Value at Risk and Bank Capital Management

Value at Risk and Bank Capital Management, 1st Edition

Risk Adjusted Performances, Capital Management and Capital Allocation Decision Making

Value at Risk and Bank Capital Management, 1st Edition,Francesco Saita,ISBN9780123694669


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A unique combination of concise, expert academic analysis of the latest technical VaR measures and their applications and the practical realities of bank decision making about capital management and capital allocation.

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Key Features

*Contains concise, expert analysis of the latest technical VaR measures but without the highly mathematical component of other books
*Discusses practical applications of these measures in the real world of banking, focusing on effective decision making for capital management and allocation
*Author is based at Bocconi University in Milan, Italy, one of the foremost institutions for banking in Europe


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„· 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 ¡§aggregated¡¨ 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.


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.

Francesco Saita

Affiliations and Expertise

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.

Value at Risk and Bank Capital Management, 1st Edition



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

Quotes and reviews

"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
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