Chapter 3 - Market Risk

Abstract

Different methodologies are available to a risk manager in order to calculate the value at risk (VaR) for trading positions exposed to market risks. One of the most well-known solutions is the variance–covariance approach, which assumes jointly normally distributed returns for either the risk factors or the benchmark assets that can be used to model the behavior of a given real portfolio. The variance–covariance method requires one first to select the key risk factors/benchmark assets and then to map the real portfolio into an equivalent portfolio exposed only to the key risk factors or benchmark assets. This step is conceptually simple but practically very relevant, since it will condition the quality of the final value at risk (VaR) estimate. After one completes the mapping phase, portfolio VaR measurement requires estimating volatilities and correlations of key risk factors or benchmark assets. There are different ways to calculate volatilities, and exponential weighted moving averages or GARCH models, which explicitly recognize that volatility is not constant through time, are usually the favorite solutions. An alternative to the variance–covariance approach is represented by simulation methods. In particular, historical simulations calculate VaR by reconstructing the return distribution of the current portfolio on any of the n past days, based on actual daily historical returns, and then identifying the desired percentile of the portfolio return distribution. VaR would be the difference between the current portfolio value and its value in the extreme percentile. VaR models can also be used under certain conditions to calculate minimum capital requirements for market risk, according to Basel Committee's 1996 Market Risk Amendment.