with a Portfolio object. The purpose of asset diversification is to balance the exposure of the portfolio to any given asset to reduce volatility over a period of time. Given the sensitivity of the minimum variance portfolio to the estimation of the covariance matrix, some practitioners have added diversification techniques to the portfolio selection with the hope of minimizing risk measures other than the variance measures such as turnover, maximum drawdown, and so on.

A robust formulation of portfolio optimization with uncertainty in the assets returns. It uses estimateCustomObjectivePortfolio to solve a robust Portfolio problem for a maximum return problem with an ellipsoidal uncertainty. Robust portfolio optimization, in contrast to the deterministic Markowitz mean-variance formulation, considers the uncertainty in the parameters of the problem: the assets' expected returns and their covariance matrix. In the traditional mean-variance model, the mean and covariance are assumed to take the point-values of the historical mean and covariance. However, in robust optimization, the mean and covariance are live in a set that contains the most likely realizations, and the problem is optimized with respect to the worst possible outcome in that set.

Compute a portfolio that minimizes the tracking error subject to a benchmark portfolio. This example uses estimateCustomObjectivePortfolio to solve a problem for a minimum variance Portfolio with a tracking error penalty. The example also shows how to add the tracking error as a "soft constraint" to any portfolio optimization problem. The tracking error measures the standard deviation of the divergence between a portfolio's return and that of a benchmark.

Use estimateCustomObjectivePortfolio to solve a portfolio problem for minimum tracking error with a net return constraint using a custom objective.