• A Guide to Equity Index Construction :
• Portfolio Construction and Risk Budgeting : Third Edition
• Portfolio Analysis : Advanced Topics in Performance Measurement, Risk and Attribution
• Capital Market Campaigning : The Impact of NGOs on Companies, Shareholder Value and Reputational Risk
• Investing in China : New Opportunities in a Transforming Stock Market
• The European Retail Structured Investment Products Market :

More recommendations

• Make an informed decision about how to implement and execute a ‘risk unit allocation’ investment policy
• Analysis of techniques to assess how risk might impact long-term investment returns
• Introduces methods to allocate assets based on the ‘risk unit’ exposures - in individual asset classes and on a portfolio basis, to meet long-term pension obligations and investment return objectives
• Investigates ways to use VAR to accommodate a long-term investment horizon
• Contributions from leading experts drawn from consultancies; large institutional investors; pension plans; investment banks and academia

CONTENTS

Introduction
Leslie Rahl

Part 1: OVERVIEW

1 Risk Budgeting: The Next Step of the Risk Management
Journey - The Veteran’s Prospective
Leslie Rahl

2 Crisis and Risk Management
Myron Scholes

PART 2: UNDERSTANDING RISK BUDGETING

3 Risk Budgeting: Managing Active Risk at the Total Fund Level
Kurt Winkelmann

4 The Dangers of Historical Hedge Fund Data
Andrew B. Weisman and Jerome Abernathy

5 Value-at-Risk for Asset Managers
Christopher L. Culp, Ron Mensink and Andrea M.P. Neves

6 Risk Budgeting fore Pension Funds and Investment
Managers using VAR
Michelle McCarthy

7 Risk Budgeting for Active Investment Managers
Robert Litterman, Jacques Longerstaey, Jacob Rosengarten and Kurt Winkelmann

8 Risk Obsession: Does it Lead to Risk Aversion?
Amy B. Hirsch

9 Market Neutral and Hedged Strategies
Joseph G. Nicholas

10 The Infrastructure Challenge: Empowering the Stakeholder through the Successful Deployment of Technology and Data
Gabriel Bousbib

PART 3: PRACTITIONERS’ THOUGHTS: CASE STUDIES IN RISK BUDGETING

11 Risk Budgeting in a Pension Fund
Leo de Bever, Wayne Kozun and Barbara Zvan

12 Risk Budgeting with Conditional Risk Tolerance
Michael de Marco and Todd E. Petzel

13 VAR for Fund Managers
Stephen Rees

Risk Budgeting Tradeoffs

Hedge funds that appear to offer the best tradeoff of risk and return may actually be the worst choice for placing your money.

That’s the contention of two contributing authors of the book “Risk Budgeting: A New Approach to Investing,” edited by Leslie Rahl, president of Capital Market Risk Advisors, New York.

In a captivating chapter called “The Dangers of Historical Hedge Fund Data,” Andrew B. Weisman and Jerome D. Abernathy, make a strong argument that conventional methods for evaluating asset classes can steer institutions into the worst possible alternative strategies.

Understandably, when institutions are confronted with an alternative strategy or vehicle like a hedge fund, they turn to methods they know, like optimization. “It’s the wrong thing to do,” said Mr. Weisman in an interview. Many alternative strategies at hedge funds don’t behave in a linear fashion, a prerequisite for optimization analysis.

Instead, Mr. Weisman advocates a method he developed with Mr. Abernathy to evaluate hedge fund risk called Generic Model Decomposition. GMD seeks to recreate a generic version of a hedge fund manager’s investment methods, and then uses that model to estimate risk of the strategy over the long term. GMD allows managers with short track records to be evaluated for the long term. The method combines quantitative and some qualitative research.

Mr. Weisman, who is chief investment officer for Nikko Securities International Inc., New York, and Mr. Abernathy, who is managing partner of Stonebrook Structured Products LLC, New York, also said two core lessons regarding hedge fund investing were revealed when developing GMD.

For one, certain classes of hedge fund managers use methods that carry hidden short option exposure, leading investors to allocate too much to that class when using optimization techniques. Implicit short options exposures can lead to high Sharpe ratios-suggesting that the investment offers a good tradeoff of risk and return. But in reality, one of the infrequent “volatility events” linked to that strategy has not yet occurred, so risk is improperly measured on the downside. Once that event occurs, or by simulating the strategy using GMD, a more accurate measure of risk can be identified.

Moreover, hedge fund managers tend to understate the volatility of their portfolios by way of inaccurate pricing. It’s not that hedge fund managers are trying to deceive, it’s just that many of the illiquid securities and positions they hold are difficult to price properly. Risk calculations based on market values may then be understated. (Mr. Weisman recently presented a well-received paper with a related theme to the Institute for Quantitative Research in Finance, known as the Q Group.)

For hedge fund professionals, the chapter by Messrs. Weisman and Abernathy alone makes the book a worthy read. The authors essentially point out what could be a fundamental flaw in the way hedge funds manage assets for institutional investors. Ignore it at your own risk.

Value at Risk

The rest of the book, which is aimed at institutions, is more typical of financial compilations, offering explanations and discussions of the basics and a little more. Among the highlights: Ms. Rahl offers a strong synopsis of the state of Value at Risk. There are no great revelations in her opening chapter, but she provides the proper, broad perspective needed for such a book.

Michelle McCarthy, managing director for Deutsche Bank, contributes a clear-eyed guide for using Value at Risk at the customer level. Ms. McCarthy punches holes in some misconceptions about VAR-such as that VAR can only be computed for short-term holding periods-and points to the specific risks investors should be managing.

A group of authors that work in the Research and Economics department of the Ontario Teachers’ Pension Plan Board, North York, show how VAR can be applied in the real world. Leo de Bever, senior vice president, Wayne Kozun, director, and Barbara Zvan, director, describe how the Ontario pension fund budgets and allocates risk among its portfolio managers. The authors deserve recognition for writing about a dry subject in an interesting fashion.

Similarly, Michael de Marco, senior vice president for Putnam Institutional Management, Boston, and Todd E. Petzel, president and chief investment officer for Commonfund Asset Management Co. Inc., Wilton, Conn., deliver a readable and practical guide for institutional investors seeking to use VAR.

The book can give VAR neophytes a glimpse into the complicated world of risk management; while more advanced practitioners can use it as a reference to call upon when structuring their own VAR programs.

By Paul Barr, Reporter
PBarr@HedgeWorld.com

Reviewed by Douglas Long, Principia Partners.

Risk budgeting, a relatively new concept for long-term investments, aims to overturn or at least supplement the traditional asset allocation techniques with a modern risk management framework. The market is already beginning to move towards this new paradigm, where asset allocation is not just based on measures like standard deviations, performance, Sharpe and information ratios but also takes into account the latest risk management practices including VaR, stress testing and risk-adjusted returns. This allows for a more informed decision-making process regarding the fund/portfolio compositions. These ideas, although not new in themselves, have not been systematically applied in this field.

The book is edited and introduced by Leslie Rahl, an influential and highly regarded risk management and derivatives professional with some 20 years experience in the industry. Her experience is evident from both the introduction and article selection.

Risk budgeting is first of all introduced in two articles, one by Leslie Rahl and the other by Myron Scholes, which provide an excellent overview and experienced views of historical and current investment risk management techniques and trends. The book then proceeds with 11 chapters that are aimed at giving the reader a greater understanding of the concepts and implementation procedures behind risk budgeting.

The collection of articles is taken from all angles within the industry and as such would be very useful for all practitioners in the market, whether they are asset managers or investors/plan sponsors. In particular, as investors become increasingly aware and sophisticated they are requiring more objective and informative data to aid and monitor their investment decisions.

In all Rahl has done an excellent job in providing a collection of articles that clearly bring together the concepts surrounding risk budgeting, which should be essential reading for anyone involved in this area.

Ms Rahl was named among the “Top 50 Women in Finance” by Euromoney in 1997 and was profiled in both the fifth and 10th anniversary issues of Risk magazine. She has been published numerous times.

She was a director of the International Swaps and Derivatives Association (ISDA) for 5 years and is currently a member of the Board of the International Association of Financial Engineers and the Fischer Black Memorial Foundation and a member of the Board of Advisors for the financial engineering programme at the Sloan School. Ms Rahl received her undergraduate degree in computer science from the Massachusetts Institute of Technology and her MBA from the Sloan School of Management.

• Interest Rate Derivatives : A Practical Guide to Applications, Pricing and Modelling

• Covers the theories, models, measures, applications, software and regulation issues that have shaped the industry and offers an abundance of realistic and considered future perspectives
• Includes new perspectives on various risk related issues as well as new case-studies on derivatives disasters and rogue trading
• Each contributing author represents the pinnacle of their respective field including: John Hull, Mark Rubinstein and Robert Jarrow, Paul Samuelson and Robert Merton
• Features anecdotal autobiographies from leading risk and finance figures in the field including, Nobel prize winners
• A single-source volume covering every major theory and model - the definitive reference tool for the risk management professional or academic

CONTENTS

Introduction
Peter Field

Timeline
Risk magazine

PART I: THE RATIONALE OF RISK MANAGEMENT

1 Risk Management as a Process
David Mengle

2 An Overview of the Evolution of the Over-the-counter Derivatives Market
Carola von Schenk

PART II: THE ROOTS AND DEVELOPMENT OF MODERN FINANCIAL MODELLING TECHNIQUES

3 Option Pricing Models and Stochastic Methods in Finance, 1900-1990
William Margrabe

4 Markowitz Mean-Variance Portfolio Theory
Neil D. Pearson

5 Equilibrium Asset Pricing and Discount Factors: Overview and Implications for Derivatives Valuation and Risk Management
John H. Cochrane and Christopher L. Culp

6 The Modigliani-Miller Propositions
Christopher L. Culp

7 The Past, Present and Future of Term Structure Modelling
Lane Hughston

PART III: THE DEVELOPMENT OF RISK MANAGEMENT SOFTWARE

8 The Development of Risk Management Software
Dan Rosen

PART IV: THE DEVELOPMENT OF RISK MEASURES AND METHODOLOGIES

9 The Origin and Development of Value-at-Risk
Olivier Scaillet

10 Stress Testing in Risk Management
Vineer Bhansali

11 Extreme Value Theory and Statistics for Heavy Tail Data
Silvia Caserta and Casper G. de Vries

12 The Copula
David A. Chapman

13 Modelling Volatility
Jin-Chuan Duan

14 The Evolution of Counterparty Credit Risk Management
David M. Rowe

15 Theory and Practice of Model Risk Management
Riccardo Rebonato

PART V: THE DEVELOPMENT OF FINANCIAL RISK IDENTIFICATION

16 A Retrospective Look at Market Risk
Barbara Kavanagh

17 Credit Risk from a Bank’s Perspective
Arnaud de Servigny and Olivier Renault

18 Operational Risk: Past, Present and Future
Marcelo Cruz

19 Enterprise-wide Risk Management
James Lam

20 Endogenous Risk
Jon Danielsson and Hyun Song Shin

PART VI: THE USE OF RISK MANAGEMENT

21 Multi-National Corporate Risk Management Practice
Arnold Miyamoto and Ramon Espinosa

22 The Use of Risk Management by Corporations
Rohan Williamson

23 Risk in US Energy Markets
Edward N. Krapels

24 Risk Management in Asset Management
Gregory Connor and Robert A. Korajczyk

25 Risk Management for Hedge Funds and Funds of Hedge Funds
Virginia Reynolds Parker

26 Evolution of the Global Weather Derivatives Market
Jeffrey Porter

PART VII: REGULATORY ISSUES AND BANKING SUPERVISION

27 Regulatory Origins of Risk Management
David Mengle

28 Regulatory Capital Treatment of Counterparty Credit Risk: the Need for a Reform
Emmanuelle Sebton

29 Operational Risk - The Empiricists Strike Back?
Richard Metcalfe

PART VIII: FUTURE PERSPECTIVES

30 Use of Price Derivatives in Commodity Producing Developing Countries
Panos Varangis, John Nash and Funke Oyewole

PART IX: DERIVATIVES DISASTERS - CASE STUDIES

31 No Surprises
Yana O’Sullivan and Geoff Kates

32 Medium-Term Risk Management Lessons from Long-Term Capital Management
Philippe Jorion

33 Metallgesellschaft
Christopher L. Culp

34 Analysis of the Orange County Disaster
Alan C. Shapiro

35 Allied Irish Bank
Nikki Marmery

36 Scenes from a Tragedy - Bankers Trust and Procter & Gamble
William Falloon and Richard Irving

37 Singapore Sting - Barings
Mark Nicholls

38 A Question of Authority - Hammersmith and Fulham
Mark Nicholls

39 Full Metal Racket - Sumitomo Corporation
Mark Nicholls

APPENDIX: FINANCE AND RISK THINKERS

40 Remembering Fischer Black (1938-1995)
Emanuel Derman

41 John Cox - Improving on Black-Scholes
Navroz Patel

42 The Worlds of Yesterday
Emanuel Derman

43 Perspectives on Risk Management
John Hull

44 Jonathan Ingersoll - Driven to Simplicity
Paul Lyon

45 Mathematics and Finance: A Fruitful Relationship
Robert Jarrow

46 Adventures in Portfolio Theory
Harry M. Markowitz

47 Unexpected Roads, Happily Travelled
Robert C. Merton

48 Remembering Merton Miller (1923-2000)
John Ferry

49 Inspired by America
Franco Modigliani

50 Stephen Ross - Dedicated to the Real World
Navroz Patel

51 All in All, it’s been a Good Life
Mark Rubinstein

52 Memoirs of an Early Finance Theorist
Paul A. Samuelson

53 Myron Scholes - From Theory to Practice
Keith Brody

54 William Sharpe - A Career-defining Risk
Dwight Cass

http://db.riskwaters.com/public/showPage.html?page=book_page&tempPageName=154149#contents

55 Reflections on a Revolution
Oldrich Vasicek

This ground-breaking executive report provides you with a complete operational risk methodology specifically tailored to hedge fund management. Stay ahead of the anticipated requirements on systemic risks, operational systems and potential capital adequacy by applying the principles and recommendations presented in this accessible report.

CONTENTS

PART 1: PRODUCTS AND TRADING

1 Diversity Scoring for Market Value CDOs
C. Rouvinez
Capital Dynamics

A useful concept, the collateralised debt obligation (CDO) diversity score measures the size of a fictional pool of identical, uncorrelated assets that has similar distributional properties to the real collateral pool underlying a cash flow CDO. Here, Christophe Rouvinez shows how to generalise the concept to market value CDOs, where the collateral is actively traded.

2 I Will Survive
Jon Gregory; Jean-Paul Laurent
BNP Paribas

Jon Gregory and Jean-Paul Laurent apply an analytical conditional dependence framework to the valuation of default baskets and synthetic CDO tranches, matching Monte Carlo results for pricing and showing significant improvement in the calculation of deltas.

3 All Your Hedges in One Basket
Leif Andersen; Jakob Sidenius; Susanta Basu
Banc of America Securities

Leif Andersen, Jakob Sidenius and Susanta Basu present new techniques for single-tranche CDO sensitivity and hedge ratio calculations. Using factorisation of the copula correlation matrix, discretisation of the conditional loss distribution followed by a recursion-based probability calculation, and derivation of analytical formulas for deltas, they demonstrate a significant improvement in computational speeds.

4 Credit Barrier Models
Claudio Albanese; Oliver Chen; Andrei Zavidonov; Giuseppe Campolieti
University of Toronto; NumeriX; Wilfred Laurier University

Claudio Albanese, Giuseppe Campolieti, Oliver Chen and Andrei Zavidonov construct an analytic credit barrier model driven by credit ratings, constrained to fit the term structure of credit spreads.

5 On the Dependence of Equity and Asset Returns
Roy Mashal; Marco Naldi; Assaf Zeevi
Lehman Brothers; Columbia University

Asset returns play an important role in credit risk modelling. Here, Roy Mashal, Marco Naldi and Assaf Zeevi investigate the co-dependence behaviour of asset returns semi-parametrically. They find that the Student-t copula outperforms the normal copula as a description of the co-dependence structure. They also find that the joint tail dependence of equity and asset returns is similar, suggesting that equity returns are a good proxy for asset returns, both for investmentgrade and high-yield names.

6 Index Volatility Surface via Moment-Matching Techniques
Peter Lee; Limin Wang; Abdelkerim Karim
Lehman Brothers

Peter Lee, Limin Wang and Abdelkerim Karim present a basket construction technique using Gram-Charlier-Edgeworth expansions. They show how to express basket option skews and smiles in terms of its underlying components, and demonstrate how market-dependent correlation is necessary to fit observed properties of index options.

7 Capturing the Smile
Simon Johnson; Han Lee
NumeriX Ltd.

Since the discovery that traditional calibration methods fail to capture the dynamics of the smile, new approaches based on mixtures or ensembles of models have been developed. Simon Johnson and Han Lee present a variant of this approach that can be used to simultaneously calibrate European-style and barrier options, as well as cliquets.

8 Dealing with Discrete Dividends
Remco Bos; Anna Shepeleva; Alexander Gairat
ING; Fortis Bank

Over the past year, we have published several papers on the issue of options on stocks with discrete dividends. At least three distinct models are used by practitioners, involving trade-offs between accuracy and tractability. Here, Remco Bos, Alexander Gairat and Anna Shepeleva discuss how to use mixtures of discrete dividend models in a consistent way.

9 Why Be Backward?
Peter Carr; Ali Hirsa
New York University; Morgan Stanley

Originally developed as a tool for calibrating smile models, so-called forward methods can also be used to price options and derive Greeks. Here, Peter Carr and Ali Hirsa apply the technique to the pricing of continuously exercisable American-style put options, developing a forward partial integro-differential equation within a jump diffusion framework.

10 From Horses to Hedging
Ken Baron; Jeffrey Lange
Longitude

Financial derivatives rely on liquid underlying markets to work properly, but what happens when such underlying markets do not exist, as is the case for indexes such as GDP or unemployment? Here, Ken Baron and Jeffrey Lange suggest a parimutuel auction system adapted from the betting industry as a solution to this problem.

11 Assessing Views
Gianluca Fusai; Attilio Meucci
University of Piemonte Orientale; Relative Value International

A key breakthrough in portfolio management theory was the Black-Litterman framework for finding which subjective view of market performance was best supported by empirical data. However, the question remains of how to measure the divergence of a single manager view conditioned using this framework with a firm-wide view of the market embodying the equilibrium returns found from data. Here, Gianluca Fusai and Attilio Meucci provide a technique for doing this.

12 Real Option Valuation and Equity Markets
Thomas Dawson; Jennifer Considine
D2 Capital; Energy politics

Many non-financial assets can be viewed as ‘real options’ linked to some underlying variable such as a commodity price. Here, Thomas Dawson and Jennifer Considine show that the stock price of a well-known electricity generating company is significantly correlated with the volatility of electricity-gas spark spreads, providing empirical support for real options valuation.

13 A Liquidity Haircut for Hedge Funds
Hari Krishnan; Izzy Nelken
Morgan Stanley; Super Computer Consulting

Investors in hedge funds have learned to be cautious when making decisions due to problems of survivorship bias, autocorrelation and hidden optionality. Here, Hari Krishnan and Izzy Nelken show how to quantify such caution. By analysing the incentive structure of hedge fund managers using an option pricing approach, they derive a liquidity haircut to compensate for lockup periods, and an illiquidity premium that effectively increases volatility.

14 Bidding Principles
Robert Almgren; Neil Chriss
University of Toronto; SAC Capital

Robert Almgren and Neil Chriss show how principal bid programme trades can be priced and evaluated as part of a trading business. By annualising the price impacts and variances of such trades, they construct an information ratio measure that can be used to set hurdles below which bids at a given discount should not be accepted.

15 Black Smirks
Fei Zhou
Lehman Brothers

Fei Zhou presents a simple stochastic volatility extension of the Black interest rate option pricing model widely used by traders. Using a perturbative expansion in volatility of volatility, he derives modified Black formulas that correctly fit the observed volatility smirk, and can be used in turn to calibrate more sophisticated models.

16 Shadow Interest
Viatcheslav Gorovoi; Vadim Linetsky
Northwestern University

Using a Vasicek process for the shadow rate, Viatcheslav Gorovoi and Vadim Linetsky develop an analytical solution for pricing zerocoupon bonds using eigenfunction expansions, and show how to calibrate their model to the Japanese bond market. This article is not the last word on the subject - in particular, the relationship between shadow interest rates, real rates and inflation should be explored - but we hope it will encourage further research.

PART 2 : RISK AND CAPITAL

17 Extreme Forex Moves
Peter Blum; Michel M. Dacorogna
ETH; Converium Ltd

What is the appropriate statistical description of tail risk in a market portfolio? In the context of foreign exchange, Peter Blum and Michel Dacorogna address this problem using extreme value theory. Using 20 years of data, they estimate parameters for an appropriate tail event probability distribution and use it to calculate risk limits for open overnight foreign exchange positions.

18 What Causes Crashes?
Didier Sornette; Yannick Malevergne; Jean-François Muzy
University of Nice-Sophia Antipolis and University of California; University of Lyon; University of Coralca

Are large market events caused by easily identifiable exogenous shocks such as major news events, or can they occur endogenously, without apparent external cause, as an inherent property of the market itself? Here, Didier Sornette, Yannick Malevergne and Jean-François Muzy ask this question of a number of large stock market events and conclude that endogenous crashes do exist.

19 VAR: History or Simulation?
George Skiadopoulos; Greg Lambadiaris; Louiza Papadopoulou; Yiannis Zoulis
University of Piraeus; University of Warwick

Greg Lambadiaris, Louiza Papadopoulou, George Skiadopoulos and Yiannis Zoulis assess the performance of historical and Monte Carlo simulation in calculating VAR, using data from the Greek stock and bond market. They find that while historical simulation results in over-commitment of capital for linear stock portfolios, the results for non-linear bond portfolios are less clear.

20 Random Tranches
Michael Gordy; David Jones
US Federal Reserve Board

How should economic or regulatory capital be allocated to tranches of securitisations? The standard Basel conditional dependence calculations are complicated in this case by non-linearity effects and complex deal dependence. Here, Michael Gordy and David Jones present an uncertainty in loss provision approach that simplifies these problems, and leads to a single economic capital formula suitable for regulatory purposes.

21 Analysing Counterparty Risk
Eduardo Canabarro; Evan Picoult; Tom Wilde
Goldman Sachs; Citigroup; Credit Suisse First Boston

In an attempt to improve on existing regulatory approaches to derivatives counterparty credit risk, Eduardo Canabarro, Evan Picoult and Tom Wilde present a new method based on expected positive exposure (EPE). Using a one-factor conditional independence framework, they derive a formula for the ratio of EPE to fixed loan-equivalent exposures, showing its dependence on various portfolio parameters and comparing analytical with Monte Carlo calculations.

22 Testing Rating Accuracy
Bernd Engelmann; Evelyn Hayden; Dirk Tasche
Deutsche Bundesbank; University of Vienna; Deutsche Bundesbank

As Basel II approaches the implementation stage, regulators have identified internal ratings validation as a key challenge for banks using this approach. Here, Bernd Engelmann, Evelyn Hayden and Dirk Tasche build upon previous research showing how to use the so-called receiver operator characteristic method in ratings validation, testing their results on a real database of small and medium-sized enterprise loans.

23 Market-Implied Ratings
Ludovic Breger; Lisa Goldberg; Oren Cheyette
Barra

There has been much debate over the respective merits of credit ratings and market-based indicators. Ludovic Breger, Lisa Goldberg and Oren Cheyette present a new approach that tries to incorporate the benefits of both approaches. Starting with agency ratings, they ask how the information obtained from market credit spreads can be used to improve them.

24 Benchmarking Asset Correlations
Alfred Hamerle; Daniel Rösch; Thilo Liebig
University of Regensburg; Deutsche Bundesbank

Basel II stipulates that the asset correlation to be used in calibration of obligor risk weights is 20%. Here, Alfred Hamerle, Thilo Liebig and Daniel Rösch use a parametric model to empirically obtain asset correlations from a large database of historical defaults. They find the observed correlation to be an order of magnitude less than the Basel assumption, and suggest that the parameter could be made adjustable as a result.

25 Correlation Evidence
Arnaud de Servigny; Olivier Renault
Standard & Poor’s Risk Solutions

Like ratings, default correlation is an area of fierce industry debate. But any fundamental, long-term investor searching for fair value in credit correlation will want to understand what the historical data actually says. Here, Arnaud de Servigny and Olivier Renault address this need. By exploring a large rating agency database, they suggest that the link between equity and default correlations is obscured by statistical noise, while risk-free interest rates appear to have little measurable effect.

26 A False Sense of Security
Jon Frye
Federal Reserve Bank of Chicago

Credit portfolio models often assume that recovery rates are independent of default probabilities. Here, Jon Frye presents empirical evidence showing that such assumptions are wrong. Using US historical default data, he shows that not only are recovery rates sensitive to the economic cycle, but also that they vary more for senior debt than for junior debt categories.

27 Ultimate Recoveries
Craig Friedman; Sven Sandow
Standard & Poor’s

Measuring recovery using the ultimate rate observed at emergence from bankruptcy may be conceptually desirable, but modelling it is difficult. Craig Friedman and Sven Sandow tackle the problem by maximising the creditor’s utility function, constructed from a recovery rate probability distribution, conditional on information that ought to influence it, such as collateral quality and debt seniority.

28 Unexpected Recovery Risk
Michael Pykhtin
KeyCorp

For credit portfolio managers, the priority is to properly incorporate recovery rates into existing models. Here, Michael Pykhtin improves upon earlier approaches, allowing recovery rates to depend on the idiosyncratic part of a borrower’s asset return, in addition to the systematic factor. Using a lognormal distribution of collateral value, ensuring that it always remains positive, he derives closed-form expressions for expected loss and economic capital.

29 Credit Ensembles
Kevin Thompson; Roland Ordovas
BNP Paribas; BSCH

Kevin Thompson and Roland Ordovas address the question of how individual counterparties contribute to the total credit risk of a portfolio. They provide an analytic method, new to credit modelling, to estimate all joint default statistics conditional upon a given portfolio loss. The results clarify how the structure of the portfolio changes with loss amount and how clusters of default arise in credit portfolios.

30 The Road to Partition
Kevin Thompson; Roland Ordovas
BNP Paribas; Caixa Catalunya

Applying the ensemble approach developed in these pages last month, Kevin Thompson and Roland Ordovas calculate risk contributions and show how to measure higher-order default dependence using the method of partitions. The results provide tools allowing credit portfolio managers to assess the risks within their portfolios conditional upon different levels of loss.

31 Coarse-Grained CDOs
Michael Pykhtin; Ashish Dev
Keycorp

While analytical models of credit portfolio risk using conditional independence have been one of the most promising areas of recent research, they often involve granularity assumptions that are violated in CDO reference portfolios. Here, Michael Pykhtin and Ashish Dev lift the usual fine-grained portfolio restriction to calculate CDO loss distributions for coarse-grained reference portfolios. Interestingly, they show that senior tranches are particularly sensitive to the level of granularity.

32 Residual Risk in Auto Leases
Michael Pykhtin; Ashish Dev
Keycorp

Michael Pykhtin and Ashish Dev use a conditional independence framework to calculate the economic loss distribution for a portfolio of auto leases. Using the fact that portfolios of this type are usually fine-grained, the authors derive an analytic formula for the economic capital dependent on systematic risk factors.

33 Contributions to Credit Risk
Alexandre Kurth; Dirk Tasche
UBS Wealth Management; Deutsche Bundesbank

Optimisation of credit portfolios requires that risk contributions be quantified. However, there has been disagreement over which of three popular tail risk measures should be used. Here, Alexandre Kurth and Dirk Tasche offer a way forward, showing how to calculate all three measures in the context of CreditRisk+, and then applying the calculation to a set of sample portfolios, with interesting results.

34 Enhancing CreditRisk+
Götz Giese
Commerzbank

Of the various analytical approaches to credit portfolio modelling, CreditRisk+ has become the most popular due to its tractability. However, the model suffers from the restrictive assumption of sector independence. Moreover, the recursion relation for calculating the loss distribution is unstable for very large portfolios. Here, Götz Giese presents an improved version of the model with a stable recursion scheme and sector correlations, which compares favourably with other approximation techniques when used to calculate loss distributions.

35 Using the Grouped t-Copula
Stéphane Daul; Enrico De Giorgi; Filip Lindskog; Alexander McNeil
Swiss Re; University of Zurich; Risk Lab; ETH Zurich

Student-t copula models are popular, but can be over-simplistic when used to describe credit portfolios where the risk factors are numerous or dissimilar. Here, Stéphane Daul, Enrico De Giorgi, Filip Lindskog and Alexander McNeil construct a new, generalised model - the ‘grouped t-copula’ - that clusters individual risk factors within various geographical sectors. The authors show how to estimate parameters for the grouped t-copula, and compare estimates for VAR and expected shortfall with those given by other models.

36 Overcoming the Hurdle
Thomas C. Wilson
Oliver, Wyman & Company

How should capital be allocated to different business lines in a financial institution? Thomas Wilson explores this question from an investor’s perspective by constructing a statistical model that measures the risk of individual business types. The results suggest that capital allocation decisions that ignore variations in the cost of capital are erroneous.

NB - This table of contents is provisional until final publication of the book. Small changes to chapter titles and order may occur.