Financial Risk Manager Handbook 2e
Risk professionals looking to earn the Financial Risk Manager (FRM™) certification, corporate training programs, professors, and graduate students all rely on one book for the most comprehensive and uptodate information on financial risk management–the Financial Risk Manager Handbook. Presented in a clear and consistent fashion, this completely updated Second Edition is the best way to prepare for the Financial Risk Manager (FRM) exam and has become the core text for risk management training programs worldwide.
This definitive guide supports candidates studying for GARP’s annual FRM exam and prepares you to assess and control risk in today’s rapidly changing financial world. Financial Risk Manager Handbook, Second Edition summarizes the core body of knowledge for financial risk managers, covering such topics as quantitative methods, capital markets, as well as credit, operational, market, and integrated risk management. It also discusses relevant regulatory, legal, and accounting issues essential to risk professionals.
The FRM is recognized as the world’s most prestigious global certification program–created to measure a financial risk manager’s capabilities. With the FRM exam fast becoming an essential requirement for risk managers around the world, the Financial Risk Manager Handbook, Second Edition focuses on practical financial risk management techniques and solutions that are emphasized on the test–and essential in the real world. Questions from previous exams are explained through tutorials so that you may prepare yourself or your employees for this comprehensive exam and for the risk management scenarios you will face at some point in your career.
Table of Contents
Preface.
Introduction.
Part I: Quantitative Analysis.
Ch. 1: Bond Fundamentals.
1.1 Discounting, Present, and Future Value.
1.2 PriceYield Relationship.
1.2.1 Valuation.
1.2.2 Taylor Expansion.
1.2.3 Bond Price Derivatives.
1.2.4 Interpreting Duration and Convexity.
1.2.5 Portfolio Duration and Convexity.
1.3 Answers to Chapter Examples.
Ch. 2: Fundamentals of Probability.
2.1 Characterizing Random Variables.
2.1.1 Univariate Distribution Functions.
2.1.2 Moments.
2.2 Multivariate Distribution Functions.
2.3 Functions of Random Variables.
2.3.1 Linear Transformation of Random Variables.
2.3.2 Sum of Random Variables.
2.3.3 Portfolios of Random Variables.
2.3.4 Product of Random Variables.
2.3.5 Distributions of Transformations of Random Variables.
2.4 Important Distribution Functions.
2.4.1 Uniform Distribution.
2.4.2 Normal Distribut ion.
2.4.3 Lognormal Distribution.
2.4.4 Student’s Distribution.
2.4.5 Binomial Distribution.
2.5 Answers to Chapter Examples.
Ch. 3: Fundamentals of Statistics.
3.1 Real Data.
3.1.1 Measuring Returns.
3.1.2 Time Aggregation.
3.1.3 Portfolio Aggregation.
3.2 Parameter Estimation.
3.3 Regression Analysis.
3.3.1 Bivariate Regression.
3.3.2 Autoregression.
3.3.3 Multivariate Regression.
3.3.4 Example.
3.3.5 Pitfalls with Regressions.
3.4 Answers to Chapter Examples.
Ch. 4: Monte Carlo Methods.
4.1 Simulations with One Random Variable.
4.1.1 Simulating Markov Processes.
4.1.2 The Geometric Brownian Motion.
4.1.3 Simulating Yields.
4.1.4 Binomial Trees.
4.2 Implementing Simulations.
4.2.1 Simulation for VAR.
4.2.2 Simulation for Derivatives.
4.2.3 Accuracy.
4.3 Multiple Sources of Risk.
4.3.1 The Cholesky Factorization.
4.4 Answers to Chapter Examples.
Part II: Capital Markets.
Ch. 5: Introduction to Derivatives.
5.1 Overview of Derivatives Markets.
5.2 Forward Contracts.
5.2.1 Definition.
5.2.2 Valuing Forward Contracts.
5.2.3 Valuing an OffMarket Forward Contract.
5.2.4 Valuing Forward Contracts with Income Payments.
5.3 Futures Contracts.
5.3.1 Definitions of Futures.
5.3.2 Valuing Futures Contracts.
5.4 Swap Contracts.
5.5 Answers to Chapter Examples.
Ch. 6: Options.
6.1 Option Payoffs.
6.1.1 Basic Options.
6.1.2 PutCall Parity.
6.1.3 Combination of Options.
6.2 Valuing Options.
6.2.1 Option Premiums.
6.2.2 Early Exercise of Options.
6.2.3 BlackScholes Valuation.
6.2.4 Market vs. Model Prices.
6.3 Other Option Contracts.
6.4 Valuing Options by Numerical Methods.
6.5 Answers to Chapter Examples.
Ch. 7: FixedIncome Securities.
7.1 Overview of Debt Markets.
7.2 FixedIncome Securities.
7.2.1 Instrument Types.
7.2.2 Methods of Quotation.
7.3 Analysis of FixedIncome Securities.
7.3.1 The NPV Approach.
7.3.2 Duration.
7.4 Spot and Forward Rates.
7.5 MortgageBacked Securities.
7.5.1 Description.
7.5.2 Prepayment Risk.
7.5.3 Financial Engineering and CMOs.
7.6 Answers to Chapter Examples.
Ch. 8: FixedIncome Derivatives.
8.1 Forward Contracts.
8.2 Futures.
8.2.1 Eurodollar Futures.
8.2.2 Tbond Futures.
8.3 Swaps.
8.3.1 Definitions.
8.3.2 Quotations.
8.3.3 Pricing.
8.4 Options.
8.4.1 Caps and Floors.
8.4.2 Swaptions.
8.4.3 ExchangeTraded Options.
8.5 Answers to Chapter Examples.
Ch. 9: Equity Markets.
9.1 Equities.
9.1.1 Overview.
9.1.2 Valuation.
9.1.3 Equity Indices.
9.2 Convertible Bonds and Warrants.
9.2.1 Definitions.
9.2.2 Valuation.
9.3 Equity Derivatives.
9.3.1 Stock Index Futures.
9.3.2 Single Stock Futures.
9.3.3 Equity Options.
9.3.4 Equity Swaps.
9.4 Answers to Chapter Examples.
Ch. 10: Currencies and Commodities Markets.
10.1 Currency Markets.
10.2 Currency Swaps.
10.2.1 Definitions.
10.2.2 Pricing.
10.3 Commodities.
10.3.1 Products.
10.3.2 Pricing of Futures.
10.3.3 Futures and Expected Spot Prices.
10.4 Answers to Chapter Examples.
Part III: Market Risk Management.
Ch. 11: Introduction to Market Risk Measurement.
11.1 Introduction to Financial Market Risks.
11.2 VAR as Downside Risk.
11.2.1 VAR: Definition.
11.2.2 VAR: Caveats.
11.2.3 Alternative Measures of Risk.
11.3 VAR: Parameters.
11.3.1 Confidence Level.
11.3.2 Horizon.
11.3.3 Application: The Basel Rules.
11.4 Elements of VAR Systems.
11.4.1 Portfolio Positions.
11.4.2 Risk Factors.
11.4.3 VAR Methods.
11.5 StressTesting.
11.6 Cash Flow at Risk.
11.7 Answers to Chapter Examples.
Ch. 12: Identification of Risk Factors.
12.1 Market Risks.
12.1.1 Absolute and Relative Risk.
12.1.2 Directional and Nondirectional Risk.
12.1.3 Market vs. Credit Risk.
12.1.4 Risk Interaction.
12.2 Sources of Loss: A Decomposition.
12.2.1 Exposure and Uncertainty.
12.2.2 Specific Risk.
12.3 Discontinuity and Event Risk.
12.3.1 Continuous Processes.
12.3.2 Jump Process.
12.3.3 Event Risk.
12.4 Liquidity Risk.
12.5 Answers to Chapter Examples.
Ch. 13: Sources of Risk.
13.1 Currency Risk.
13.1.1 Currency Volatility.
13.1.2 Correlations.
13.1.3 Devaluation Risk.
13.1.4 CrossRate Volatility.
13.2 FixedIncome Risk.
13.2.1 Factors Affecting Yields.
13.2.2 Bond Price and Yield Volatility.
13.2.3 Correlations.
13.2.4 Global Interest Rate Risk.
13.2.5 Real Yield Risk.
13.2.6 Credit Spread Risk.
13.2.7 Prepayment Risk.
13.3 Equity Risk.
13.3.1 Stock Market Volatility.
13.3.2 Forwards and Futures.
13.4 Commodity Risk.
13.4.1 Commodity Volatility Risk.
13.4.2 Forwards and Futures.
13.4.3 Delivery and Liquidity Risk.
13.5 Risk Simplification.
13.5.1 Diagonal Model.
13.5.2 Factor Models.
13.5.3 FixedIncome Portfolio Risk.
13.6 Answers to Chapter Examples.
Ch. 14: Hedging Linear Risk.
14.1 Introduction to Futures Hedging.
14.1.1 Unitary Hedging.
14.1.2 Basis Risk.
14.2 Optimal Hedging.
14.2.1 The Optimal Hedge Ratio.
14.2.2 The Hedge Ratio as Regression Coefficient.
14.2.3 Example.
14.2.4 Liquidity Issues.
14.3 Applications of Optimal Hedging.
14.3.1 Duration Hedging.
14.3.2 Beta Hedging.
14.4 Answers to Chapter Examples.
Ch. 15: Nonlinear Risk: Options.
15.1 Evaluating Options.
15.1.1 Definitions.
15.1.2 Taylor Expansion.
15.1.3 Option Pricing.
15.2 Option “Greeks”.
15.2.1 Option Sensitivities: Delta and Gamma.
15.2.2 Option Sensitivities: Vega.
15.2.3 Option Sensitivities: Rho.
15.2.4 Option Sensitivities: Theta.
15.2.5 Option Pricing and the “Greeks”.
15.2.6 Option Sensitivities: Summary.
15.3 Dynamic Hedging.
15.3.1 Delta and Dynamic Hedging.
15.3.2 Implications.
15.3.3 Distribution of Option Payoffs.
15.4 Answers to Chapter Examples.
Ch. 16: Modeling Risk Factors.
16.1 The Normal Distribution.
16.1.1 Why the Normal?
16.1.2 Computing Returns.
16.1.3 Time Aggregation.
16.2 Fat Tails.
16.3 TimeVariation in Risk.
16.3.1 GARCH.
16.3.2 EWMA.
16.3.3 Option Data.
16.3.4 Implied Distributions.
16.4 Answers to Chapter Examples.
Ch. 17: VAR Methods.
17.1 VAR: Local vs. Full Valuation.
17.1.1 Local Valuation.
17.1.2 Full Valuation.
17.1.3 DeltaGamma Method.
17.2 VAR Methods: Overview.
17.2.1 Mapping.
17.2.2 DeltaNormal Method.
17.2.3 Historical Simulation Method.
17.2.4 Monte Carlo Simulation Method.
17.2.5 Comparison of Methods.
17.3 Example.
17.3.1 MarktoMarket.
17.3.2 Risk Factors.
17.3.3 VAR: Historical Simulation.
17.3.4 VAR: DeltaNormal Method.
17.4 Risk Budgeting.
17.5 Answers to Chapter Examples.
Part IV: Credit Risk Management.
Ch. 18: Introduction to Credit Risk.
18.1 Settlement Risk.
18.1.1 Presettlement vvs. Settlement Risk.
18.1.2 Handling Settlement Risk.
18.2 Overview of Credit Risk.
18.2.1 Drivers of Credit Risk.
18.2.2 Measurement of Credit Risk.
18.2.3 Credit Risk vs. Market Risk.
18.3 Measuring Credit Risk.
18.3.1 Credit Losses.
18.3.2 Joint Events.
18.3.3 An Example.
18.4 Credit Risk Diversification.
18.5 Answers to Chapter Examples.
Ch. 19: Measuring Actuarial Default Risk.
19.1 Credit Event. . . . . . . . . . . . . . . . . . . . . . . . . . . 412
19.2 Default Rates.
19.2.1 Credit Ratings.
19.2.2 Historical Default Rates.
19.2.3 Cumulative and Marginal Default Rates.
19.2.4 Transition Probabilities.
19.2.5 Predicting Default Probabilities.
19.3 Recovery Rates.
19.3.1 The Bankruptcy Process.
19.3.2 Estimates of Recovery Rates.
19.4 Application to Portfolio Rating.
19.5 Assessing Corporate and Sovereign Rating.
19.5.1 Corporate Default.
19.5.2 Sovereign Default.
19.6 Answers to Chapter Examples.
Ch. 20: Measuring Default Risk from Market Prices.
20.1 Corporate Bond Prices.
20.1.1 Spreads and Default Risk.
20.1.2 Risk Premium.
20.1.3 The CrossSection of Yield Spreads.
20.1.4 The TimeSeries of Yield Spreads.
20.2 Equity Prices.
20.2.1 The Merton Model.
20.2.2 Pricing Equity and Debt.
20.2.3 Applying the Merton Model.
20.2.4 Example.
20.3 Answers to Chapter Examples.
Ch. 21: Credit Exposure.
21.1 Credit Exposure by Instrument.
21.2 Distribution of Credit Exposure.
21.2.1 Expected and Worst Exposure.
21.2.2 Time Profile.
21.2.3 Exposure Profile for InterestRate Swaps.
21.2.4 Exposure Profile for Currency Swaps.
21.2.5 Exposure Profile for Different Coupons.
21.3 Exposure Modifiers.
21.3.1 Marking to Market.
21.3.2 Exposure Limits.
21.3.3 Recouponing.
21.3.4 Netting Arrangements.
21.4 Credit Risk Modifiers.
21.4.1 Credit Triggers.
21.4.2 Time Puts.
21.5 Answers to Chapter Examples.
Ch. 22: Credit Derivatives.
22.1 Introduction.
22.2 Types of Credit Derivatives.
22.2.1 Credit Default Swaps.
22.2.2 Total Return Swaps.
22.2.3 Credit Spread Forward and Options.
22.2.4 CreditLinked Notes.
22.3 Pricing and Hedging Credit Derivatives.
22.3.1 Methods.
22.3.2 Example: Credit Default Swap.
22.4 Pros and Cons of Credit Derivatives.
22.5 Answers to Chapter Examples.
Ch. 23: Managing Credit Risk.
23.1 Measuring the Distribution of Credit Losses.
23.2 Measuring Expected Credit Loss.
23.2.1 Expected Loss over a Target Horizon.
23.2.2 The Time Profile of Expected Loss.
23.3 Measuring Credit VAR.
23.4 Portfolio Credit Risk Models.
23.4.1 Approaches to Portfolio Credit Risk Models.
23.4.2 CreditMetrics.
23.4.3 CreditRisk+.
23.4.4 Moody’s KMV.
23.4.5 Credit Portfolio View.
23.4.6 Comparison.
23.5 Answers to Chapter Examples.
Part V: Operational and Integrated Risk Management.
Ch. 24: Operational Risk.
24.1 The Importance of Operational Risk. 24.1.1 Case Histories.
24.1.2 Business Lines.
24.2 Identifying Operational Risk.
24.3 Assessing Operational Risk.
24.3.1 Comparison of Approaches.
24.3.2 Acturial Models.
24.4 Managing Operational Risk.
24.4.1 Capital Allocation and Insurance.
24.4.2 Mitigating Operational Risk.
24.5 Conceptual Issues.
24.6 Answers to Chapter Examples.
Ch. 25: Risk Capital and RAROC.
25.1 RAROC.
25.1.1 Risk Capital.
25.1.2 RAROC Methodology.
25.1.3 Application to Compensation.
25.2 Performance Evaluation and Pricing.
25.3 Answers to Chapter Examples.
Ch. 26: Best Practices Reports.
26.1 The G30 Report.
26.2 The Bank of England Report on Barings.
26.3 The CRMPG Report on LTCM.
26.4 Answers to Chapter Examples.
Ch. 27: Firmwide Risk Management.
27.1 Types of Risk.
27.2 ThreePillar Framework.
27.2.1 BestPractice Policies.
27.2.2 BestPractice Methodologies.
27.2.3 BestPractice Infrastructure.
27.3 Organizational Structure.
27.4 Controlling Traders.
27.4.1 Trader Compensation.
27.4.2 Trader Limits.
27.5 Answers to Chapter Examples.
Part VI: Legal, Accounting, and Tax Risk Management.
Ch. 28: Legal Issues.
28.1 Legal Risks with Derivatives.
28.2 Netting.
28.2.1 G30 Recommendations.
28.2.2 Netting under the Basel Accord.
28.2.3 WalkAway Clauses.
28.2.4 Netting and Exchange Margins.
28.3 ISDA Master Netting Agreement.
28.4 The 2002 SarbanesOxley Act.
28.5 Glossary.
28.5.1 General Legal Terms.
28.5.2 Bankruptcy Terms.
28.5.3 Contract Terms.
28.6 Answers to Chapter Examples.
Ch. 29: Accounting and Tax Issues.
29.1 Internal Reporting.
29.1.1 Purpose of Internal Reporting. 29.1.2 Comparison of Methods.
29.1.3 Historical Cost versus MarkingtoMarket.
29.2 External Reporting: FASB.
29.2.1 FAS 133.
29.2.2 Definition of Derivative.
29.2.3 Embedded Derivative.
29.2.4 Disclosure Rules.
29.2.5 Hedge Effectiveness.
29.2.6 General Evaluation of FAS 133.
29.2.7 Accounting Treatment of SPEs.
29.3 External Reporting: IASB.
29.3.1 IAS 37.
29.3.2 IAS 39.
29.4 Tax Considerations.
29.5 Answers to Chapter Examples.
Part VII: Regulation and Compliance.
Ch. 30: Regulation of Financial Institutions.
30.1 Definition of Financial Institutions.
30.2 Systemic Risk.
30.3 Regulation of Commercial Banks.
30.4 Regulation of Securities Houses.
30.5 Tools and Objectives of Regulation.
30.6 Answers to Chapter Examples.
Ch. 31: The Basel Accord.
31.1 Steps in The Basel Accord.
31.1.1 The 1988 Accord.
31.1.2 The 1996 Amendment.
31.1.3 The New Basel Accord.
31.2 The 1988 Basel Accord.
31.2.1 Risk Capital.
31.2.2 OnBalanceSheet Risk Charges.
31.2.3 OffBalanceSheet Risk Charges.
31.2.4 Total Risk Charge.
31.3 Illustration.
31.4 The New Basel Accord.
31.4.1 Issues with the 1988 Basel Accord.
31.4.2 The New Basel Accord: Credit Risk Charges.
31.4.3 Securitization and Credit Risk Mitigation.
31.4.4 The Basel Operational Risk Charge.
31.5 Answers to Chapter Examples.
31.6 Further Information.
Ch. 32: The Basel Market Risk Charges.
32.1 The Standardized Method.
32.2 The Internal Models Approach.
32.2.1 Qualitative Requirements.
32.2.2 The Market Risk Charge.
32.2.3 Combination of Approaches.
32.3 StressTesting.
32.4 Backtesting.
32.4.1 Measuring Exceptions.
32.4.2 Statistical Decision Rules.
32.4.3 The Penalty Zones.
32.5 Answers to Chapter Examples.
Index.
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