Risk Analysis Techniques
1998 GARP FRM Exam Review Class Notes
Available at:
http://www.EuclidResearch.com/
current.htm
2
..........
Risk Analysis Techniques
GARP FRM Exam Review Class Notes
Ian Hawkins September 1998
Table of Contents
Introduction ..............................................................................3
VaR Assumptions ....................................................................3
Delta-Normal Methodology .....................................................5
Delta-Gamma Methodology ....................................................6
Historical Simulation................................................................7
Stress Testing...........................................................................8
Monte Carlo Simulation...........................................................8
Raroc .........................................................................................9
Model Risk ..............................................................................10
Implementation Strategy .......................................................13
Warning Signs........................................................................14
Conclusion..............................................................................15
Other Sources.........................................................................15
Answers to Sample Exam Questions ..................................16
Answers to Risktek Risk Olympics™ Questions ...............16
3
Introduction1
The purpose of this class is to provide an idiosyncratic review of the techniques for risk
analysis that a risk management professional should be familiar with. This document contains
a large number of references and you should spend some time tracking a few of them down,
particularly in areas where you feel less comfortable with your own experience or the class
content. There is no guarantee that the information presented here is either correct or what the
examiners will be questioning you on.
Let’s assume that our overall goal is to create a quantitative measure of risk that can be
applied to the business unit we are responsible for. Sitting on our hands doing nothing is not
an option. We need a measure of risk that can be applied at all levels of an organization either
to an isolated business unit or in aggregate to make decisions about the level of risk being
assumed in those business units and whether it is justified by the potential returns. A sensible
objective is to conform to (no more than) industry best practice at a reasonable cost. The
standard industry approaches set out below are a starting point. I will defer most of the debate
as to why and whither VaR to the end of the session.
This class material can be organized into three areas: the syllabus topics, some additional
practical topics I think you will find of interest, and sample exam questions and answers.
Let’s begin with the syllabus. The structure of the syllabus follows Thomas Wilson’s chapter
in the Handbook of Risk Management and Analysis2. Duffie and Pan provide another good
review3. While the sheer volume of material can be overwhelming the RiskMetrics™
technical document and the quarterly RiskMetrics monitors4 are excellent and well worth
whatever time you can spend with them. For a gentler read try Linsmeier and Pearson5, or, if
you have an expense account, Gumerlock, Litterman et al6.
VaR Assumptions
The Value at Risk of a portfolio is defined as the portfolio’s maximum expected loss from an
adverse market move, within a specified confidence interval, over a defined time horizon.
There is a considerable amount of research directed at removing the qualifier “within a
specified confidence interval”7,8,9,10, but this paper will stick with current market practice.
1 Thanks to Lev Borodovsky, Randi Hawkins, Yong Li, Christophe Rouvinez, Rob Samuel and Paul
Vogt for encouragement, helpful comments and/or reviewing earlier drafts. Please send any questions
or comments to IanHawkins@aol.com © Ian Hawkins 1997-8
2 Calculating Risk Capital, Thomas Wilson, in the Handbook of Risk Management and Analysis. Carol
Alexander (ed) Wiley 1996 ISBN 0-471-95309-1
3 An Overview of Value at Risk, Darrell Duffie and Jun Pan, Journal of Derivatives, Spring 1997, pp7-
49
4 http://www.jpmorgan.com/RiskManagement/RiskMetrics/pubs.html
5 Risk Measurement: An Introduction to Value at Risk, Thomas Linsmeier and Neil Pearson, University
of Illonois at Urbana-Campaign, July 1996 at
http://econwpa.wustl.edu/eprints/fin/papers/9609/9609004.abs
6 The Practice of Risk Management, Robert Gumerlock, Robert Litterman et al, Euromoney Books,
1998 ISBN 1 85564 627 7
7 Thinking coherently, Phillipe Artzner et al, Risk V10, #11, November 1997
8 Expected Maximum Loss of Financial Returns, Emmanuel Acar and David Prieul, Derivatives Week,
September 22, 1997
9 Living On The Edge, Paul Embrechts et al, Risk, January 1998
10 History Repeating, Alexander McNeil, Risk, January 1998.
1998 GARP FRM Exam Review Class Notes
Available at:
http://www.EuclidResearch.com/
current.htm
2
..........
Risk Analysis Techniques
GARP FRM Exam Review Class Notes
Ian Hawkins September 1998
Table of Contents
Introduction ..............................................................................3
VaR Assumptions ....................................................................3
Delta-Normal Methodology .....................................................5
Delta-Gamma Methodology ....................................................6
Historical Simulation................................................................7
Stress Testing...........................................................................8
Monte Carlo Simulation...........................................................8
Raroc .........................................................................................9
Model Risk ..............................................................................10
Implementation Strategy .......................................................13
Warning Signs........................................................................14
Conclusion..............................................................................15
Other Sources.........................................................................15
Answers to Sample Exam Questions ..................................16
Answers to Risktek Risk Olympics™ Questions ...............16
3
Introduction1
The purpose of this class is to provide an idiosyncratic review of the techniques for risk
analysis that a risk management professional should be familiar with. This document contains
a large number of references and you should spend some time tracking a few of them down,
particularly in areas where you feel less comfortable with your own experience or the class
content. There is no guarantee that the information presented here is either correct or what the
examiners will be questioning you on.
Let’s assume that our overall goal is to create a quantitative measure of risk that can be
applied to the business unit we are responsible for. Sitting on our hands doing nothing is not
an option. We need a measure of risk that can be applied at all levels of an organization either
to an isolated business unit or in aggregate to make decisions about the level of risk being
assumed in those business units and whether it is justified by the potential returns. A sensible
objective is to conform to (no more than) industry best practice at a reasonable cost. The
standard industry approaches set out below are a starting point. I will defer most of the debate
as to why and whither VaR to the end of the session.
This class material can be organized into three areas: the syllabus topics, some additional
practical topics I think you will find of interest, and sample exam questions and answers.
Let’s begin with the syllabus. The structure of the syllabus follows Thomas Wilson’s chapter
in the Handbook of Risk Management and Analysis2. Duffie and Pan provide another good
review3. While the sheer volume of material can be overwhelming the RiskMetrics™
technical document and the quarterly RiskMetrics monitors4 are excellent and well worth
whatever time you can spend with them. For a gentler read try Linsmeier and Pearson5, or, if
you have an expense account, Gumerlock, Litterman et al6.
VaR Assumptions
The Value at Risk of a portfolio is defined as the portfolio’s maximum expected loss from an
adverse market move, within a specified confidence interval, over a defined time horizon.
There is a considerable amount of research directed at removing the qualifier “within a
specified confidence interval”7,8,9,10, but this paper will stick with current market practice.
1 Thanks to Lev Borodovsky, Randi Hawkins, Yong Li, Christophe Rouvinez, Rob Samuel and Paul
Vogt for encouragement, helpful comments and/or reviewing earlier drafts. Please send any questions
or comments to IanHawkins@aol.com © Ian Hawkins 1997-8
2 Calculating Risk Capital, Thomas Wilson, in the Handbook of Risk Management and Analysis. Carol
Alexander (ed) Wiley 1996 ISBN 0-471-95309-1
3 An Overview of Value at Risk, Darrell Duffie and Jun Pan, Journal of Derivatives, Spring 1997, pp7-
49
4 http://www.jpmorgan.com/RiskManagement/RiskMetrics/pubs.html
5 Risk Measurement: An Introduction to Value at Risk, Thomas Linsmeier and Neil Pearson, University
of Illonois at Urbana-Campaign, July 1996 at
http://econwpa.wustl.edu/eprints/fin/papers/9609/9609004.abs
6 The Practice of Risk Management, Robert Gumerlock, Robert Litterman et al, Euromoney Books,
1998 ISBN 1 85564 627 7
7 Thinking coherently, Phillipe Artzner et al, Risk V10, #11, November 1997
8 Expected Maximum Loss of Financial Returns, Emmanuel Acar and David Prieul, Derivatives Week,
September 22, 1997
9 Living On The Edge, Paul Embrechts et al, Risk, January 1998
10 History Repeating, Alexander McNeil, Risk, January 1998.
