Market Risk Analysis Volume IV: Value-at-Risk Models

IV.1

Value at Risk and Other Risk Metrics

IV.1.1 INTRODUCTION

A market risk metric is a measure of the uncertainty in the future value of a portfolio, i.e. a measure of uncertainty in the portfolio's return or profit and loss (P&L). Its fundamental purpose is to summarize the potential for deviations from a target or expected value. To determine the dispersion of a portfolio's return or P&L we need to know about the potential for individual asset prices to vary and about the dependency between movements of different asset prices. Volatility and correlation are portfolio risk metrics but they are only sufficient (in the sense that these metrics alone define the shape of a portfolio's return or P&L distribution) when asset or risk factor returns have a multivariate normal distribution. When these returns are not multivariate normal (or multivariate Student t) it is inappropriate and misleading to use volatility and correlation to summarize uncertainty in the future value of a portfolio.¹

Statistical models of volatility and correlation, and more general models of statistical dependency called copulas, are thoroughly discussed in Volume II of Market Risk Analysis. The purpose of the present introductory chapter is to introduce other types of risk metric that are commonly used by banks, corporate treasuries, portfolio management firms and other financial practitioners.

Following the lead from both regulators and large international banks during the mid-1990s, almost all financial institutions ...