Value at Risk and Bank Capital Management,

(dedication)

Preface


Chapter 1
Value at Risk, Capital Management and Capital Allocation

1.1. An Introduction to Value at Risk

1.2. Capital management and capital allocation. The structure of the book.



Chapter 2
What Is ¡§Capital¡¨ Management?



2.1. Regulatory Capital and the Evolution towards Basel II
2.1.1. The 1988 Basel I Accord and the 1996 Amendment
2.1.2. The Concept of Regulatory Capital

2.2. An Overview of the Basel II Capital Accord
2.2.1. Pillar 1: Minimum Capital Requirements. The Main Changes Introduced by Basel II
Box 2-1. The Impact of the Basel II Accord on the Level of Minimum Regulatory Capital Requirements
2.2.2. Pillar 2: Supervisory Review Process
2.2.3. Pillar 3: Market Discipline
2.2.4. The Debate about Basel II Adoption and Implementation

2.3. Bank¡¦s Estimates of Required Capital and the Different Notions of Bank Capital
2.3.1. Book Value of Capital and the Impact of IAS/IFRS
2.3.2. Market Capitalization and the Double Perspective of Bank Managers
2.3.3. The Impact of Alternative Notions of Capital on Capital Management and Allocation

2.4. Summary

2.5. Further Readings


Chapter 3
Market Risk

3.1. The Variance-Covariance Approach
3.1.1. A Simplified Example
3.1.2. The Choice of the Relevant Random Variables
3.1.3. Mapping Exposures
Box 3-1. Mapping Equity Positions Through Beta: An Example
3.1.4. VaR for a Portfolio
Box 3-2. Calculating VaR for a Three-Stock Portfolio
Box 3-3. Why Mapping Is Important
3.1.5. Estimating Volatility and Correlation: Simple Moving Averages
3.1.6. Estimating Volatility and Correlation: Exponentially Weighted Moving Averages and GARCH Models
3.1.7. VaR Estimates and the Relevance of the Time Horizon
3.1.8. Implied Volatilities and Correlations
Box 3-4. Deriving Implied Volatility from Option Prices

3.2. Simulation Approaches: Historical and Monte Carlo Simulation
3.2.1. Historical Simulation
3.2.2. The Hybrid Approach
3.2.3. Monte Carlo Simulations
3.2.4. Filtered Historical Simulations

3.3. Value at Risk for Option Positions
3.3.1. The Problems in Option VaR Measurement
3.3.2. Potential Solutions for Option VaR Measurement

3.4. Extreme Value Theory and Copulas
3.4.1. Extreme Value Theory
3.4.2. Copulas

3.5. Expected Shortfall and the Problem of VaR Non-Subadditivity

3.6. Backtesting Market Risk Models
3.6.1. Which Series Should Be Considered? Actual vs. Theoretical Portfolio Returns
3.6.2. Backtesting VaR Forecasts: Unconditional Accuracy and Independence

3.7. Internal VaR Models and Market Risk Capital Requirements

3.8. Stress Testing

3.9. Summary

3.10. Further Readings




Chapter 4
Credit Risk

4.1. Defining Credit Risk. Expected and Unexpected Losses

4.2. Agency Ratings
4.2.1. External Rating Assignment
4.2.2. Transition Matrixes and Cumulative and Marginal Default Probabilities

4.3. Quantitative Techniques for Stand-alone Credit Risk Evaluation: Moody¡¦s/KMV EDF and External Scoring Systems
4.3.1. Merton¡¦s (1974) Model and Moody¡¦s/KMV Expected Default Frequency
Box 4-1. Deriving the Theoretical Credit Spread for Risky Bonds in the Merton (1974) Model
4.3.2. Credit Scoring Systems

4.4. Capital Requirements for Credit Risk under Basel II
4.4.1. The Standardized Approach
4.4.2. Foundation and Advanced Internal Rating Based approaches

4.5. Internal Ratings
4.5.1. Internal Rating Assignment Process
4.5.2. Rating Quantification and the Definition of Default
4.5.3. Point-in-Time versus Through-the-Cycle Internal Ratings

4.6. Estimating Loss Given Default

4.7. Estimating Exposure at Default

4.8. The Interaction between Basel II and International Accounting Standards

4.9. Alternative Approaches to Credit Portfolio Risk Modelling
4.9.1. CreditMetrics„·
4.9.2. Moody¡¦s/KMV PortfolioManager„·
4.9.3. Credit Portfolio View
4.9.4. CreditRisk+

4.10. A comparison of main credit portfolio models
Box 4-2. Industry Practices Concerning Credit Portfolio Models
Box 4-3. How Close Are Results Obtained from Credit Risk Portfolio Models?

4.11. Summary

4.12. Further Readings



Chapter 5
Operational Risk and Business Risk


5.1. Capital Requirements for Operational Risk Measurement: the Three Approaches Proposed by Basel II
5.1.1. The Basic Indicator Approach (BIA)
5.1.2. The Standardized Approach (SA)
5.1.3. The Advanced Measurement Approach

5.2. The Objectives of Operational Risk Management

5.3. Quantifying Operational Risk: Building the Data Sources
5.3.1. Operational Risk Mapping and the Identification of Key Risk Indicators
5.3.2. Building an Internal Loss Database
5.3.3. External Loss Databases
5.3.4. Scenario Analysis

5.4. Quantifying Operational Risk: from Loss Frequency and Severity to Operational Risk Capital

5.4.1. Modelling Severity Based on Internal Loss Data
5.4.2. Integrating Internal Severity Data with External Data and Scenario Analysis
5.4.3. Estimating Operational Loss Frequency
5.4.4. Estimating Correlation or Dependence among Operational Events
5.4.5. Deriving Operational Risk Capital Estimates Through Simulation
5.4.6. Is Risk Measurement the Final Step?

5.5. Case Study: U.S. Banks¡¦ Progress on Measuring Operational Risk (by Patrick de Fontnouvelle and Victoria Garrity, Supervision, Regulation and Credit Department,
Federal Reserve Bank of Boston)

5.6. The Role of Business Risk and Earnings at Risk Measures

5.7. Measuring Business Risk in Practice: Defining an Earnings at Risk Measure

5.8. From Earnings at Risk to Capital at Risk

5.9. Summary

5.10. Further Readings


Chapter 6
Risk Capital Aggregation

6.1. The Need for Harmonization: Time Horizon, Confidence Level and the Notion of Capital

6.2. Risk Aggregation Techniques
6.2.1. Choosing the Components to be Aggregated: Business Units versus Risk Types
6.2.2. Alternative Risk Aggregation Methodologies

6.3. Estimating Parameters for Risk Aggregation
Box 6-1 Some Examples of Linear Correlation Coefficients Estimates from Existing Studies and Their Implications on Aggregated Risk Capital

6.4. Case Study: Capital Aggregation within Fortis (by Luc Henrard, Chief Risk Officer, Fortis, and Ruben Olieslagers, Director, Central Risk Management, Fortis)

6.5. A Synthetic Comparison of Alternative Risk Aggregation Techniques

6.6. Summary

6.7. Further Readings



Chapter 7
Value at Risk and Risk Control for Market and Credit Risk


7.1. Defining VaR-based Limits for Market Risk: Identifying Risk-Taking Centers
Box 7-1 Clarifying VaR Measurement Limitations: Deutsche Bank¡¦s Example

7.2. Managing VaR Limits for Market Risk: the Links between Daily VaR and Annual Potential Losses
7.2.1. Translating Actual Daily VaR Values into an Ex-Post Yearly VaR Equivalent
Box 7-2 Daily VaR Fluctuations and Their Implications for Ex-Post Yearly VaR Equivalent: An Example Based on Real Data
7.2.2. Translating Yearly Ex-Ante Acceptable Loss into a Daily VaR Equivalent
7.2.3. The Case of Variable VaR Limits and the Role of Cumulated Losses

7.3. Managing VaR-Based Trading Limits

7.4. Identifying Risk Contributions and Internal Hedges: VaRDelta, Component VaR and Incremental VaR
Box 7-3 A Variant for the Calculation of Component CaR

7.5. Managing Risk and Pricing Limits for Credit Risk
7.5.1. Setting Loan Autonomy Limits: From Notional Size to Expected Loss
7.5.2. Setting Loan Pricing Limits
7.5.3. Case 1: Large Borrower Applying for a Loan to an Investment Bank
7.5.4. Case 2: SME Applying for a Loan to a Smaller Retail-Oriented Bank

7.6. Summary

7.7. Further Readings



Chapter 8
Risk-Adjusted Performance Measurement
8.1.Business Areas, Business Units and The Double Role of Risk-Adjusted Performance Measures

8.2. Not Only Capital at Risk: Profit Matters Too
8.2.1. Transfer Prices
8.2.2. Cost Attribution and Its Impact on RAP Measures

8.3. Capital Investment versus Capital Allocation

8.4. Choosing the Measure of Capital at Risk: (a) Allocated vs. Utilized Capital

8.5. Choosing the Measure of Capital at Risk: (b) Diversified vs. Undiversified Capital
8.5.1.A Comparison of Alternative Diversified CaR Measures
8.5.2. Criteria for Choosing Between Diversified or Undiversified CaR

8.6. Choosing the Risk-Adjusted Performance Measure: EVA vs. RAROC

8.7. Variants and Potential Extensions
8.7.1. Differentiated Target Returns
8.7.2. Alternative RAP Measures
8.7.3. Expected Shortfall and Performance Measurement

8.8. Risk-Adjusted Performances and Managers¡¦ Performance Evaluation

8.9. Summary

8.10. Further Readings



Chapter 9
Risk-adjusted performance targets, capital allocation and the budgeting process

9.1. From the Banks Cost of Equity Capital to Performance Targets for the Bank
9.1.1. Estimating the cost of equity capital
9.1.2. Defining the Target Rate of Return

9.2. Should Business Units Target Returns Be Different?
9.2.1. The Potential Impacts of a Single Hurdle Rate
9.2.2. Estimating Betas for Different Businesses
9.2.3. Applying Different Costs of Capital: Identifying the Driver
9.3. Capital Allocation and the Planning and Budgeting Process
9.3.1. Why Should Capital Allocation Be Linked to the Planning Process?
9.3.2. Why Should Capital Allocation Not Be Linked to the Planning Process?

9.4. Capital Allocation Process at UniCredit Group (by Elio Berti, head of Capital Allocation, CFO Department, UniCredit)


9.5. Summary

9.6. Further Readings


9.7. Final Remarks