PRM Handbook Introduction and Contents

PRM Handbook Introduction and Contents

The Professional Risk Managers’ Handbook

A Comprehensive Guide to Current Theory and Best Practices

___________________________________________________

Edited by Carol Alexander and Elizabeth Sheedy

The Official Handbook for the PRM Certification

Updated May 2011


Contents Author Biographies

Section I – for PRM Exam I FINANCE THEORY, FINANCIAL INSTRUMENTS AND MARKETS Section I, Part A From PRM Handbook Volume I: Book 1 – GUIDE TO FINANCIAL THEORY APPLICATION I.A.0 INTEREST RATES AND TIME VALUE I.A.0.1 COMPOUNDING METHODS I.A.0.2 INTEREST RATES: NOMINAL, PERIODIC, CONTINUOUS OR EFFECTIVE I.A.1 RISK AND RISK AVERSION I.A.1.1 I.A.1.2 I.A.1.3 I.A.1.4 I.A.1.5 I.A.1.6 I.A.1.7

INTRODUCTION MATHEMATICAL EXPECTATIONS: PRICES OR UTILITIES? THE AXIOM OF INDEPENDENCE OF CHOICE MAXIMISING EXPECTED UTILITY ENCODING A UTILITY FUNCTION THE MEAN–VARIANCE CRITERION RISK-ADJUSTED PERFORMANCE MEASURES

I.A.2 PORTFOLIO MATHEMATICS I.A.2.1 I.A.2.2 I.A.2.3 I.A.2.4 I.A.2.5 I.A.2.6 I.A.2.7

MEANS AND VARIANCES OF PAST RETURNS MEAN AND VARIANCE OF FUTURE RETURNS MEAN–VARIANCE TRADEOFFS MULTIPLE ASSETS A HEDGING EXAMPLE SERIAL CORRELATION NORMALLY DISTRIBUTED RETURNS

I.A.3 CAPITAL ALLOCATION I.A.3.1 I.A.3.2 I.A.3.3 I.A.3.4 I.A.3.5 I.A.3.6 I.A.3.7 I.A.3.8

AN OVERVIEW MEAN–VARIANCE CRITERION EFFICIENT FRONTIER: TWO RISKY ASSETS ASSET ALLOCATION COMBINING THE RISK-FREE ASSET WITH RISKY ASSETS THE MARKET PORTFOLIO AND THE CML THE MARKET PRICE OF RISK AND THE SHARPE RATIO SEPARATION PRINCIPLE

I.A.4 THE CAPM AND MULTIFACTOR MODELS I.A.4.1 I.A.4.2 I.A.4.3 I.A.4.4 I.A.4.5 I.A.4.6

OVERVIEW CAPITAL ASSET PRICING MODEL SECURITY MARKET LINE PERFORMANCE MEASURES THE SINGLE-INDEX MODEL MULTIFACTOR MODELS AND THE APT

I.A.5 BASICS OF CAPITAL STRUCTURE I.A.5.1 I.A.5.2 I.A.5.3 I.A.5.4 I.A.5.5

INTRODUCTION MAXIMISING SHAREHOLDER VALUE, INCENTIVES AND AGENCY COSTS CHARACTERISTICS OF DEBT AND EQUITY CHOICE OF CAPITAL STRUCTURE MAKING THE CAPITAL STRUCTURE DECISION

2010 © The Professional Risk Managers’ International Association

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I.A.6 THE TERM STRUCTURE OF INTEREST RATES I.A.6.1 I.A.6.2 I.A.6.3 I.A.6.4

INTRODUCTION TO THE TERM STRUCTURE OF INTEREST RATES THEORIES OF THE TERM STRUCTURE TERM STRUCTURE MODELS USING TERM STRUCTURE MODELS TO EVALUATE BONDS

I.A.7 VALUING FORWARD CONTRACTS I.A.7.1 I.A.7.2 I.A.7.3 I.A.7.4

THE DIFFERENCE BETWEEN PRICING AND VALUATION FOR FORWARD CONTRACTS PRINCIPLES OF PRICING AND VALUATION FOR FORWARD CONTRACTS ON ASSETS PRINCIPLES OF PRICING AND VALUATION FOR FORWARD CONTRACTS ON INTEREST RATES THE RELATIONSHIP BETWEEN FORWARD AND FUTURES PRICES

I.A.8 BASIC PRINCIPLES OF OPTION PRICING I.A.8.1 I.A.8.2 I.A.8.3 I.A.8.4 I.A.8.5 I.A.8.6 I.A.8.7 I.A.8.8 I.A.8.9 I.A.8.10

FACTORS AFFECTING OPTION PRICES PUT–CALL PARITY ONE-STEP BINOMIAL MODEL AND THE RISKLESS PORTFOLIO DELTA NEUTRALITY AND SIMPLE DELTA HEDGING RISK-NEUTRAL VALUATION REAL VERSUS RISK-NEUTRAL THE BLACK–SCHOLES–MERTON PRICING FORMULA THE GREEKS IMPLIED VOLATILITY INTRINSIC VERSUS TIME VALUE

Section I, Part B From PRM Handbook - Volume I: Book 2 – GUIDE TO FINANCIAL INSTRUMENTS I.B.1 GENERAL CHARACTERISTICS OF BONDS I.B.1.1 I.B.1.2 I.B.1.3 I.B.1.4

DEFINITION OF A BULLET BOND TERMINOLOGY AND CONVENTION MARKET QUOTES NON-BULLET BONDS

I.B.2 THE ANALYSIS OF BONDS I.B.2.1 I.B.2.2 I.B.2.3 I.B.2.4 I.B.2.5 I.B.2.6 I.B.2.7 I.B.2.8 I.B.2.9

FEATURES OF BONDS NON-CONVENTIONAL BONDS PRICING A CONVENTIONAL BOND MARKET YIELD RELATIONSHIP BETWEEN BOND YIELD AND BOND PRICE DURATION HEDGING BOND POSITIONS CONVEXITY SUMMARY OF MARKET RISK ASSOCIATED WITH BONDS

I.B.3 FUTURES AND FORWARDS I.B.3.1 I.B.3.2. I.B.3.3 I.B.3.4 I.B.3.5 I.B.3.6 I.B.3.7 I.B.3.8

INTRODUCTION STOCK INDEX FUTURES CURRENCY FORWARDS AND FUTURES COMMODITY FUTURES FORWARD RATE AGREEMENTS SHORT-TERM INTEREST-RATE FUTURES T-BOND FUTURES STACK AND STRIP HEDGES


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I.B.4 SWAPS I.B.4.1 I.B.4.2 I.B.4.3 I.B.4.4 I.B.4.5 I.B.4.6 I.B.4.7

WHAT IS A SWAP? TYPES OF SWAPS ENGINEERING INTEREST RATE SWAPS RISKS OF SWAPS OTHER SWAPS USES OF SWAPS SWAP CONVENTIONS

I.B.5 VANILLA OPTIONS I.B.5.1 I.B.5.2 I.B.5.3 I.B.5.4 I.B.5.5

STOCK OPTIONS – CHARACTERISTICS AND PAYOFF DIAGRAMS AMERICAN VERSUS EUROPEAN OPTIONS STRATEGIES INVOLVING A SINGLE OPTION AND A STOCK SPREAD STRATEGIES OTHER STRATEGIES

I.B.6 CREDIT DERIVATIVES I.B.6.1 I.B.6.2 I.B.6.3 I.B.6.4 I.B.6.5 I.B.6.6 I.B.6.7 I.B.6.8

INTRODUCTION CREDIT DEFAULT SWAPS CREDIT-LINKED NOTES TOTAL RETURN SWAPS CREDIT OPTIONS AND NEW INVESTMENT INSTRUMENTS SYNTHETIC COLLATERALISED DEBT OBLIGATIONS GENERAL APPLICATIONS OF CREDIT DERIVATIVES UNINTENDED RISKS IN CREDIT DERIVATIVES

I.B.7 CAPS, FLOORS AND SWAPTIONS I.B.7.1 I.B.7.2 I.B.7.3 I.B.7.4 I.B.7.5 I.B.7.6

CAPS, FLOORS AND COLLARS: DEFINITION AND TERMINOLOGY PRICING CAPS, FLOORS AND COLLARS USES OF CAPS, FLOORS AND COLLARS SWAPTIONS: DEFINITION AND TERMINOLOGY PRICING SWAPTIONS USES OF SWAPTIONS

I.B.8 CONVERTIBLE BONDS I.B.8.1 I.B.8.2 I.B.8.3 I.B.8.4 I.B.8.5

INTRODUCTION CHARACTERISTICS OF CONVERTIBLES CAPITAL STRUCTURE IMPLICATIONS FOR BANKS MANDATORY CONVERTIBLES VALUATION AND RISK ASSESSMENT

I.B.9 SIMPLE EXOTICS I.B.9.1 I.B.9.2 I.B.9.3 I.B.9.4 I.B.9.5 I.B.9.6 I.B.9.7 I.B.9.8 I.B.9.9 I.B.9.10 I.B.9.11 I.B.9.12 I.B.9.13 I.B.9.14

INTRODUCTION A SHORT HISTORY CLASSIFYING EXOTICS NOTATION DIGITAL OPTIONS TWO ASSET OPTIONS QUANTOS SECOND-ORDER CONTRACTS DECISION OPTIONS AVERAGE OPTIONS OPTIONS ON BASKETS OF ASSETS BARRIER AND RELATED OPTIONS OTHER PATH-DEPENDENT OPTIONS RESOLUTION METHODS


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Section 1, Part C From PRM Handbook Volume I: Book 3 – GUIDE TO FINANCIAL MARKETS I.C.1 THE STRUCTURE OF FINANCIAL MARKETS I.C.1.1 I.C.1.2 I.C.1.3 I.C.1.4 I.C.1.5 I.C.1.6 I.C.1.7 I.C.1.8 I.C.1.9

INTRODUCTION GLOBAL MARKETS AND THEIR TERMINOLOGY DRIVERS OF LIQUIDITY LIQUIDITY AND FINANCIAL RISK MANAGEMENT EXCHANGES VERSUS OTC MARKETS TECHNOLOGICAL CHANGE POST-TRADE PROCESSING RETAIL AND WHOLESALE BROKERAGE NEW FINANCIAL MARKETS

I.C.2 THE MONEY MARKETS I.C.2.1 I.C.2.2 I.C.2.3 I.C.2.4

INTRODUCTION CHARACTERISTICS OF MONEY MARKET INSTRUMENTS DEPOSITS AND LOANS MONEY MARKET SECURITIES

I.C.3 BOND MARKETS I.C.3.1 I.C.3.2 I.C.3.3 I.C.3.4 I.C.3.5

INTRODUCTION THE PLAYERS BONDS BY ISSUERS THE MARKETS CREDIT RISK

I.C.4 THE FOREIGN EXCHANGE MARKET I.C.4.1 I.C.4.2 I.C.4.3 I.C.4.4 I.C.4.5 I.C.4.6

INTRODUCTION THE INTERBANK MARKET EXCHANGE-RATE QUOTATIONS DETERMINANTS OF FOREIGN EXCHANGE RATES SPOT AND FORWARD MARKETS STRUCTURE OF A FOREIGN EXCHANGE OPERATION

I.C.5 THE STOCK MARKET I.C.5.1 I.C.5.2 I.C.5.3 I.C.5.4 I.C.5.5 I.C.5.6 I.C.5.7 I.C.5.8 I.C.5.9

INTRODUCTION THE CHARACTERISTICS OF COMMON STOCK STOCK MARKETS AND THEIR PARTICIPANTS THE PRIMARY MARKET – IPOS AND PRIVATE PLACEMENTS THE SECONDARY MARKET – THE EXCHANGE VERSUS OTC MARKET TRADING COSTS BUYING ON MARGIN SHORT SALES AND STOCK BORROWING COSTS EXCHANGE-TRADED DERIVATIVES ON STOCKS

I.C.6 THE FUTURES MARKETS I.C.6.1 I.C.6.2 I.C.6.3 I.C.6.4 I.C.6.5 I.C.6.6 I.C.6.7 I.C.6.8

INTRODUCTION HISTORY OF FORWARD-BASED DERIVATIVES AND FUTURES MARKETS FUTURES CONTRACTS AND MARKETS OPTIONS ON FUTURES FUTURES EXCHANGES AND CLEARING HOUSES MARKET PARTICIPANTS – HEDGERS MARKET PARTICIPANTS – SPECULATORS MARKET PARTICIPANTS – MANAGED FUTURES INVESTORS


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I.C.7. THE STRUCTURE OF COMMODITIES MARKETS I.C.7.1 I.C.7.2 I.C.7.3 I.C.7.4 I.C.7.5 I.C.7.6

INTRODUCTION THE COMMODITY UNIVERSE AND ANATOMY OF MARKETS SPOT–FORWARD PRICING RELATIONSHIPS SHORT SQUEEZES, CORNERS AND REGULATION RISK MANAGEMENT AT THE COMMODITY TRADING DESK THE DISTRIBUTION OF COMMODITY RETURNS

I.C.8 THE ENERGY MARKETS I.C.8.1 I.C.8.2 I.C.8.3 I.C.8.4 I.C.8.5 I.C.8.6

INTRODUCTION MARKET OVERVIEW ENERGY FUTURES MARKETS OTC ENERGY DERIVATIVE MARKETS EMERGING ENERGY MARKETS THE FUTURE OF ENERGY TRADING

Section II – for PRM Exam II MATHEMATICAL FOUNDATIONS OF RISK MEASUREMENTS From PRM Handbook Volume II: Mathematical Foundations of Risk Measurements II.A FOUNDATIONS II.A.1 II.A.2 II.A.3 II.A.4 II.A.5 II.A.6

SYMBOLS AND RULES SEQUENCES AND SERIES EXPONENTS AND LOGARITHMS EQUATIONS AND INEQUALITIES FUNCTIONS AND GRAPHS CASE STUDY − CONTINUOUS COMPOUNDING

II.B DESCRIPTIVE STATISTICS II.B.1 II.B.2 II.B.3 II.B.4 II.B.5 II.B.6

INTRODUCTION DATA THE MOMENTS OF A DISTRIBUTION MEASURES OF LOCATION OR CENTRAL TENDENCY – AVERAGES MEASURES OF DISPERSION BIVARIATE DATA

II.C CALCULUS II.C.1 II.C.2 II.C.3 II.C.4 II.C.5 II.C.6 II.C.7

DIFFERENTIAL CALCULUS CASE STUDY: MODIFIED DURATION OF A BOND HIGHER-ORDER DERIVATIVES FINANCIAL APPLICATIONS OF SECOND DERIVATIVES DIFFERENTIATING A FUNCTION OF MORE THAN ONE VARIABLE INTEGRAL CALCULUS OPTIMISATION

II.D LINEAR MATHEMATICS AND MATRIX ALGEBRA II.D.1 II.D.2 II.D.3 II.D.4 II.D.5

MATRIX ALGEBRA APPLICATION – MATRIX ALGEBRA AND SIMULTANEOUS LINEAR EQUATIONS QUADRATIC FORMS CHOLESKY DECOMPOSITION EIGENVALUES AND EIGENVECTORS

II.E PROBABILITY THEORY IN FINANCE II.E.1

DEFINITIONS AND RULES


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II.E.2 II.E.3 II.E.4

PROBABILITY DISTRIBUTIONS JOINT DISTRIBUTIONS SPECIFIC PROBABILITY DISTRIBUTIONS

II.F REGRESSION ANALYSIS IN FINANCE II.F.1 II.F.2 II.F.3 II.F.4 II.F.5 II.F.6 II.F.7 II.F.8 II.F.9

SIMPLE LINEAR REGRESSION MULTIPLE LINEAR REGRESSION EVALUATING THE REGRESSION MODEL CONFIDENCE INTERVALS HYPOTHESIS TESTING PREDICTION BREAKDOWN OF THE OLS ASSUMPTIONS RANDOM WALKS AND MEAN REVERSION MAXIMUM LIKELIHOOD ESTIMATION

II.G NUMERICAL METHODS II.G.1 II.G.2 II.G.3

SOLVING (NON-DIFFERENTIAL) EQUATIONS NUMERICAL OPTIMISATION NUMERICAL METHODS FOR VALUING OPTIONS

Section III – for PRM Exam III RISK MANAGEMENT PRACTICES From PRM Handbook Volume III: Risk Management Practices Additionally, three publically available readings for Exam III can be found on the PRMIA website at http://prmia.org/index.php?page=exam&option=trainingWebBasedResource and, for those who have purchased PRM Handbook Volume III: Risk Management Practices, four supplemental papers can be found in your PRMIA "My Library". III.0 CAPITAL ALLOCATION AND RAPM III.0.1 III.0.2 III.0.3 III.0.4 III.0.5

INTRODUCTION ECONOMIC CAPITAL REGULATORY CAPITAL CAPITAL ALLOCATION AND RISK CONTRIBUTIONS RAROC AND RISK-ADJUSTED PERFORMANCE

III.A.1 MARKET RISK MANAGEMENT III.A.1.1 III.A.1.2 III.A.1.3 III.A.1.4 III.A.1.5 III.A.1.6 III.A.1.7

INTRODUCTION MARKET RISK MARKET RISK MANAGEMENT TASKS THE ORGANISATION OF MARKET RISK MANAGEMENT MARKET RISK MANAGEMENT IN FUND MANAGEMENT MARKET RISK MANAGEMENT IN BANKING MARKET RISK MANAGEMENT IN NON-FINANCIAL FIRMS

III.A.2 INTRODUCTION TO VALUE AT RISK MODELS III.A.2.1 III.A.2.2 III.A.2.3 III.A.2.4 III.A.2.5 III.A.2.6 III.A.2.7 III.A.2.8

INTRODUCTION DEFINITION OF VAR INTERNAL MODELS FOR MARKET RISK CAPITAL ANALYTICAL VAR MODELS MONTE CARLO SIMULATION VAR HISTORICAL SIMULATION VAR MAPPING POSITIONS TO RISK FACTORS BACKTESTING VAR MODELS


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III.A.2.9 WHY FINANCIAL MARKETS ARE NOT ‘NORMAL’ III.A.3: ADVANCED VALUE AT RISK MODELS III.A.3.1 III.A.3.2 III.A.3.3 III.A.3.4 III.A.3.5 III.A.3.6 III.A.3.7

INTRODUCTION STANDARD DISTRIBUTIONAL ASSUMPTIONS MODELS OF VOLATILITY CLUSTERING VOLATILITY CLUSTERING AND VAR ALTERNATIVE SOLUTIONS TO NON-NORMALITY DECOMPOSITION OF VAR PRINCIPAL COMPONENT ANALYSIS

III.A.4 STRESS TESTING III.A.4.1 INTRODUCTION III.A.4.2 HISTORICAL CONTEXT III.A.4.3 CONCEPTUAL CONTEXT III.A.4.4 STRESS TESTING IN PRACTICE III.A.4.5 APPROACHES TO STRESS TESTING: AN OVERVIEW III.A.4.6 HISTORICAL SCENARIOS III.A.4.7 HYPOTHETICAL SCENARIOS III.A.4.8 ALGORITHMIC APPROACHES TO STRESS TESTING III.A.4.9 EXTREME-VALUE THEORY AS A STRESS-TESTING METHOD III.A.4.10 SUMMARY AND CONCLUSIONS III LIQUIDITY RISK MANAGEMENT FUNDING LIQUIDITY: RISK ANALYSIS AND MANAGEMENT (SEE “MY LIBRARY”) by Selwyn Blair-Ford and Ioannis Akkizidis III STRESS AND SCENARIO TESTING This section is focused on 3 papers from financial authorities and regulators. These papers are publically available on the PRMIA website at http://prmia.org/index.php?page=exam&option=trainingWebBasedResource  Principles for sound stress testing practices and supervision Basel Committee on Banking Supervision (BCBS)  Stress and Scenario Testing Financial Services Authority (FSA)  The Supervisory Capital Assessment Program: Overview of Results Board of Governors of the Federal Reserve System. III.B.1 CREDIT RISK MANAGEMENT III.B.1.1 INTRODUCTION III.B.1.2 A CREDIT TO-DO LIST III.B.1.3 OTHER TASKS III.B.2 FOUNDATIONS OF CREDIT RISK MODELLING III.B.2.1 III.B.2.2 III.B.2.3 III.B.2.4 III.B.2.5 III.B.2.6

INTRODUCTION WHAT IS DEFAULT RISK? EXPOSURE, DEFAULT AND RECOVERY PROCESSES THE CREDIT LOSS DISTRIBUTION EXPECTED AND UNEXPECTED LOSS RECOVERY RATES

III.B.3 CREDIT EXPOSURE III.B.3.1 III.B.3.2 III.B.3.3 III.B.3.4

INTRODUCTION PRE-SETTLEMENT VERSUS SETTLEMENT RISK EXPOSURE PROFILES MITIGATION OF EXPOSURES


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III.B.4 DEFAULT AND CREDIT MIGRATION III.B.4.1 III.B.4.2 III.B.4.3 III.B.4.4 III.B.4.5 III.B.4.6

DEFAULT PROBABILITIES AND TERM STRUCTURES OF DEFAULT RATES CREDIT RATINGS AGENCY RATINGS CREDIT SCORING AND INTERNAL RATING MODELS MARKET-IMPLIED DEFAULT PROBABILITIES CREDIT RATING AND CREDIT SPREADS

III.B.5 PORTFOLIO MODELS OF CREDIT LOSS III.B.5.1 III.B.5.2 III.B.5.3 III.B.5.4 III.B.5.5 III.B.5.6 III.B.5.7

INTRODUCTION WHAT ACTUALLY DRIVES CREDIT RISK AT THE PORTFOLIO LEVEL? CREDIT MIGRATION FRAMEWORK CONDITIONAL TRANSITION PROBABILITIES– CREDITPORTFOLIOVIEW THE CONTINGENT CLAIM APPROACH TO MEASURING CREDIT RISK THE KMV APPROACH THE ACTUARIAL APPROACH

III.B.6 CREDIT RISK CAPITAL CALCULATION III.B.6.1 III.B.6.2 III.B.6.3 III.B.6.4 III.B.6.5 III.B.6.6 III.B.6.7

INTRODUCTION ECONOMIC CREDIT CAPITAL CALCULATION REGULATORY CREDIT CAPITAL: BASEL I REGULATORY CREDIT CAPITAL: BASEL II BASEL II: CREDIT MODEL ESTIMATION AND VALIDATION BASEL II: SECURITISATION ADVANCED TOPICS ON ECONOMIC CREDIT CAPITAL

III.C.1 THE OPERATIONAL RISK MANAGEMENT FRAMEWORK III.C.1.1 INTRODUCTION III.C.1.2 EVIDENCE OF OPERATIONAL FAILURES III.C.1.3 DEFINING OPERATIONAL RISK III.C.1.4 TYPES OF OPERATIONAL RISK III.C.1.5 AIMS AND SCOPE OF OPERATIONAL RISK MANAGEMENT III.C.1.6 KEY COMPONENTS OF OPERATIONAL RISK III.C.1.7 SUPERVISORY GUIDANCE ON OPERATIONAL RISK III.C.1.8 IDENTIFYING OPERATIONAL RISK – THE RISK CATALOGUE III.C.1.9 THE OPERATIONAL RISK ASSESSMENT PROCESS III.C.1.10 THE OPERATIONAL RISK CONTROL PROCESS III.C.1.11 SOME FINAL THOUGHTS III.C.2 OPERATIONAL RISK PROCESS MODELS III.C.2.1 III.C.2.2 III.C.2.3 III.C.2.4 III.C.2.5 III.C.2.6 III.C.2.7 III.C.2.8 III.C.2.9

INTRODUCTION THE OVERALL PROCESS SPECIFIC TOOLS ADVANCED MODELS KEY ATTRIBUTES OF THE ORM FRAMEWORK INTEGRATED ECONOMIC CAPITAL MODEL MANAGEMENT ACTIONS RISK TRANSFER IT OUTSOURCING

III.C.3 OPERATIONAL VALUE-AT-RISK III.C.3.1 III.C.3.2 III.C.3.3 III.C.3.4 III.C.3.5 III.C.3.6

THE ‘LOSS MODEL’ APPROACH THE FREQUENCY DISTRIBUTION THE SEVERITY DISTRIBUTION THE INTERNAL MEASUREMENT APPROACH THE LOSS DISTRIBUTION APPROACH AGGREGATING ORC


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III ENTERPRISE INFORMATION RISK ENTERPRISE RISK INFORMATION MANAGEMENT (SEE “MY LIBRARY” ON THE PRMIA WEBSITE) by Dilip Krishna and Robert Mark III SYSTEMIC RISK WHY BANKS FAILED THE STRESS TESTS (SEE “MY LIBRARY” ON THE PRMIA WEBSITE) by Andrew G. Haldane VIEWING THE FINANCIAL CRISIS FROM 20,000 FEET UP (SEE “MY LIBRARY” ON THE PRMIA WEBSITE) by Stephen Figlewski


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Introduction If you're reading this, you are seeking to attain a higher standard. Congratulations! Those who have been a part of financial risk management for the past twenty years, have seen it change from an on-the-fly profession, with improvisation as a rule, to one with substantially higher standards, many of which are now documented and expected to be followed. It’s no longer enough to say you know. Now, you and your team need to prove it. As its title implies, this book is the Handbook for the Professional Risk Manager. It is for those professionals who seek to demonstrate their skills through certification as a Professional Risk Manager (PRM) in the field of financial risk management. And it is for those looking simply to develop their skills through an excellent reference source. With contributions from nearly 40 leading authors, the Handbook is designed to provide you with the materials needed to gain the knowledge and understanding of the building blocks of professional financial risk management. Financial risk management is not about avoiding risk. Rather, it is about understanding and communicating risk, so that risk can be taken more confidently and in a better way. Whether your specialism is in insurance, banking, energy, asset management, weather, or one of myriad other industries, this Handbook is your guide. In Volume II, we take you through the mathematical foundations of risk assessment. While there are many nuances to the practice of risk management that go beyond the quantitative, it is essential today for every risk manager to be able to assess risks. The chapters in this section are accessible to all PRM members, including those without any quantitative skills. The Excel spreadsheets that accompany the examples are an invaluable aid to understanding the mathematical and statistical concepts that form the basis of risk assessment. After studying all these chapters, you will have read the materials necessary for passage of Exam II of the PRM Certification program. Those preparing for the PRM certification will also be preparing for Exam I on Finance Theory, Financial Instruments and Markets, covered in Volume I of the PRM Handbook, Exam III on Risk Management Practices, covered in Volume III of the PRM Handbook and Exam IV - Case Studies, Standards of Best Practice Conduct and Ethics and PRMIA Governance. Exam IV is where we study some failed practices, standards for the performance of the duties of a Professional Risk Manager, and the governance structure of our association, the Professional Risk Managers’ International Association. The materials for Exam IV are freely available on our website (see http://prmia.org/index.php?page=exam&option=trainingWebBasedResource ) and 2010 © The Professional Risk Managers’ International Association

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are thus outside of the Handbook. For Exam IV Learning Outcomes, see PRM Study Guide for Exam IV or go to PRMIA webpage for link: http://prmia.org/index.php?page=exam. At the end of your progression through these materials, you will find that you have broadened your knowledge and skills in ways that you might not have imagined. You will have challenged yourself as well. And, you will be a better risk manager. It is for this reason that we have created the Professional Risk Managers’ Handbook. Our deepest appreciation is extended to Prof. Carol Alexander and Prof. Elizabeth Sheedy, dedicated PRMIA Leaders, for their editorial work on this document. The commitment they have shown to ensuring the highest level of quality and relevance is beyond description. Our thanks also go to the authors who have shared their insights with us. The demands for sharing of their expertise are frequent. Yet, they have each taken special time for this project and have dedicated themselves to making the Handbook and you a success. We are very proud to bring you such a fine assembly. Much like PRMIA, the Handbook is a place where the best ideas of the risk profession meet. We hope that you will take these ideas, put them into practice and certify your knowledge by attaining the PRM designation. Among our membership are several hundred Chief Risk Officers / Heads of Risk and tens of thousands of other risk professionals who will note your achievements. They too know the importance of setting high standards and the trust that capital providers and stakeholders have put in them. Now they put their trust in you and you can prove your commitment and distinction to them. We wish you much success during your studies and for your performance in the PRM exams! PRMIA


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Section I Finance Theory, Financial Instruments and Markets Preface to Section I: Finance Theory, Financial Instruments and Markets For Exam I Learning Outcomes, see PRM Study Guide for Exam I. See PRMIA webpage for link: http://prmia.org/index.php?page=exam Section I of this Handbook has been written by a group of leading scholars and practitioners and represents a broad overview of the theory, instruments and markets of finance. This section corresponds to Exam I in the Professional Risk Manager (PRM) certification programme. The modern theory of finance is the solid basis of risk management and thus it naturally represents the basis of the PRM certification programme. All major areas of finance are involved in the process of risk management: from the expected utility approach and risk aversion, which were the forerunners of the capital asset pricing model (CAPM), to portfolio theory and the riskneutral approach to pricing derivatives. All of these great financial theories and their interactions are presented in Part I.A (Finance Theory). Many examples demonstrate how the concepts are applied in practical situations. Part I.B (Financial Instruments) describes a wide variety of financial products and connects them to the theoretical development in Part I.A. The ability to value all the instruments/assets within a trading or asset portfolio is fundamental to risk management. This part examines the valuation of financial instruments and also explains how many of them can be used for risk management. The designers of the PRM curriculum have correctly determined that financial risk managers should have a sound knowledge of financial markets. Market liquidity, the role of intermediaries and the role of exchanges are all features that vary considerably from one market to the next and over time. It is crucial that professional risk managers understand how these features vary and their consequences for the practice of risk management. Part I.C (Financial Markets) describes where and how instruments are traded, the features of each type of financial asset or commodity and the various conventions and rules governing their trade. This background is absolutely necessary for professional risk management, and Exam I therefore represents a significant portion of the whole PRM certification programme. For a practitioner who left academic studies several years ago, this part of the Handbook will provide efficient revision of finance theory, financial instruments and markets, with emphasis on practical


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application to risk management. Such a person will find the chapters related to his/her work easy reading and will have to study other topics more deeply. The coverage of financial topics included in Section I of the Handbook is typically deeper and broader than that of a standard MBA syllabus.

But the concepts are well explained and

appropriately linked together. For example, Chapter I.B.6 on credit derivatives covers many examples (such as credit-linked notes and credit default swaps) that are not always included in a standard MBA-level elective course on fixed income. Chapter I.B.9 on simple exotics also provides examples of path-dependent derivatives beyond the scope of a standard course on options. All chapters are written for professionals and assume a basic understanding of markets and their participants. Finance Theory Chapter I.A.1 provides a general overview of risk and risk aversion, introduces the utility function and mean–variance criteria. Various risk-adjusted performance measures are described. A summary of several widely used utility functions is presented in the appendix. Chapter I.A.2 provides an introduction to portfolio mathematics, from means and variances of returns to correlation and portfolio variance. This leads the reader to the efficient frontier, portfolio theory and the concept of portfolio diversification. Eventually this chapter discusses normally distributed returns and basic applications for value-at-risk, as well as the probability of reaching a target or beating a benchmark. This chapter is very useful for anybody with little experience in applying basic mathematical models in finance. The concept of capital allocation is another fundamental notion for risk managers. Chapter I.A.3 describes how capital is allocated between portfolios of risky and riskless assets, depending on risk preference. Then the efficient frontier, the capital markets line, the Sharpe ratio and the separation principle are introduced. These concepts lead naturally to a discussion of the CAPM model and the idea that marginal risk (rather than absolute risk) is the key issue when pricing risky assets. Chapter I.A.4 provides a rigorous description of the CAPM model, including betas, systematic risk, alphas and performance measures. Arbitrage pricing theory and multifactor models are also introduced in this chapter. Capital structure is an important theoretical concept for risk managers since capital is viewed as the last defence against extreme, unexpected outcomes.

Chapter I.A.5 introduces capital

structure, advantages and costs related to debt financing, various agency costs, various types of debt and equity, return on equity decomposition, examples of attractive and unattractive debt, bankruptcy and financial distress costs. 2010 © The Professional Risk Managers’ International Association

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Most valuation problems involve discounting future cash flows, a process that requires knowledge of the term structure of interest rates. Chapter I.A.6 describes various types of interest rates and discounting, defines the term structure of interest rates, introduces forward rates and explains the three main economic term structure theories. These days all risk managers must be well versed in the use and valuation of derivatives. The two basic types of derivatives are forwards (having a linear payoff) and options (having a non-linear payoff). All other derivatives can be decomposed to these underlying payoffs or alternatively they are variations on these basic ideas. Chapter I.A.7 describes valuation methods used for forward contracts. Discounting is used to value forward contracts with and without intermediate cash flow. Chapter I.A.8 introduces the principles of option pricing. It starts with definitions of basic put and call options, put–call parity, binomial models, risk-neutral methods and simple delta hedging. Then the Black–Scholes–Merton formula is introduced. Finally, implied volatility and smile effects are briefly described. Financial Instruments Having firmly established the theoretical basis for valuation in Part I.A, Part I.B applies these theories to the most commonly used financial instruments. Chapter I.B.1 introduces bonds, defines the main types of bonds and describes the market conventions for major types of treasuries, strips, floaters (floating-rate notes) and inflationprotected bonds in different countries. Bloomberg screens are used to show how the market information is presented. Chapter I.B.2 analyses the main types of bonds, describes typical cash flows and other features of bonds and also gives a brief description of non-conventional instruments. Examples of discounting, day conventions and accrued interest are provided, as well as yield calculations. The connection between yield and price is described, thus naturally leading the reader to duration, convexity and hedging interest-rate risk. While Chapter I.A.7 explained the principles of forward valuation, Chapter I.B.3 examines and compares futures and forward contracts. Usage of these contracts for hedging and speculation is discussed. Examples of currency, commodity, bonds and interest-rate contracts are used to explain the concept and its applications. Mark-to-market, quotation, settlements and other specifications are described here as well. The principles of forward valuation are next applied to swap contracts, which may be considered to be bundles of forward contracts. Chapter I.B.4 analyses some of the most popular swap varieties, explaining how they may be priced and used for managing risk.


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The remaining chapters in Part I.B all apply the principles of option valuation as introduced in Chapter I.A.8. The power of the option concept is obvious when we see its applications to so many instruments and risk management problems. Chapter I.B.5 begins with an analysis of vanilla options. Chapter I.B.6 covers one of the newer applications of options: the use of credit risk derivatives to manage credit risk. Chapter I.B.7 addresses caps, floors and swaptions, which are the main option strategies used in interest-rate markets. Yet another application of the option principle is found in Chapter I.B.8 – convertible bonds. These give investors the right to convert a debt security into equity. Finally, Chapter I.B.9 examines exotic option payoffs. In every case the author defines the instrument, discusses its pricing and illustrates its use for risk management purposes. Financial Markets Financial risk management takes place in the context of markets and varies depending on the nature of the market. Chapter I.C.1 is a general introduction to world financial markets. They can be variously classified – geographically, by type of exchange, by issuers, liquidity and type of instruments – all are provided here.

The importance of liquidity, the distinction between

exchange and over-the-counter markets and the role of intermediaries in their various forms are explained in more detail. Money markets are the subject of Chapter I.C.2. These markets are of vital importance to the risk manager as the closest thing to a ‘risk-free’ asset is found here. This chapter covers all shortterm debt securities, whether issued by governments or corporations. It also explains the repo markets – markets for borrowing/lending on a secured basis. The market for longer-term debt securities is discussed in Chapter I.C.3, which classifies bonds by issuer: government, agencies, corporate and municipal. There is a comparison of bond markets in major countries and a description of the main intermediaries and their roles. International bond markets are introduced as well. Chapter I.C.4 turns to the foreign exchange market – the market with the biggest volume of trade. Various aspects of this market are explained, such as quotation conventions, types of brokers, and examples of cross rates. Economic theories of exchange rates are briefly presented here along with central banks’ policies. Forward rates are introduced together with currency swaps. Interest-rate parity is explained with several useful examples. Chapter I.C.5 provides a broad introduction to stock markets. This includes the description and characteristics of several types of stocks, stock market indices and priorities in the case of liquidation.

Dividends and dividend-based stock valuation methods are described in this

chapter. Primary and secondary markets are distinguished. Market mechanics, including types of 2010 © The Professional Risk Managers’ International Association

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orders, market participants, margin and short trades, are explained here with various examples clarifying these transactions. Some exchange-traded options on stocks are introduced as well. Chapter I.C.6 introduces the futures markets; this includes a comparison of the main exchangetraded markets, options on futures, specifications of the most popular contracts, the use of futures for hedging, trade orders for futures contracts, mark-to-market procedures, and various expiration conventions. A very interesting description of the main market participants concludes this chapter. Chapter I.C.7 introduces the structure of the commodities market. It starts with the spot market and then moves to commodity forwards and futures. Specific features, such as delivery and settlement methods, are described. The spot–forward pricing relationship is used to decompose the forward price into spot and carry.

Various types of price term structure (such as

backwardation and contango) are described, together with some economic theory. The chapter also describes short squeezes and regulations. Risk management at the commodity trading desk is given at a good intuitive level.

The chapter concludes with some interesting facts on

distribution of commodity returns. Finally, Chapter I.C.8 examines one of the most rapidly developing markets for risk – the energy markets. These markets allow participants to manage the price risks of oil and gas, electricity, coal and so forth. Some other markets closely linked with energy are also briefly discussed here, including markets for greenhouse gas emissions, weather derivatives and freight. Energy markets create enormous challenges and opportunities for risk managers – in part because of the extreme volatility of prices that can occur. As a whole, Section I gives an overview of the theoretical and practical aspects of finance that are used in the management of financial risks. Many concepts, some quite complex, are explained in a relatively simple language and are demonstrated with numerous examples. Studying this part of the Handbook should refresh your knowledge of financial models, products and markets and provide the background for risk management applications.


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Section II Mathematical Foundations of Risk Measurement Preface to Section II: Mathematical Foundations of Risk Measurement For Exam II Learning Outcomes, see PRM Study Guide for Exam II. See PRMIA webpage for link: http://prmia.org/index.php?page=exam The role of risk management in financial firms has evolved far beyond the simple insurance of identified risks. Today it is recognised that risks cannot be properly managed unless they are quantified. And the assessment of risk requires mathematics. Take, for instance, a large portfolio of stocks. The relationship between the portfolio returns and the market returns – and indeed other potential risk factor returns – is typically estimated using a statistical regression analysis. And the systematic risk of the portfolio is then determined by a quadratic form, a fundamental concept in matrix algebra that is based on the covariance matrix of the risk factor returns. Volatility is not the only risk metric that financial risk managers need to understand. During the last decade value-at-risk (VaR) has become the ubiquitous tool for risk capital estimation. To understand a VaR model, risk managers require knowledge of probability distributions, simulation methods and a host of other mathematical and statistical techniques. Market VaR is assessed by mapping portfolios to their risk factors and forecasting the volatilities and correlations of these factors. The diverse quantitative techniques that are commonly applied in the assessment of market VaR include eigenvectors and eigenvalues, Taylor expansions and partial derivatives. Credit VaR can be assessed using firm-value models that are based on the theory of options, or statistical and/or macro-econometric models. Probability distributions are even applied to operational risks, though they are very difficult to quantify because the data are sparse and unreliable. Indeed, the actuarial or loss model approach has been adopted as industry standard for operational VaR models. Even if not directly responsible for designing and coding a risk capital model, middle office risk managers must understand these models sufficiently well to be competent to assess them. And the risk management role encompasses many other responsibilities. Ten years ago my best students aspired to become traders because of the high salaries and status – risk management was viewed (by some) as a ‘second-rate’ job that did not require very special expertise. Now, this situation has definitely changed. Today, the middle office risk manager’s responsibility has expanded to include the independent validation of traders’ models, as well as risk capital assessment. And the role of risk management in the front office itself has expanded, with the need to hedge increasingly complex options portfolios. So today, the hallmark of a good risk 2010 © The Professional Risk Managers’ International Association

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manager is not just having the statistical skills required for risk assessment – a comprehensive knowledge of pricing and hedging financial instruments is equally important. No wonder, therefore, that the PRM qualification includes an entire exam on mathematical and statistical methods. However, we do recognise that many students will not have degrees in mathematics, physics or other quantitative disciplines. So this section of the Handbook is aimed at students having no quantitative background at all. It introduces and explains all the mathematics and statistics that are essential for financial risk management. Every chapter is presented in a pedagogical manner, with associated Excel spreadsheets explaining the numerous practical examples. And, for clarity and consistency, we chose two much respected authors of the highly acclaimed textbook Quantitative Methods in Finance to write the entire section. Keith Parramore and Terry Watsham have put considerable effort into making the PRM material accessible to everyone, irrespective of their quantitative background. The first chapter, II.A (Foundations), reviews the fundamental mathematical concepts: the symbols used and the basic rules for arithmetic, equations and inequalities, functions and graphs, etc. Chapter II.B (Descriptive Statistics) introduces the descriptive statistics that are commonly used to summarise the historical characteristics of financial data: the sample moments of returns distributions, ‘downside’ risk statistics, and measures of covariation (e.g. correlation) between two random variables. Chapter II.C (Calculus) focuses on differentiation and integration, Taylor expansion and optimisation. Financial applications include calculating the convexity of a bond portfolio and the estimation of the delta and gamma of an options portfolio. Chapter II.D (Linear Mathematics and Matrix Algebra) covers matrix operations, special types of matrices and the laws of matrix algebra, the Cholesky decomposition of a matrix, and eigenvalues and eigenvectors.

Examples of financial applications include: manipulating covariance matrices;

calculating the variance of the returns to a portfolio of assets; hedging a vanilla option position; and simulating correlated sets of returns. Chapter II.E (Probability Theory) first introduces the concept of probability and the rules that govern it. Then some common probability distributions for discrete and continuous random variables are described, along with their expectation and variance and various concepts relating to joint distributions, such as covariance and correlation, and the expected value and variance of a linear combination of random variables. Chapter II.F (Regression Analysis) covers the simple and multiple regression models, with applications to the capital asset pricing model and arbitrage pricing theory. The statistical inference section deals with both prediction and hypothesis testing, for instance, of the efficient market hypothesis. Finally, Chapter II.G (Numerical Methods) looks at solving implicit equations (e.g. the Black– Scholes formula for implied volatility), lattice methods, finite differences and simulation. Financial applications include option valuation and estimating the ‘Greeks’ for complex options.


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Whilst the risk management profession is no doubt becoming increasingly quantitative, the quantification of risk will never be a substitute for good risk management. The primary role of a financial risk manager will always be to understand the markets, the mechanisms and the instruments traded. Mathematics and statistics are only tools, but they are necessary tools. After working through this part of the Handbook you will have gained a thorough and complete grounding in the essential quantitative methods for your profession.


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Section III

Risk Management Practices Preface to Section III: Risk Management Practices For Exam III Learning Outcomes, see PRM Study Guide for Exam III. See PRMIA webpage for link: http://prmia.org/index.php?page=exam Section III is the ultimate part of The PRM Handbook in both senses of the word. Not only is it the final section, but it represents the final aims and objectives of the Handbook. Sections I (Finance Theory, Financial Instruments and Markets) and II (Mathematical Foundations of Risk Measurement) laid the necessary foundations for this discussion of risk management practices – the primary concern of most readers. Here some of the foremost practitioners and academics in the field provide an up-to-date, rigorous and lucid statement of modern risk management. The practice of risk management is evolving at a rapid pace, especially with the impending arrival of Basel II.

Aside from these regulatory pressures, shareholders and other stakeholders

increasingly demand higher standards of risk management and disclosure of risk. In fact, it would not be an overstatement to say that risk consciousness is one of the defining features of modern business. Nowhere is this truer than in the financial services industry. Interest in risk management is at an unprecedented level as institutions gather data, upgrade their models and systems, train their staff, review their remuneration systems, adapt their business practices and scrutinise controls for this new era. Section III is itself split into three parts which address market risk, credit risk and operational risk in turn. These three are the main components of risk borne by any organisation, although the relative importance of the mix varies. For a traditional commercial bank, credit risk has always been the most significant. It is defined as the risk of default on debt, swap, or other counterparty instruments. Credit risk may also result from a change in the value of a security, contract or asset resulting from a change in the counterparty’s creditworthiness. In contrast, market risk refers to changes in the values of securities, contracts or assets resulting from movements in exchange rates, interest rates, commodity prices, stock prices, etc. Operational risk, the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events, is not, strictly speaking, a financial risk. Operational risks are, however, an inevitable consequence of any business undertaking. For financial institutions and fund managers, credit and market risks are taken intentionally with the objective of earning returns, while operational risks are a by-product to be controlled. While the importance of operational risk management is


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increasingly accepted, it will probably never have the same status in the finance industry as credit and market risk which are the chosen areas of competence. For non-financial firms, the priorities are reversed. The focus should be on the risks associated with the particular business; the production and marketing of the service or product in which expertise is held. Market and credit risks are usually of secondary importance as they are a byproduct of the main business agenda. The last line of defence against risk is capital, as it ensures that a firm can continue as a going concern even if substantial and unexpected losses are incurred. Accordingly, one of the major themes of Section III is how to determine the appropriate size of this capital buffer. How much capital is enough to withstand unusual losses in each of the three areas of risk?

The

measurement of risk has further important implications for risk management as it is increasingly incorporated into the performance evaluation process. Since resources are allocated and bonuses paid on the basis of performance measures, it is essential that they be appropriately adjusted for risk.

Only then will appropriate incentives be created for behaviour that is beneficial for

shareholders and other stakeholders. Chapter III.0 explores this fundamental idea at a general level, since it is relevant for each of the three risk areas that follow. Market Risk Chapter III.A.1 introduces the topic of market risk as it is practised by bankers, fund managers and corporate treasurers. It explains the four major tasks of risk management (identification, assessment, monitoring and control/mitigation), thus setting the scene for the quantitative chapters that follow. These days one of the major tasks of risk managers is to measure risk using value-at-risk (VaR) models. VaR models for market risk come in many varieties. The more basic VaR models are the topic of Chapter III.A.2, while the advanced versions are covered in III.A.3 along with some other advanced topics such as risk decomposition. The main challenge for risk managers is to model the empirical characteristics observed in the market, especially volatility clustering. The advanced models are generally more successful in this regard, although the basic versions are easier to implement. Realistically, there will never be a perfect VaR model, which is one of the reasons why stress tests are a popular tool. They can be considered an ad hoc solution to the problem of model risk. Chapter III.A.4 explains the need for stress tests and how they might usefully be constructed. Credit Risk Chapter III.B.1 introduces the sphere of credit risk management. Some fundamental tools for managing credit risk are explained here, including the use of collateral, credit limits and credit derivatives. Subsequent chapters on credit risk focus primarily on its modelling. Foundations for 2010 © The Professional Risk Managers’ International Association

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modelling are laid in Chapter III.B.2, which explains the three basic components of a credit loss: the exposure, the default probability and the recovery rate. The product of these three, which can be defined as random processes, is the credit loss distribution. Chapter III.B.3 takes a more detailed look at the exposure amount. While relatively simple to define for standard loans, assessment of the exposure amount can present challenges for other credit sensitive instruments such as derivatives, whose values are a function of market movements. Chapter III.B.4 examines in detail the default probability and how it can evolve over time. It also discusses the relationship between credit ratings and credit spreads, and credit scoring models. Chapter III.B.5 tackles one of the most crucial issues for credit risk modelling: how to model credit risk in a portfolio context and thereby estimate credit VaR. Since diversification is one of the most important tools for the management of credit risk, risk measures on a portfolio basis are fundamental. A number of tools are examined, including the credit migration approach, the contingent claim or structural approach, and the actuarial approach. Finally, Chapter III.B.6 extends the discussion of credit VaR models to examine credit risk capital. It compares both economic capital and regulatory capital for credit risk as defined under the new Basel Accord. Operational Risk The framework for managing operational risk is first established in Chapter III.C.1. After defining operational risk, it explains how it may be identified, assessed and controlled. Chapter III.C.2 builds on this with a discussion of operational risk process models.

By better

understanding business processes we can find the sources of risk and often take steps to reengineer these processes for greater efficiency and lower risk. One of the most perplexing issues for risk managers is to determine appropriate capital buffers for operational risks. Operational VaR is the subject of Chapter III.C.3, including discussion of loss models, standard functional forms, both analytical and simulation methods, and the aggregation of operational risk over all business lines and event types.


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PRM Handbook Introduction and Contents

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