COVERS EVERY LEARNING OBJECTIVE ON THE EXAM FRM EXAM REVIEW STUDY GUIDE: RT BITE-SIZED LESSON FORMAT WILEY Wiley FRM Exam Review Study Guide 2017 Fart II Wiley FRM Exam Review Study Guide 2017 Part II Market Risk Measurement and Management, Credit Risk Measurement and Management, Operational and Integrated Risk Management, Risk Management and Investment Management, Current Issues in Financial Markets Christian H Cooper, CFA, FRM W il ey Cover image: Loewy Design Cover design: Loewy Design Copyright © 2017 by John Wiley & Sons, Inc All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or 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10 Contents How to Study for the Exam xi About the Author xii Market Risk Measurement and Management Lesson: Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley & Sons, 2005) Chapter Estimating Market Risk Measures: An Introduction and Overview Lesson: Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley & Sons, 2005) Chapter Non-Parametric Approaches 11 Lesson: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition (New York: McGraw-Hill, 2007) Chapter Backtesting VaR 15 Lesson: Philippe Jorion, Vaiue-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition (New York: McGraw-Hill, 2007) Chapter 11 VaR Mapping 19 Lesson: "Messages from the Academic Literature on Risk Measurement for the Trading Book," Basel Committee on Banking Supervision, Working Paper No 19, January 2011 25 Lesson: Gunter Meissner, Correlation Risk Modeling and Management (Hoboken, NJ: John Wiley & Sons, 2014) Chapter Some Correlation Basics: Properties, Motivation, Terminology 31 Lesson: Gunter Meissner, Correlation Risk Modeling and Management (Hoboken, NJ: John Wiley & Sons, 2014) Chapter Empirical Properties of Correlation: How Do Correlations Behave in the Real World? 37 Lesson: Gunter Meissner, Correlation Risk Modeling and Management (New York: John Wiley & Sons, 2014) Chapter Statistical Correlation Models— Can We Apply Them to Finance? 41 Lesson: Gunter Meissner, Correlation Risk Modeling and Management (Hoboken, NJ: John Wiley & Sons, 2014) Chapter Financial Correlation Modeling— Bottom-Up Approaches (Sections 4.3.0 (intro), 4.3.1, and 4.3.2 only) 43 ©2017 Wiley CONTENTS Lesson: M c e T u c k m n , Fixed Income Securities, M Edition (Hoboken, NJ: John Wiley & Sons, 2011) Chapter Empirical Approaches to Risk Metrics and Hedges 49 Lesson: Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011) Chapter The Science of Term Structure Models 53 Lesson: BruceTuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011) Chapter The Evolution of Short Rates and the Shape of the Term Structure 63 Lesson: BruceTuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011) Chapter The Art of Term Structure Models: Drift 67 Lesson: BruceTuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011) Chapter 10 The Art of Term Structure Models: Volatility and Distribution 77 Lesson: John Hull, Options, Futures, and Other Derivatives, 9th Edition (New York: Pearson Prentice Hall, 2014) Chapter OIS Discounting, Credit Issues, and Funding Costs 81 Lesson: John Hull, Options, Futures, and Other Derivatives, 9th Edition (New York: Pearson Prentice Hall, 2014) Chapter 20 Volatility Smiles 85 Credit Risk Measurement and Management Vi Lesson: Jonathan Golin and Philippe Delhaise, The Bank Credit Analysis Handbook (Hoboken, NJ: John Wiley & Sons, 2013) Chapter The Credit Decision 91 Lesson: Jonathan Golin and Philippe Delhaise, The Bank Credit Analysis Handbook (Hoboken, NJ: John Wiley & Sons, 2013) Chapter The Credit Analyst 95 Lesson: Giacomo De Laurentis, Renato Maino, and Luca Molteni, Developing, Validating and Using Internal Ratings (West Sussex, United Kingdom: John Wiley & Sons, 2010) Chapter Classifications and Key Concepts of Credit Risk 97 Lesson: Giacomo De Laurentis, Renato Maino, and Luca Molteni, Developing, Validating and Using Internal Ratings (West Sussex, United Kingdom: John Wiley & Sons, 2010) Chapter Ratings Assignment Methodologies 105 Lesson: Rene Stulz, Risk Management & Derivatives (Florence, KY: Thomson South-Western, 2002) Chapter 18 Credit Risks and Credit Derivatives 119 Lesson: Allan Malz, Financial Risk Management: Models, History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011) Chapter Spread Risk and Default Intensity Models 127 Lesson: Allan Malz, Financial Risk Management: Models, History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011) Chapter Portfolio Credit Risk (Sections 8.1,8.2,8.3 only) 135 Lesson: Allan Malz, Financial Risk Management: Models, History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011) Chapter Structured Credit Risk 139 ©2017 Wiley Lesson: Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012) Chapter Defining Counterparty Credit Risk 147 Lesson: Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012) Chapter Netting, Compression, Resets, and Termination Features 151 Lesson: Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012) Chapter Collateral 153 Lesson: Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012) Chapter Central Counterparties 159 Lesson: Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012) Chapter Credit Exposure 165 Lesson: Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012) Chapter 10 Default Probability, Credit Spreads, and Credit Derivatives 171 Lesson: Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012) Chapter 12 Credit Value Adjustment 177 Lesson: Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012) Chapter 15 Wrong-Way Risk 181 Stress Testing: Approaches, Methods, and Applications, Edited by Akhtar Siddique and Iftekhar Hasan (London: Risk Books, 2013) Chapter The Evolution of Stress Testing Counterparty Exposures 183 Lesson: Michel Crouhy, Dan Galai, and Robert Mark, The Essentials o f Risk Management, 2nd Edition (New York: McGraw-Hill, 2014) Chapter Credit Scoring and Retail Credit Risk Management 191 Lesson: Michel Crouhy, Dan Galai, and Robert Mark, The Essentials o f Risk Management, 2nd Edition (New York: McGraw-Hill, 2014) Chapter 12 The Credit Transfer Markets— and Their Implications 197 Lesson: Moorad Choudhry, Structured Credit Products: Credit Derivatives & Synthetic Securitization, 2nd Edition (Hoboken, NJ: John Wiley & Sons, 2010) Chapter 12 An Introduction to Securitization 205 Lesson: Adam Ashcraft and Til Schuermann/'Understanding the Securitization of Subprime Mortgage Credit," Federal Reserve Bank of New York Staff Reports, No 318 (March 2008) 215 ©2017 Wiley CONTENTS Operational and Integrated Risk Management Lesson: "Principles for the Sound Management of Operational Risk" (Basel Committee on Banking Supervision Publication, June 2011) 221 Lesson: Brian Noccoand Rene Stulz,"Enterprise Risk Management: Theory and Practice, Journal o f Applied Corporate Finance 18, no (2006): -2 229 Lesson: "Observations on Developments in Risk Appetite Frameworks and IT Infrastructure," Senior Supervisors Group, December 2010 233 Lesson: Anthony Tarantino and Deborah Cernauskas, Risk Management in Finance: Six Sigma and Other Next Generation Techniques (Hoboken, NJ: John Wiley & Sons, 2009) Chapter Information Risk and Data Quality Management 239 Lesson: Marcelo G Cruz, Gareth W Peters, and Pavel V Shevchenko, Fundamental Aspects o f Operational Risk and Insurance Analytics: A Handbook o f Operational Risk (Hoboken, NJ: John Wiley & Sons, 2015) Chapter OpRisk Data and Governance 241 Lesson: Philippa X Girling, Operational Risk Management: A Complete Guide to a Successful Operational Risk Framework (Hoboken, NJ: John Wiley & Sons, 2013) Chapter External Loss Data 247 Lesson: Philippa X Girling, Operational Risk Management: A Complete Guide to a Successful Operational Risk Framework (Hoboken, NJ: John Wiley & Sons, 2013) Chapter 12 Capital Modeling 251 Lesson: "Standardised Measurement Approach for Operational Risk— Consultative Document" (Basel Committee on Banking Supervision Publication, March 2016) 255 Lesson: Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2005) Chapter Parametric Approaches (II): Extreme Value 259 Lesson: Giacomo De Laurentis, Renato Maino, and Luca Molteni, Developing, Validating, and Using Internal Ratings (Hoboken, NJ: John Wiley & Sons, 2010 Chapter Validating Rating Models 263 Lesson: Michel Crouhy, Dan Galai, and Robert Mark, The Essentials o f Risk Management, 2nd Edition (New York: McGraw-Hill, 2014) Chapter 15 Model Risk 267 Lesson: Michel Crouhy, Dan Galai, and Robert Mark, The Essentials o f Risk Management, 2nd Edition (New York: McGraw-Hill, 2014) Chapter 17 Risk Capital Attribution and Risk-Adjusted Performance Measurement 271 Lesson: "Range of Practices and Issues in Economic Capital Frameworks" (Basel Committee on Banking Supervision Publication, March 2009) 275 Lesson: "Capital Planning at Large Bank Holding Companies: Supervisory Expectations and Range of Current Practice," Board of Governors of the Federal Reserve System, August 2013 285 ©2017 Wiley M a r k e t Ri s k M e a s u r e m e n t M a n a g e m e n t (MR) a nd The broad areas of knowledge covered in readings related to Market Risk Measurement and Management include the following: • • • • • VaR and other risk measures: o Parametric and nonparametric methods of estimation o VaR mapping o Backtesting VaR o Expected shortfall (ES) and other coherent risk measures o Extreme value theory (EVT) Modeling dependence: correlations and copulas Term structure models of interest rates Discount rate selection Volatility: smiles and term structures ©2017 Wiley © Do w d , Ch a pt e r Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2005) Chapter Estimating Market Risk Measures: An Introduction and Overview After completing this reading you should be able to: • • • • • • • Estimate VaR using a historical simulation approach Estimate VaR using a parametric approach for both normal and lognormal return distributions Estimate the expected shortfall given P/L or return data Define coherent risk measures Estimate risk measures by estimating quantiles Evaluate estimators of risk measures by estimating their standard errors Interpret QQ plots to identify the characteristics of a distribution Reading notes: This is a very dense reading about 20 pages long with a lot of VaR “estimate” questions This is probably one of the most important readings in the Market Risk Measurement and Management section of the exam Make sure you can calculate these answers and be able to qualitatively discuss these topics However, don’t get lost in the technical material that asks you to “describe.” The assigned readings go into deep detail that isn’t required for the exam Make sure you are paying attention to what you are actually asked Learning objective: Estimate VaR using a historical simulation approach First recognize that as flawed as VaR is, using VaR based on historical data is even worse The idea here is to order the historical losses observed in a portfolio, ordered by the actual amount of the loss So, if we have 1,000 loss observations ordered from smallest to largest and we are interested in the 97% confidence level, that implies that 30 observations will be in the tail of the distribution that will define the VaR of this portfolio So “estimate” here really means “observe,” and in the example the 31st loss observation would be the amount of the expected VaR of the portfolio based on the losses the portfolio has historically experienced VaR is flawed when used incorrectly, and VaR based on historical observation is really flawed There is no insight into the risk the portfolio has, no idea how that risk may change in the future, and so on There are almost too many problems here to mention and even more problems when used with a portfolio that has embedded options Learning objective: Estimate VaR using a parametric approach for both normal and lognormal return distributions I will move forward on the assumption you are very comfortable with the lognormal and normal distributions; take a break here if you need a review ©2017 Wiley © MARKET RISK MEASUREMENT AND MANAGEMENT (MR) Starting first with the assumption of a normal distribution, we have to define the mean and standard deviation of the portfolio in order to calculate the VaR Likely this will be given to you on the exam, but in the real world this will be estimated parameters based on the risk manager’s expectations Since we want to interpret VaR in terms of lost money, our formula for losses is: VaR - - | i + oZ a where negative mu is expected losses, sigma is the standard deviation of the loss, and Z is the standard normal variate corresponding to the level of significance we are looking for Recall that the standard normal variate at the 95% level of significance is 1.645 If profits and losses over some period are normally distributed with mean of 20 and standard deviation of 30, the 95% VaR is calculated as: VaR = -20 + 30(1.645) = -29.35 This is straightforward enough, but the learning objective is asking about a normal and lognormal distribution of returns, not dollars gained or lost When we transition to returns, we have to add additional parameters to describe the starting dollar value and ending dollar value so we can arrive at the return estimate Furthermore, we have to establish some critical value r* so we can compare our expected probability to our critical value return where that probability is equal to our level of confidence Taking the previous equation: V a R - - j i + oZ a I am going to modify it to: r* = - f t + c Z a This will be our return critical value that we need to establish a confidence interval around the return of our portfolio at any given time, rt Also, since any given return is the starting value relative to ending value, we can define rt as: Pt - Pt-i Don’t let all the equations fool you; we are defining return as you normally would: My return is my portfolio value at time t minus what it was before, divided by the starting value ©2017 Wiley DOWD, CHAPTER However, since we are thinking about VaR at risk, we are only concerned with the losses We can extend the relationship to include VaR and recover our critical value: * _ fi - Pm _ VaR Pm Pm Now, substitute into this equation: r* = - |i + c Z a to arrive at: and last, VaR = (-(I + oZ a )Pt_! The only difference between the normal and lognormal version is going to be the critical values Let’s learn a quick calculation If I know returns are normally distributed at 12% with standard deviation of 18% and I want the 95% level VaR: -12% +18% (1.645) = 0.1761 (converting from percentages) On the exam, you may be given estimates of profits and losses, which would mean you don’t use the population parameters of mu and sigma, but the math and order are the same Lognormal Version The real dividing issue between normal and lognormal that should be clear by now is that a normal distribution is symmetric and assigns an equal probability of going up or down in price This implies that prices can be negative if you use the normal distribution Now for stocks, this doesn’t make sense since they have a zero floor That is why when we talk about financial assets we often refer to the distribution of returns being normally distributed, not the asset prices themselves, which, of course, is the lognormal distribution This is why we need the lognormal So how we calculate VaR when lognormally distributed? From the discussion of normally distributed VaR, we know we are dealing with potential returns instead of dollar values of potential loss (price moves) under the normal distribution, so we have the extra step of converting our lognormally derived VaR back into dollar terms You not have to memorize the derivation of this formula, but you will use the very last line in the calculation ©2017 Wiley MARKET RISK MEASUREMENT AND MANAGEMENT (MR) As in the normal, we are going to use this formula from before, but let’s call VaR a new random variable that will correspond to a loss equal to our VaR Ultimately, this is what we want to know Our original equation: VaR = - |i + oZ a becomes: X* = - p + a Z a Since we are using geometric returns, we insert a term that describes the price at some period right now (assuming a loss) relative to some time in the past to establish our return It sounds complicated, but this is the same as a $50 stock that goes to $45 so the loss is 10% 45/50 = 90 & (1 - 0.90) = 0.10 We are going to the exact same thing here X* = ln(Pricenow/Pricepast) Reordering terms and using the properties of logarithms so the ratio of logarithms can be expressed as the difference of two logarithms: X* = ln(Pricenow) - ln(Pricepast) ^ 0 0 Remember, X is our critical value that ultimately becomes our VaR as some certainty, alpha Reordering terms, ln(Pricenow) = X* + ln(Pricepast) Distribute the logarithm across: This goes back to early calculus, but don’t worry—you don’t need to know it; just remember the last step (Pricenow) - (Pricepast)ex Insert original equation for X*: (Pricenow) = (Price past )e_tl+aZa Skipping a few messy steps that are unnecessary to know for the exam, we arrive at what you need to know for VaR under a lognormal distribution of returns, and that is this relationship: VaR = Ppast[l - exp(p - oZ)] ©2017 Wiley DOWD, CHAPTER To bring this all together, and since this is an “estimate” question, you may be asked to calculate/evaluate this on exam day: Let’s assume returns are normally distributed with mean 10% and standard deviation 18%, and our portfolio is $100 We can express the lognormal VaR at the 95% level as: - exp(0.10 -0 * 1.645) = 0.26 or $26 Learning objective: Estimate the expected shortfall given P/L or return data Risk as Shortfall Another way to specify a risk objective is by means of the expected portfolio standard deviation, which is the square root of the expected portfolio variance For example, the S&P 500 might have an annual portfolio standard deviation of 23% Using this figure and either a normal or lognormal distribution, we can quantify the probability that a given portfolio will have a loss, or a return below a certain minimum requirement (this probability is called a shortfall risk) As might be expected, the focus of this criterion is minimizing the chances that a specified minimum return (say RL) is not achieved If the portfolio return (call it RP) is normally distributed, then it is not very difficult to calculate the probability that RP will fall short of Rl —in other words, P(RP < RL)—or to calculate the number of standard deviations RL falls below the expected portfolio return, E(RP) Note that the portfolio that maximizes E(RP) - RL will at the same time minimize P(RP < RL) If we divide the expression E(RP) - RL by the standard deviation of the portfolio, we get the safety margin in units of portfolio standard deviation This ratio is called Roy’s safety-first criterion (SFRatio): SFRatio = E