Key Features

  • Mean-variance, MAD, and CVaR-based portfolio optimization
  • Cash flow analysis, risk analysis, financial time-series modeling, date math, and calendar math
  • Basic fixed-income analysis and option pricing
  • Regression and estimation with missing data
  • Technical indicators and financial charts
  • Monte Carlo simulations of SDE models
  • Credit scorecard modeling and analysis

Example of a financial modeling application for options and asset portfolios.


Asset Allocation and Portfolio Optimization

Financial Toolbox provides a comprehensive suite of portfolio optimization and analysis tools for performing capital allocation, asset allocation, and risk assessment. With these tools, you can:

  • Estimate asset return and total return moments from price or return data
  • Compute portfolio-level statistics, such as mean, variance, value at risk (VaR), and conditional value at risk (CVaR)
  • Perform portfolio optimization and analysis
  • Examine the time evolution of efficient portfolio allocations
  • Perform capital allocation
  • Account for turnover and transaction costs in portfolio optimization problems
Portfolio optimization application built using MATLAB, Financial Toolbox, and object-oriented design. The application enables the interactive selection of a portfolio, comparison to a benchmark, visualization, and reporting of key performance metrics.

Portfolio Construction and Analysis

The portfolio optimization object provides a tool for defining and solving portfolio optimization problems.

The toolbox supports three approaches to portfolio optimization:

  • Mean-variance portfolio optimization
  • Mean absolute deviation (MAD) portfolio optimization
  • Conditional value-at-risk (CVaR) portfolio optimization

Supported constraints include: linear inequality, linear equality, bound, budget, group, group ratio, average turnover, one-way turnover, minimum number of assets, and maximum number of assets.

Additionally, you can apply transaction costs on either gross or net portfolio return optimization. 

Efficient frontiers plot for a sample portfolio optimization problem at different turnover thresholds.


Error Checking and Portfolio Validation

The portfolio optimization object provides error checking during the portfolio construction phase. For complex problems defined with multiple constraints, validating your inputs to or outputs from the portfolio optimization can reduce error-checking time prior to solving the optimization problem. Methods to estimate bounds and check problem feasibility are available.


Efficient Portfolio and Efficient Frontiers

Depending on your goals, you can identify efficient portfolios or efficient frontiers. The portfolio optimization object provides methods for both. You can solve for efficient portfolios by providing one or more target risks or returns.

Additionally, you can model long-short portfolios with or without turnover constraints.

Plot of efficient frontiers with and without a turnover constraint of 130-30. The Sharpe-ratio maximized portfolio is marked with an X on the 130-30 efficient frontier.

Postprocessing and Trade Reporting

After you identify a portfolio’s risk and return, you can use the portfolio optimization object methods to:

  • Troubleshoot questionable results
  • Adjust the problem definition to move toward an efficient portfolio
  • Set up an asset trading record

The portfolio object supports the generation of a trade record as a dataset array. You can use the dataset array to keep track of purchases and sales of assets and to capture trades to execute.


Risk Analysis and Investment Performance

Financial Toolbox provides a comprehensive suite of tools for analyzing and assessing risk and investment performance.

Performance metrics include:

  • Sharpe ratio
  • Information ratio
  • Tracking error
  • Risk-adjusted return
  • Sample and expected lower partial moments
  • Maximum drawdown and expected maximum drawdown

The toolbox provides a collection of tools for credit risk analysis that enable you to:

  • Perform credit scorecard modeling
  • Preprocess and estimate transition probabilities from credit ratings data
  • Aggregate credit ratings data into categories
  • Convert from transition probabilities to credit quality thresholds and vice versa

Surface plot showing the relationship between the EMA, RSI parameters and Sharpe ratio.


Fixed-Income Analysis and Option Pricing

Cash Flow Analysis

Financial Toolbox offers time-value-of-money functionality to:

  • Calculate present and future values
  • Determine nominal, effective, and modified internal rates of return
  • Calculate amortization and depreciation
  • Determine the periodic interest rate paid on a loan or annuity

Basic SIA-Compliant Fixed-Income Security Analysis

The toolbox provides Securities Industry Association or SIA-compatible analytics are provided for pricing, yield curve modeling, and sensitivity analysis for government, corporate, and municipal fixed-income securities. Specific analytics include:

  • Complete cash flow date, cash flow amounts, and time-to-cash-flow mapping for a bond
  • Price and yield maturity
  • Duration and convexity

You can price stepped and zero-coupon bonds with Financial Instruments Toolbox.


Basic Option Pricing

With Financial Toolbox, you can:

  • Use a standard option pricing with Black and Black-Scholes formulas
  • Compute the option greeks, such as delta, gamma, and theta

With Financial Instruments Toolbox, you can price derivatives using a range of models and methods, including Heath-Jarrow-Morton and Cox-Ross-Rubinstein binomial models.

Plot showing the option greeks gamma (z-axis height) and delta (color) for a portfolio of call options.


Financial Time Series Analysis

Financial Toolbox provides a collection of tools for analyzing time series data in the financial markets. The toolbox supports:

  • Technical analysis
  • Charting and graphics

With Econometrics Toolbox™, you can perform time series analysis using various econometrics models. You can also load data in the tool directly from a file, database (with Database Toolbox™), or financial datafeed provider (with Datafeed Toolbox™).


Regression and Estimation with Missing Data

Financial Toolbox provides tools for performing multivariate normal regression with or without missing data. You can:

  • Perform common regressions based on the underlying model, such as seemingly unrelated regression (SUR)
  • Estimate log-likelihood function and standard errors for hypothesis testing
  • Complete calculations in the presence of missing data

Missing data estimation functionality helps you determine the effect of data quality on your models and simulations. For example, you can account for the effects of missing data on estimating coefficients of CAPM models or on calculating the efficient frontier of a portfolio of assets. Missing data effects can result in significantly different results.

Explore gallery (2 images)


Technical Indicators and Financial Charts

Financial Toolbox provides numerous well-known technical indicators, performance metrics, and specialized plots, including:

  • Moving averages
  • Oscillators, stochastics, indexes, and indicators
  • Maximum drawdown and expected maximum drawdown
  • Charts, including Bollinger bands, candlestick plots, and moving averages

Financial charts and technical indicators.


Monte Carlo Simulation of SDE Models

Financial Toolbox offers a variety of Stochastic Differential Equation (SDE) models. SDE models are used in many different ways, such as pricing financial derivatives, interest-rate modeling, risk analysis, and back-testing. Supported SDE models include:

  • Brownian Motion (BM)
  • Geometric Brownian Motion (GBM)
  • Constant Elasticity of Variance (CEV)
  • Cox-Ingersoll-Ross (CIR)
  • Hull-White/Vasicek (HWV)
  • Heston

Single path of a multi-dimensional market model.