Linear Models and Time-Series Analysis

11Risk Prediction and Portfolio Optimization

Building on the framework from Chapter 10, we now consider some applications of univariate GARCH modeling when working with weekly, daily, or higher frequency financial asset returns data. Section 11.1 overviews their use in conjunction with prediction of value at risk (VaR) and expected shortfall (ES), along with a description of other methods designed for that purpose. Section 11.2 scratches the surface of multivariate GARCH modeling by presenting four such methods, all of which are such that estimation is primarily based on univariate GARCH, thus avoiding the curse of the dimensionality issue in estimation and other problems associated with some high‐dimensional (and highly parameterized) multivariate GARCH models that have been proposed. The most basic one is the constant‐conditional‐correlation GARCH, referred to as CCC, and its popular extension, dynamic CC, or DCC. These are used in Section 11.3 to introduce the basics of portfolio optimization, where also the so‐called univariate collapsing method for portfolio allocation is discussed, along with the concept of ES span.

11.1 Value at Risk and Expected Shortfall Prediction

The value‐at‐risk (VaR) and expected shortfall (ES) are among the most popular tail risk measures used in quantitative risk management. For continuous random variable with finite expected value, the ‐level ...