An Introduction to Value-at-Risk E-Book

Moorad Choudhry

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Securities and Investment Institute
• Sprache: Englisch

Seitenzahl: 248

Veröffentlichungsjahr: 2013

Beschreibung

The value-at-risk measurement methodology is a widely-used tool in financial market risk management. The fifth edition of Professor Moorad Choudhry's benchmark reference text An Introduction to Value-at-Risk offers an accessible and reader-friendly look at the concept of VaR and its different estimation methods, and is aimed specifically at newcomers to the market or those unfamiliar with modern risk management practices. The author capitalises on his experience in the financial markets to present this concise yet in-depth coverage of VaR, set in the context of risk management as a whole. Topics covered include: * Defining value-at-risk * Variance-covariance methodology * Portfolio VaR * Credit risk and credit VaR * Stressed VaR * Critique and VaR during crisis Topics are illustrated with Bloomberg screens, worked examples and exercises. Related issues such as statistics, volatility and correlation are also introduced as necessary background for students and practitioners. This is essential reading for all those who require an introduction to financial market risk management and risk measurement techniques. Foreword by Carol Alexander, Professor of Finance, University of Sussex.

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This fifth edition published by John Wiley & Sons Ltd in 2013

Copyright © 2013 Moorad Choudhry

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Contents

Series Page

Title

Copyright

Dedication

Foreword

Preface

Preface to the first edition

Acknowledgements

About the Author

Epigraph

Chapter 1: Introduction to Risk

Defining Risk

The Elements of Risk: Characterising Risk

Risk Management

Quantitative Measurement of Risk–Reward

Chapter 2: Volatility and Correlation

Statistical concepts

Volatility

The Normal Distribution and VaR

Correlation

Chapter 3: Value-at-Risk

What is VaR?

Methodology

How to Calculate VaR

Comparison between Methods

Comparing VaR Calculation for different Methodologies

Summary

Chapter 4: Value-at-Risk for Fixed Interest Instruments

Fixed Income Products

Interest Rate Products

Applying VaR for a FRA

VaR for an Interest Rate Swap

Applying VaR for a Bond Futures Contract

The Historical Method

Simulation Methodology

Bloomberg Screens

Chapter 5: Options: Risk and Value-at-Risk

Option Valuation Using the Black–Scholes Model

The Greeks

Risk Measurement

Applying VaR for Options

Chapter 6: Monte Carlo simulation and Value-at-risk

Introduction: Monte Carlo Simulation

Chapter 7: Regulatory Issues and Stress-Testing

Capital Adequacy

Stress-testing

The Crash and Basel III

Stressed VaR

Chapter 8: Credit Risk and Credit Value-at-Risk

Types of Credit Risk

Credit Ratings

Credit Derivatives

Modelling Credit Risk

CreditMetrics

Applications of credit VaR

Integrating the Credit Risk and Market Risk Functions

Chapter 9: A Review of Value-at-Risk

VaR in Crisis

Weaknesses Revealed

New Regulation and Development

Beyond the Current Paradigm

Exercises

Simple Exercises

Bank Risk Exposure and Value-at-Risk

Appendix: Taylor's Expansion

Abbreviations

Selected Bibliography

Index

Other Titles by the Author

Foreword

Far too many books have been written on Value-at-Risk (VaR). An Amazon search of texts with ‘Value at Risk’ in the title produces about 75 distinct results. The sheer quantity of literature on VaR is not surprising, since (for better or worse) this is the metric used by the world's major banks, and other financial firms, to determine both regulatory capital to cover market risks and economic capital to allocate internal resources efficiently. However, many textbooks have achieved relatively modest sales before fading quietly into obscurity.

This little book is one of the few that stand out against the rest, enduring now into its fifth edition, because it clearly fills two significant gaps in the market.

First, it is the perfect self-taught introduction to VaR for the non-specialist. Technical details are kept to the bare minimum as the text focuses on explaining the main concepts, with Moorad's characteristically accessible flair. He has an unusually deep, practical and comprehensive knowledge of risk (a brief scan of his bio shows that his work experience spans banking, trading, structuring and treasury management and that his market knowledge extends far beyond the interest rate and credit-sensitive instruments for which he is so well known) and a real empathy with his readers' needs.

Second, the book covers both market and credit risks, and within market risk it covers the basic building blocks of interest rate sensitive instruments and option portfolios. As such it is an ideal, self-contained textbook for university courses, or indeed for professional training. With seminars covering the worked examples provided, such a course could span approximately 12–18 contact hours of teaching at MBA or undergraduate level.

I am writing this foreword while stranded for the night on the snowbound A23 between Brighton and London. But, as my iPod battery fades, and 101 alternative uses for the energy come to mind, I am at least happy for my friend that I will make the publisher's deadline tomorrow. Indeed, Moorad has been a dear friend for many years. I very much admire his directness, honesty, knowledge, intelligence, kindness, warmth and modesty. I also think he is one of the best writers for not-too-quant-finance audiences of this era. His ideas are always sound and well argued, and he has a natural, fluid writing style which keeps the reader's attention by being both concise and crystal clear – a rare combination.

So, if you are seeking a short, sensible book on VaR that covers all the goal posts – eschewing unnecessary frills – and which is written in an exceptionally clear and readable style, then look no further. Moorad's Introduction to VaR, now in its fifth edition, is my strong recommendation.

Professor Carol Alexander

University of Sussex, UK

Preface

Here is how I began the Preface in the Fourth Edition of this book:

In 1998 I put together an introductory course on value-at-risk for the Securities Institute in London, at the invitation of Zena Doidge. This was a departure for me: my background and work experience up to then had not been in risk management; I had spent the previous 6 years as a bond and money markets trader. However due to personal circumstances I found myself in the position of teaching courses on various bond market subjects. This particular course forced me to actually research the topic though, and not just rely on practical experience and winging it as I might have done when I taught a course on (say) swaps or repo. Thus began an interest in writing, more specifically writing incorporating research and academic rigour rather than just practical experience. Anyway, I delivered the course in June or July that year and it seemed to go down okay. Then Zena suggested that the course companion that I had produced for the course might make a useful textbook on the subject. I had not thought at all about doing this, but as it happened the Institute had its own publishing arm, so there was no need for me to go out and try to get a publishing deal! Thus my first ever book was born, which was published in March 1999.

And here we are with the Fifth Edition of that book, and as I always keep telling myself, destined to be my last book!

Since that edition came out, we've had a banking crash and ongoing economic recession in the West. And VaR did not emerge from these events unscathed; it didn't have a good crisis. In 2012 JPMorgan reported a trading loss at its London-based investment office that was rumoured to be anything from 10 to 100 times greater than what the bank's VaR model had suggested was its maximum expected loss in a non-crash scenario. Is there any point calculating and reporting VaR if it is going to be this far away from reality?

To be fair to VaR, no mathematical model had a good 2007–08. It was only ever a risk measurement tool, and an estimate at that, and should always have been used under understood assumptions and limitations. Now that we know how inaccurate it can be, we can use its output more judiciously. For example, if one is going to set trading limits and risk limits within a VaR framework, one must ensure that the limit is well below what the model suggests it should be, so that if one is caught short, or the wrong way round, one is less surprised that the lost amount is so large. This book largely ignores the crash, except in the final chapter when we respond to the recent critiques of VaR with some recommendations for a change in approach.

At the end of the day VaR is still widely used in many banks, as well as by bank regulators, which is why we have deemed a revision of this book necessary. As well as a general update, the additional highlights in this Fifth Edition include:

a comparison of results using different VaR methodologies, using Bloomberg screens to illustrate;

an introduction to stressed VaR;

a new set of problems and exercises, with solutions supplied.

The final chapter provides a more than worthy finale to the book. I am pleased to enhance considerably the value of this Fifth Edition with the inclusion of a chapter written by Max Wong, who is in market risk management with RBS in Singapore. Max contributes a technical yet accessible critique of VaR and its performance at the time of the 2007–08 crash. He also makes some recommendations on how VaR might be better employed. In essence, he calls for a different approach to risk management itself, and shows there is still a place for VaR provided it is interpreted in the appropriate way. It's tremendous good fortune for me to have his expertise available here and I am sure readers will value his contribution.

As always we remain true to the spirit of the First Edition: that is, as befits a book directed at newcomers to the market, material is kept simple and accessible throughout. I welcome comments, please feel free to email me direct on [email protected]

All the best.

Moorad Choudhry

Surrey, England

4 January 2013

Preface to the First Edition

The concept of Value-at-Risk (VaR) has become a mainstay of financial markets risk management since its introduction by JPMorgan in 1994. An increasing number of banks and securities houses, and corporates, now use VaR as their main tool for providing management information on the size of their risk exposure. Initially VaR was used to measure the extent of market risk exposure; this was followed by the application of VaR methodology to the measurement of credit risk exposure.

As this is an introduction to the subject we have attempted to place VaR in context; hence the book begins by defining risk and describing the risk management function and other tools of risk measurement in the financial markets. VaR is best viewed as a tool within an overall risk management framework and hopefully the contents within will communicate this to the reader. An integrated risk management function within a bank or securities house will wish to incorporate VaR as part of its overall risk exposure and control framework. When such a framework is effective it serves an important purpose in providing comfort to a firm's shareholders that the management of trading, market and credit risk is no longer a significant cause for concern. At this point VaR as a risk measurement tool might be said to have come of age, and perhaps have assisted in the realisation of shareholder value.

This book has been written for those with little or no previous understanding of or exposure to the concept of risk management and Value-at-Risk; however, it also describes the subject in sufficient depth to be of use as a reference to a more experienced practitioner. It is primarily aimed at front office, middle office and back office banking and fund management staff who are involved to some extent in risk management. Others including corporate and local authority treasurers may wish to refer to the contents. Undergraduate and postgraduate students and MBA students specialising in financial markets will also find this book useful as a reference text. Comments on the text should be sent to the author care of the Securities Institute Services.

Moorad Choudhry

14 December 1998

Acknowledgements

First Edition

Parts of this book were originally written for the introductory course on Value-at-Risk run by the Securities Institute in London. My thanks to Zena Doidge at the Institute, whom it was a pleasure to work with, for giving me the opportunity to teach this course. Thanks to Debra Maddison in the Institute's publishing department, and Simon Chapman and Kalbinder Dhillon for graphics help.

I would also like to thank Richard Thornton at KPMG for lending me his book on VaR.

Fourth Edition

Love, affection and respect to Paul Claxton, Harry Cross, Abukar Ali, Didier Joannas, Khurram Butt, Michael Nicoll, Mo Dualeh, Phil Broadhurst, and all those to whom I want to tell that it's a privilege to call my friends.

Nothing lasts forever. But then again, some things never change …

Fifth Edition

Thanks to the Raynes Park Footy Boys. And to the lads in RBS GBM Treasury, CBD Treasury and Group Treasury that I played footy and volleyball with…

About the Authors

Moorad Choudhry is Head of Treasury, Corporate Banking Division at The Royal Bank of Scotland plc, in London. He was previously Head of Treasury at Europe Arab Bank, Head of Treasury at KBC Financial Products, and Vice President in Structured Finance Services at JPMorgan Chase Bank.

He is Visiting Professor at the Department of Mathematical Sciences, Brunel University, and Visiting Teaching Fellow at the Department of Management, Birkbeck, University of London.

Moorad is a Fellow of the Chartered Institute for Securities & Investment, a Fellow of the ifs-School of Finance, a Fellow of the Global Association of Risk Professionals, and a Fellow of the Institute of Sales and Marketing Management. He is Managing Editor of the International Journal of Monetary Economics and Finance, and a member of the Editorial Boards of Qualitative Research in Financial Markets, Securities and Investment Review, the Journal of Structured Finance, and American Securitization.

Moorad is Vice-Chair of the Board of Directors of PRMIA.

Max Wong heads the VaR model validation team at The Royal Bank of Scotland. Prior to this, he worked in roles as market strategist, futures trader and financial analyst at various financial institutions. He was an open outcry pit trader during the Asian crisis in 1997 and a quant risk manager during the credit crisis in 2007. He holds a BSc degree in Physics and an MSc in Financial Engineering.

Max is author of Bubble Value at Risk: A Countercyclical Risk Management Approach, Revised Edition, John Wiley & Sons (2013).

Epigraph

Disappointments and setbacks have to be faced in life. There must be no recriminations. I had learnt this lesson when I was dropped from the Marlborough XI on the morning of our match against Rugby at Lord's. There is always something else ahead.

– Lt. Gen. Sir Hugh Stockwell, quoted in Turner, B. (2006), Suez 1956, London: Hodder & Stoughton

In my life, why do I give valuable time, to people who don't care if I live or die?

In my life, why do I give valuable time, to people who I'd much rather kick in the eye?

– The Smiths, Heaven Knows I'm Miserable Now, Rough Trade Records 1984

Chapter 1

Introduction to Risk

The risk management department was one of the fastest growing areas in investment and commercial banks during the 1990s, and again after the crash of 2008. A string of high-profile banking losses and failures, typified by the fall of Barings Bank in 1995, highlighted the importance of risk management to bank managers and shareholders alike. In response to the volatile and complex nature of risks that they were exposed to, banks set up specialist risk management departments, whose functions included both measuring and managing risk. As a value-added function, risk management can assist banks not only in managing risk, but also in understanding the nature of their profit and loss, and so help increase return on capital. It is now accepted that senior directors of banks need to be thoroughly familiar with the concept of risk management. One of the primary tools of the risk manager is value-at-risk (VaR), which is a quantitative measure of the risk exposure of an institution. For a while VaR was regarded as somewhat inaccessible, and only the preserve of mathematicians and quantitative analysts. Although VaR is indeed based on statistical techniques that may be difficult to grasp for the layman, its basic premise can, and should, be explained in straightforward fashion, in a way that enables non-academics to become comfortable with the concept. The problem with VaR is that while it was only ever a measure, based on some strong assumptions, of approximate market risk exposure (it is unsuited to measuring risk exposure in the banking book), it suffers in the eyes of its critics in having the cachet of science. This makes it arcane and inaccessible, while paradoxically being expected to be much more accurate than it was ever claimed to be. Losses suffered by banks during the crash of 2007–08 were much larger than any of their VaR values, which is where the measure comes in for criticism. But we can leave that aside for now, and concentrate just on introducing the technicalities.

Later in the book we describe and explain the calculation and application of VaR. We begin here with a discussion of risk.

Defining Risk

Any transaction or undertaking with an element of uncertainty as to its future outcome carries an element of risk: risk can be thought of as uncertainty. To associate particular assets such as equities, bonds or corporate cash flows with types of risk, we need to define ‘risk’ itself. It is useful to define risk in terms of a risk horizon, the point at which an asset will be realised, or turned into cash. All market participants, including speculators, have an horizon, which may be as short as a half-day. Essentially then, the horizon is the time period relating to the risk being considered.

Once we have established a notion of horizon, a working definition of risk is the uncertainty of the future total cash value of an investment on the investor's horizon date. This uncertainty arises from many sources. For participants in the financial markets risk is essentially a measure of the volatility of asset returns, although it has a broader definition as being any type of uncertainty as to future outcomes. The types of risk that a bank or securities house is exposed to as part of its operations in the bond and capital markets are characterised below.

The Elements of Risk: Characterising Risk

Banks and other financial institutions are exposed to a number of risks during the course of normal operations. The different types of risk are broadly characterised as follows:

Market risk

– risk arising from movements in prices in financial markets. Examples include foreign exchange (

FX

) risk, interest rate risk and basis risk. In essence market risk applies to ‘tradeable’ instruments, ones that are

marked-to-market

in a trading book, as opposed to assets that are held to maturity, and never formally repriced, in a banking book.

Credit risk

– something called

issuer risk

refers to risk that a customer will default. Examples include sovereign risk, marginal risk and

force majeure

risk.

Liquidity risk

– this refers to two different but related issues: for a Treasury or money markets’ person, it is the risk that a bank has insufficient funding to meet commitments as they arise. That is, the risk that funds cannot be raised in the market as and when required. For a securities or derivatives trader, it is the risk that the market for assets becomes too thin to enable fair and efficient trading to take place. This is the risk that assets cannot be sold or bought as and when required. We should differentiate therefore between funding liquidity and trading liquidity whenever using the expression

liquidity

.

Operational risk

– risk of loss associated with non-financial matters such as fraud, system failure, accidents and ethics.

Table 1.1

assigns sources of risk for a range of fixed interest, FX, interest rate derivative and equity products. The classification has assumed a 1-year horizon, but the concepts apply to any time horizon.

Table 1.1 Characterising risk.

Forms of market risk

Market risk reflects the uncertainty as to an asset's price when it is sold. Market risk is the risk arising from movements in financial market prices. Specific market risks will differ according to the type of asset under consideration:

Currency risk

– this arises from exposure to movements in FX rates. A version of currency risk is

transaction

risk, where currency fluctuations affect the proceeds from day-to-day transactions.

Interest rate risk

– this arises from the impact of fluctuating interest rates and will directly affect any entity borrowing or investing funds. The most common exposure is simply to the level of interest rates but some institutions run positions that are exposed to changes in the shape of the yield curve. The basic risk arises from revaluation of the asset after a change in rates.

Equity risk

– this affects anyone holding a portfolio of shares, which will rise and fall with the level of individual share prices and the level of the stock market.

Other market risk

– there are residual market risks which fall in this category. Among these are

volatility

risk, which affects option traders, and

basis

risk, which has a wider impact. Basis risk arises whenever one kind of risk exposure is hedged with an instrument that behaves in a similar, but not necessarily identical manner. One example would be a company using 3-month interest rate futures to hedge its commercial paper (

CP

) programme. Although eurocurrency rates, to which futures prices respond, are well correlated with CP rates, they do not invariably move in lock step. If CP rates moved up by 50 basis points but futures prices dropped by only 35 basis points, the 15-bps gap would be the basis risk in this case.

Other risks

Liquidity risk

– in banking, this refers to the risk that a bank cannot raise funds to refinance loans as the original borrowing becomes past due. It is sometimes also referred to as

rollover

risk. In other words, it refers to the risk of an inability to continue to raise funds to replace maturing liabilities. There is also another (related) liquidity risk, which refers to

trading liquidity

. This is the risk that an asset on the balance sheet cannot be sold at a previously perceived fair value, or cannot be sold at all, and hence experiences

illiquidity

.

Credit risk

– the risk that an

obligor

(the entity that has borrowed funds from you) defaults on the loan repayments.

Counterparty risk

– all transactions involve one or both parties in counterparty risk, the potential loss that can arise if one party were to default on its obligations. Counterparty risk is most relevant in the derivatives market, where every contract is marked-to-market daily and so a positive MTM is taken to the profit & loss (P&L) account. If the counterparty defaults before the contract has expired, there is risk that the actual P&L will not be realized. In the credit derivatives market, a counterparty that has sold protection on the third-party reference name on the credit derivative contract and which subsequently defaults will mean the other side to the trade is no longer protected against the default of that third party.

Reinvestment risk

– if an asset makes any payments before the investor's horizon, whether it matures or not, the cash flows will have to be reinvested until the horizon date. Since the reinvestment rate is unknown when the asset is purchased, the final cash flow is uncertain.

Sovereign risk

– this is a type of credit risk specific to a government bond. Post 2008, there is material risk of default by an industrialised country. A developing country may default on its obligation (or declare a debt ‘moratorium') if debt payments relative to domestic product reach unsustainable levels.

Prepayment risk

– this is specific to mortgage-backed and asset-backed bonds. For example, mortgage lenders allow the homeowner to repay outstanding debt before the stated maturity. If interest rates fall prepayment will occur, which forces reinvestment at rates lower than the initial yield.

Model risk

– some financial instruments are heavily dependent on complex mathematical models for pricing and hedging. If the model is incorrectly specified, is based on questionable assumptions or does not accurately reflect the true behaviour of the market, banks trading these instruments could suffer extensive losses.

Risk estimation

There are a number of different ways of approaching the estimation of market risk. The key factors determining the approach are the user's response to two questions:

Can the user accept the assumption of normality – is it reasonable to assume that market movements follow the normal distribution? If so, statistical tools can be employed.

Does the value of positions change linearly with changes in market prices? If not (as is typical for option positions where market movements are not very small), simulation techniques will be more useful.

Were the answers to both questions to be ‘yes’ then we could be comfortable using standard measures of risk such as duration and convexity (these concepts are covered later). If the answers are ‘no’ then we are forced to use scenario analysis combined with simulation techniques. If, as is more likely, the answer to the first question is ‘yes’ and the second ‘no’, then a combination of statistical tools and simulation techniques will be required.