Market Risk Analysis, Value at Risk Models (The Wiley Finance Series, Band 4) - Hardcover

Alexander, Carol

Hardcover

ISBN 10: 0470997885 ISBN 13: 9780470997888

Verlag: Wiley, 2009

Inhaltsangabe

Written by leading market risk academic, Professor Carol Alexander, Value-at-Risk Models forms part four of the Market Risk Analysis four volume set. Building on the three previous volumes this book provides by far the most comprehensive, rigorous and detailed treatment of market VaR models. It rests on the basic knowledge of financial mathematics and statistics gained from Volume I, of factor models, principal component analysis, statistical models of volatility and correlation and copulas from Volume II and, from Volume III, knowledge of pricing and hedging financial instruments and of mapping portfolios of similar instruments to risk factors. A unifying characteristic of the series is the pedagogical approach to practical examples that are relevant to market risk analysis in practice.

All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the the accompanying CD-ROM . Empirical examples and case studies specific to this volume include:

• Parametric linear value at risk (VaR)models: normal, Student t and normal mixture and their expected tail loss (ETL);
• New formulae for VaR based on autocorrelated returns;
• Historical simulation VaR models: how to scale historical VaR and volatility adjusted historical VaR;
• Monte Carlo simulation VaR models based on multivariate normal and Student t distributions, and based on copulas;
• Examples and case studies of numerous applications to interest rate sensitive, equity, commodity and international portfolios;
• Decomposition of systematic VaR of large portfolios into standard alone and marginal VaR components;
• Backtesting and the assessment of risk model risk;
• Hypothetical factor push and historical stress tests, and stress testing based on VaR and ETL.

Über diesen Titel

Über die Autorin bzw. den Autor

Carol Alexander is a Professor of Risk Management at the ICMA Centre, University of Reading, and Chair of the Academic Advisory Council of the Professional Risk Manager’s International Association (PRMIA). She is the author of Market Models: A Guide to Financial Data Analysis (John Wiley & Sons Ltd, 2001) and has been editor and contributor of a very large number of books in finance and mathematics, including the multi-volume Professional Risk Manager’s Handbook (McGraw-Hill, 2008 and PRMIA Publications). Carol has published nearly 100 academic journal articles, book chapters and books, the majority of which focus on financial risk management and mathematical finance.

Professor Alexander is one of the world’s leading authorities on market risk analysis. For further details, see www.carolalexander.org

Von der hinteren Coverseite

Written by leading market risk academic, Professor Carol Alexander, VALUE-AT-RISK MODELS forms part four of the MARKET RISK ANALYSIS four volume set. Building on the three previous volumes this book provides by far the most comprehensive, rigorous and detailed treatment of market VaR models. It rests on the basic knowledge of financial mathematics and statistics gained from Volume I, of factor models, principal component analysis, statistical models of volatility and correlation and copulas from Volume II and, from Volume III, knowledge of pricing and hedging financial instruments and of mapping portfolios of similar instruments to risk factors. A unifying characteristic of the series is the pedagogical approach to practical examples that are relevant to market risk analysis in practice.

All together, the MARKET RISK ANALYSIS four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the accompanying website. Excel examples and case studies provided with this volume include:

• Parametric linear value at risk (VaR) models: normal, Student t and normal mixture and their expected tail loss (ETL);
• New formulae for VaR based on autocorrelated returns;
• Historical simulation VaR models: how to scale historical VaR and volatility adjusted historical VaR;
• Monte Carlo simulation VaR models based on multivariate normal and Student t distributions, and based on copulas;
• Examples and case studies of numerous applications to interest rate sensitive, equity, commodity and international portfolios;
• Decomposition of systematic VaR of large portfolios into stand-alone and marginal VaR components;
• Backtesting and the assessment of risk model risk;
• Hypothetical and historical stress tests, liquidity adjustment to VaR, and stress testing based on VaR and ETL.

Aus dem Klappentext

MARKET RISK ANALYSIS is a series of four volumes:

VOLUME I: Quantitative Methods in Finance

VOLUME II: Practical Financial Econometrics

VOLUME III: Pricing, Hedging and Trading Financial Instruments

VOLUME IV: Value-at-Risk Models

Although the four volumes are very much interlinked, each containing numerous cross-references to other volumes, they are written as self-contained texts.

VOLUME I covers the essential mathematical and financial background for subsequent volumes. There are six comprehensive chapters covering all the calculus, linear algebra, probability and statistics, numerical methods and portfolio mathematics that are necessary for market risk analysis. It is a complete and pedagogical introduction to quantitative methods applied to finance.

VOLUME II provides a detailed understanding of financial econometrics, with a unique focus on applications to asset pricing, fund management and market risk analysis. It covers equity factor models, including a detailed analysis of the Barra model and tracking error, principal component analysis, volatility and correlation, GARCH, cointegration, copulas, Markov switching, quantile regression, discrete choice models, non-linear regression, forecasting and model evaluation.

VOLUME III has five extensive chapters on the pricing, hedging and trading of bonds and swaps, futures and forwards, options and volatility, and detailed descriptions of mapping portfolios of these financial instruments to their risk factors. There are numerous examples, all coded in interactive Excel spreadsheets, including many pricing formulae for exotic options but excluding the calibration of stochastic volatility models, for which Matlab code is provided.

VOLUME IV builds on the three previous volumes to provide a comprehensive and detailed treatment of market VaR models. The exposition starts at an elementary level but, as in all the other volumes, the pedagogical approach accompanied by numerous interactive Excel spreadsheets allows readers to experience the application of parametric linear, historical simulation and Monte Carlo VaR models to increasingly complex portfolios. Starting with simple positions, readers are soon applying risk models to large international securities portfolios, commodity futures, path dependent options and much else. This rigorous treatment includes many new results as well as applications to regulatory and economic capital allocation, measurement of VaR model risk and stress testing.

Each volume is accompanied by a website which features numerous interactive Excel spreadsheets that illustrate the vast majority of the problems and case studies in these texts. For further information see the accompanying website.

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Market Risk Analysis

Volume IV: Value at Risk ModelsBy Carol Alexander

John Wiley & Sons

Copyright © 2008 Carol Alexander
All right reserved.
ISBN: 978-0-470-99788-8

Chapter One

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. 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 now use some form of value at risk (VaR) as a risk metric. This almost universal adoption of VaR has sparked a rigorous debate. Many quants and academics argue against the metric because it is not necessarily sub-additive, which contradicts the principal of diversification and hence also the foundations of modern portfolio theory. Moreover, there is a closely associated risk metric, the conditional VaR, or what I prefer to call the expected tail loss (ETL) because the terminology is more descriptive, that is sub-additive. And it is very simple to estimate ETL once the firm has developed a VaR model, so why not use ETL instead of VaR? Readers are recommended the book by Szeg (2004) to learn more about this debate.

The attractive features of VaR as a risk metric are as follows:

It corresponds to an amount that could be lost with some chosen probability. It measures the risk of the risk factors as well as the risk factor sensitivities. It can be compared across different markets and different exposures. It is a universal metric that applies to all activities and to all types of risk. It can be measured at any level, from an individual trade or portfolio, up to a single enterprise-wide VaR measure covering all the risks in the firm as a whole. When aggregated (to find the total VaR of larger and larger portfolios) or disaggregated (to isolate component risks corresponding to different types of risk factor) it takes account of dependencies between the constituent assets or portfolios.

The purpose of this chapter is to introduce VaR in the context of other 'traditional' risk metrics that have been commonly used in the finance industry. The assessment of VaR is usually more complex than the assessment of these traditional risk metrics, because it depends on the multivariate risk factor return distribution and on the dynamics of this distribution, as well as on the risk factor mapping of the portfolio. We term the mathematical models that are used to derive the risk metric, the risk model and the mathematical technique that is applied to estimate the risk metrics from this model (e.g. using some type of simulation procedure) the resolution method.

Although VaR and its related measures such as ETL and benchmark VaR have recently been embraced almost universally, the evolution of risk assessment in the finance industry has drawn on various traditional risk metrics that continue to be used alongside VaR. Broadly speaking, some traditional risk metrics only measure sensitivity to a risk factor, ignoring the risk of the factor itself. For instance, the beta of a stock portfolio or the delta and gamma of an option portfolio are examples of price sensitivities. Other traditional risk metrics measure the risk relative to a benchmark, and we shall be introducing some of these metrics here, including the omega and kappa indices that are currently favoured by many fund managers.

The outline of the chapter is as follows. Section IV.1.2 explains how and why risk assessment in banking has evolved separately from risk assessment in portfolio management. Section IV.1.3 introduces a number of downside risk metrics that are commonly used in portfolio management. These are so called because they focus only on the risk of underperforming a benchmark, ignoring the 'risk' of outperforming the benchmark.

The reminder of the chapter focuses on VaR and its associated risk metrics. We use the whole of Section IV.1.4 to provide a thorough definition of market VaR. For instance, when VaR is used to assess risks over a long horizon, as it often is in portfolio management, we should adjust the risk metric for any difference between the expected return and the risk free or benchmark return. However, a non-zero expected excess return has negligible effect when the risk horizon for the VaR estimate is only a few days, as it usually is for banks, and so some texts simply ignore this effect.

Section IV.1.5 lays some essential foundations for the rest of this book by stating some of the basic principles of VaR measurement. These principles are illustrated with simple numerical examples where the only aim is to measure the VaR

at the portfolio level, and where

the portfolio returns are independent and identically distributed (i.i.d.).

Section IV.1.6 begins by stressing the importance of measuring VaR at the risk factor level: without this we could not quantify the main sources of risk. This section also includes two simple examples of measuring the systematic VaR, i.e. the VaR that is captured by the entire risk factor mapping. We consider two examples: an equity portfolio that has been mapped to a broad market index and a cash-flow portfolio that has been mapped to zero-coupon interest rates at standard maturities.

Section IV.1.7 discusses the aggregation and disaggregation of VaR. One of the many advantages of VaR is that is can be aggregated to measure the total VaR of larger and larger portfolios, taking into account diversification effects arising from the imperfect dependency between movements in different risk factors. Or, starting with total risk factor VaR, i.e. systematic VaR, we can disaggregate this into stand-alone VaR components, each representing the risk arising from some specific risk factors. Since we take account of risk factor dependence when we aggregate VaR, the total VaR is often less than the sum of the stand-alone VaRs. That is, VaR is often sub-additive. But it does not have to be so, and this is one of the main objections to using VaR as a risk metric. We conclude...

Details zur Ausgabe

• Verlag: Wiley
• Erscheinungsdatum: 2009
• Sprache: Englisch
• ISBN 10: 0470997885
• ISBN 13: 9780470997888
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 496
• Kontakt zum Hersteller: Wiley-VCH GmbH; product_safety@wiley.com; ; Boschstrasse 12; Weinheim; 69469; Deutschland