Value at Risk and Bank Capital Management

Risk Adjusted Performances, Capital Management and Capital Allocation Decision Making


  • Francesco Saita, Professor of Financial Markets and Institutions and Director of the M.Sc. in Finance at Bocconi University, Milan, Italy, where he is also the Vice Director of Newfin Research Center on Financial Innovation.

While the highly technical measurement techniques and methodologies of Value at Risk have attracted huge interest, much less attention has been focused on how Value at Risk and the risk-adjusted performance measures such as RAROC or economic profit/EVA‚Äě¬∑ can be effectively used to improve a bank¬°¬¶s decision making processes. Academic books are typically concerned primarily with measurement techniques, and devote only a small section to describing the applications, usually without discussing the problems that changing organizational processes in banks may have on business units¬°¬¶ behaviour. Practitioners¬°¬¶ books are often based on a single experience, presenting the approach that has been pursued by a single bank, but often do not adequately evaluate that approach. In actual practice, the choice of how to use Value at Risk and risk-adjusted performance measures has no single optimal solution, but requires effective decision making that can identify the solution that is consistent with the bank¬°¬¶s style of management and coordination mechanisms, and often with characteristics of individual business units as well. In this book, Francesco Saita of Bocconi University argues that even though risk measurement techniques have greatly improved in recent years for market, credit and now also operational risk, capital management and capital allocation decisions are far from becoming purely technical and mechanical. On one hand, decisions about capital management must consider handling different capital constraints (e.g. regulatory vs. economic capital ) and face remarkable difficulties in providing a measure of ¬°¬ßaggregated¬°¬® Value at Risk (i.e. a measure that considers the overall value at risk of the bank after diversification across risk types). On the other hand, the aim of using capital more efficiently through capital allocation cannot be achieved only through a sort of centralized asset allocation process, but rather by designing a Value at Risk limit system and a risk-adjusted performance measurement system that are designed to provide the right incentives to individual business units. This connection between sophisticated and cutting edge risk measurement techniques and practical bank decision making about capital management and capital allocation make this book unique and provide readers with a depth of academic and theoretical expertise combined with practical and real-world understanding of bank structure, organizational constraints, and decisionmaking processes.
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Primary audience: Graduate students in master's or Ph.D. programs in finance/banking; bankers and risk managers involved in capital allocation and portfolio management.Course titles: advanced topics in financial/banking risk management, portfolio management, mathematics of investment, commercial bank management.


Book information

  • Published: February 2007
  • ISBN: 978-0-12-369466-9


"This book does a great service by presenting the measurement of market risk and credit risk in one well-structured book. Aggregation methodology is also presented in detail. The inclusion of real-life examples is also a great benefit to the reader." -- Chris Matten, Partner, Financial Services Industry Practice, PricewaterhouseCoopers

Table of Contents

(dedication)PrefaceChapter 1Value at Risk, Capital Management and Capital Allocation1.1. An Introduction to Value at Risk1.2. Capital management and capital allocation. The structure of the book.Chapter 2What Is ¬°¬ßCapital¬°¬® 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 Capital2.2. An Overview of the Basel II Capital Accord 2.2.1. Pillar 1: Minimum Capital Requirements. The Main Changes Introduced by Basel IIBox 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 Implementation2.3. 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 Allocation2.4. Summary2.5. Further ReadingsChapter 3Market Risk3.1. The Variance-Covariance Approach3.1.1. A Simplified Example3.1.2. The Choice of the Relevant Random Variables3.1.3. Mapping ExposuresBox 3-1. Mapping Equity Positions Through Beta: An Example3.1.4. VaR for a PortfolioBox 3-2. Calculating VaR for a Three-Stock PortfolioBox 3-3. Why Mapping Is Important3.1.5. Estimating Volatility and Correlation: Simple Moving Averages3.1.6. Estimating Volatility and Correlation: Exponentially Weighted Moving Averages and GARCH Models3.1.7. VaR Estimates and the Relevance of the Time Horizon3.1.8. Implied Volatilities and CorrelationsBox 3-4. Deriving Implied Volatility from Option Prices3.2. Simulation Approaches: Historical and Monte Carlo Simulation3.2.1. Historical Simulation3.2.2. The Hybrid Approach3.2.3. Monte Carlo Simulations3.2.4. Filtered Historical Simulations3.3. Value at Risk for Option Positions3.3.1. The Problems in Option VaR Measurement3.3.2. Potential Solutions for Option VaR Measurement3.4. Extreme Value Theory and Copulas3.4.1. Extreme Value Theory3.4.2. Copulas3.5. Expected Shortfall and the Problem of VaR Non-Subadditivity 3.6. Backtesting Market Risk Models3.6.1. Which Series Should Be Considered? Actual vs. Theoretical Portfolio Returns3.6.2. Backtesting VaR Forecasts: Unconditional Accuracy and Independence3.7. Internal VaR Models and Market Risk Capital Requirements3.8. Stress Testing3.9. Summary3.10. Further ReadingsChapter 4Credit Risk4.1. Defining Credit Risk. Expected and Unexpected Losses4.2. Agency Ratings4.2.1. External Rating Assignment4.2.2. Transition Matrixes and Cumulative and Marginal Default Probabilities4.3. Quantitative Techniques for Stand-alone Credit Risk Evaluation: Moody¬°¬¶s/KMV EDF and External Scoring Systems4.3.1. Merton¬°¬¶s (1974) Model and Moody¬°¬¶s/KMV Expected Default FrequencyBox 4-1. Deriving the Theoretical Credit Spread for Risky Bonds in the Merton (1974) Model4.3.2. Credit Scoring Systems4.4. Capital Requirements for Credit Risk under Basel II4.4.1. The Standardized Approach4.4.2. Foundation and Advanced Internal Rating Based approaches4.5. Internal Ratings4.5.1. Internal Rating Assignment Process4.5.2. Rating Quantification and the Definition of Default4.5.3. Point-in-Time versus Through-the-Cycle Internal Ratings4.6. Estimating Loss Given Default4.7. Estimating Exposure at Default4.8. The Interaction between Basel II and International Accounting Standards4.9. Alternative Approaches to Credit Portfolio Risk Modelling4.9.1. CreditMetrics‚Äě¬∑4.9.2. Moody¬°¬¶s/KMV PortfolioManager‚Äě¬∑4.9.3. Credit Portfolio View4.9.4. CreditRisk+4.10. A comparison of main credit portfolio modelsBox 4-2. Industry Practices Concerning Credit Portfolio ModelsBox 4-3. How Close Are Results Obtained from Credit Risk Portfolio Models?4.11. Summary4.12. Further ReadingsChapter 5Operational Risk and Business Risk5.1. Capital Requirements for Operational Risk Measurement: the Three Approaches Proposed by Basel II5.1.1. 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 Sources5.3.1. Operational Risk Mapping and the Identification of Key Risk Indicators5.3.2. Building an Internal Loss Database5.3.3. External Loss Databases5.3.4. Scenario Analysis5.4. Quantifying Operational Risk: from Loss Frequency and Severity to Operational Risk Capital 5.4.1. Modelling Severity Based on Internal Loss Data5.4.2. Integrating Internal Severity Data with External Data and Scenario Analysis5.4.3. Estimating Operational Loss Frequency5.4.4. Estimating Correlation or Dependence among Operational Events 5.4.5. Deriving Operational Risk Capital Estimates Through Simulation5.4.6. 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 Measures5.7. Measuring Business Risk in Practice: Defining an Earnings at Risk Measure5.8. From Earnings at Risk to Capital at Risk5.9. Summary5.10. Further ReadingsChapter 6Risk Capital Aggregation6.1. The Need for Harmonization: Time Horizon, Confidence Level and the Notion of Capital6.2. Risk Aggregation Techniques6.2.1. Choosing the Components to be Aggregated: Business Units versus Risk Types6.2.2. Alternative Risk Aggregation Methodologies6.3. Estimating Parameters for Risk AggregationBox 6-1 Some Examples of Linear Correlation Coefficients Estimates from Existing Studies and Their Implications on Aggregated Risk Capital6.4. 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. Summary6.7. Further ReadingsChapter 7Value at Risk and Risk Control for Market and Credit Risk7.1. Defining VaR-based Limits for Market Risk: Identifying Risk-Taking CentersBox 7-1 Clarifying VaR Measurement Limitations: Deutsche Bank¬°¬¶s Example7.2. 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 EquivalentBox 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 Losses7.3. Managing VaR-Based Trading Limits7.4. Identifying Risk Contributions and Internal Hedges: VaRDelta, Component VaR and Incremental VaRBox 7-3 A Variant for the Calculation of Component CaR7.5. Managing Risk and Pricing Limits for Credit Risk7.5.1. Setting Loan Autonomy Limits: From Notional Size to Expected Loss7.5.2. Setting Loan Pricing Limits7.5.3. Case 1: Large Borrower Applying for a Loan to an Investment Bank7.5.4. Case 2: SME Applying for a Loan to a Smaller Retail-Oriented Bank7.6. Summary7.7. Further ReadingsChapter 8Risk-Adjusted Performance Measurement8.1.Business Areas, Business Units and The Double Role of Risk-Adjusted Performance Measures8.2. Not Only Capital at Risk: Profit Matters Too8.2.1. Transfer Prices8.2.2. Cost Attribution and Its Impact on RAP Measures8.3. Capital Investment versus Capital Allocation8.4. Choosing the Measure of Capital at Risk: (a) Allocated vs. Utilized Capital8.5. Choosing the Measure of Capital at Risk: (b) Diversified vs. Undiversified Capital8.5.1.A Comparison of Alternative Diversified CaR Measures8.5.2. Criteria for Choosing Between Diversified or Undiversified CaR8.6. Choosing the Risk-Adjusted Performance Measure: EVA vs. RAROC8.7. Variants and Potential Extensions8.7.1. Differentiated Target Returns8.7.2. Alternative RAP Measures8.7.3. Expected Shortfall and Performance Measurement8.8. Risk-Adjusted Performances and Managers¬°¬¶ Performance Evaluation8.9. Summary8.10. Further ReadingsChapter 9Risk-adjusted performance targets, capital allocation and the budgeting process9.1. From the Banks Cost of Equity Capital to Performance Targets for the Bank9.1.1. Estimating the cost of equity capital9.1.2. Defining the Target Rate of Return9.2. Should Business Units Target Returns Be Different?9.2.1. The Potential Impacts of a Single Hurdle Rate9.2.2. Estimating Betas for Different Businesses9.2.3. Applying Different Costs of Capital: Identifying the Driver9.3. Capital Allocation and the Planning and Budgeting Process9.3.1. 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. Summary9.6. Further Readings9.7. Final Remarks