Pit

This document summarizes the steps for calculating Value-at-Risk (VaR) for a portfolio of equity assets using S-PLUS 7.0 and S+FinMetrics 2.0. Uncon-ditional VaR is computed using empirical quantiles, the normal distribution, and an extreme value theory (EVT) Pareto tail distribution. Conditional VaR is computed using GARCH models, GARCH+EVT. The VaR models are eval-uated by examining VaR violations in a backtesting environment. 1 Basic Concepts This section reviews some basic concepts of asset returns and portfolios, and defines the market risk concepts value-at-risk (VaR) and expected tail loss (ETL) (which is also called expected shortfall (ES)). 1.1 Asset Returns The portfolio consists of i = 1,..., N equity assets. Let Pit denote the price of asset i at time t. The one-period simple return on asset i between times t − 1 and t i