Frm aim statements_2013-web

2013

FRM
Examination
AIM
Statements

2013 Financial Risk Manager (FRM®) Examination AIM Statements

FRM Examination Approach Readings
The FRM Exam is a comprehensive, prac- To facilitate a candidate’s preparation,
tice-oriented, examination with questions each knowledge point in the AIM State-
derived from a combination of theory and ments is associated with a suggested
“real-world” work experience. Candidates reading from the Study Guide which
are expected to understand risk manage- supports and explains it.
ment concepts and approaches and how
they would apply to a risk manager’s These readings were selected by the FRM
day-to-day activities. Committee to assist candidates in their
review of the subjects covered by the
It is rare that a risk manager will be faced exam. Questions for the FRM Examination
with an issue that can immediately be are related to and supported by the read-
slotted into one category and he or she ings listed under each topic outline and it is
must be able to identify any number of strongly suggested that candidates review
risk-related issues and be able to deal these readings in depth prior to sitting for
with them effectively. Therefore, the FRM the exam. All of the readings listed in the
Examination is also compre- FRM Study Guide are available through
The FRM Examination is hensive, testing a risk profes- GARP. Further information can be found
a comprehensive examina- sional on a number of risk on the GARP website.
tion, testing a risk profes- management concepts
sional on a number of risk and approaches. FRM Study Guide
management concepts and The Study Guide sets forth primary topics
approaches. FRM AIM Statements and subtopics covered in the FRM Exam.
The AIM Statements contain The topics were selected by the FRM
all of the suggested reading and Key Con- Committee as ones that risk managers
cept information that is in the Study Guide who work in practice today have to master.
as well as more detailed knowledge points The topics and their respective weightings
that form the basis for FRM Examination are reviewed yearly to ensure the FRM
questions. Candidates who compare the Exam is kept timely and relevant. Key
Key Concepts to the knowledge points will Concepts appear as bullet points at the
note that in most cases several knowledge beginning of each section of the Study
points are related to each broader Key Guide and are intended to help candidates
Concept. identify the major themes and knowledge
areas associated with that section. The
Study Guide also contains a full listing of
all of the readings that are recommended
as preparation for the FRM Examination.

© 2013 Global Association of Risk Professionals. All rights reserved. 1

2013 FRM Examination

Table of Contents

Part I AIM Statements

Foundations of Risk Management........................................................................................3

Quantitative Analysis.................................................................................................................7

Financial Markets and Products...........................................................................................12

Valuation and Risk Models.....................................................................................................19

Part II AIM Statements

Market Risk Measurement and Management ................................................................29

Credit Risk Measurement and Management..................................................................36

Operational and Integrated Risk Management ............................................................44

Risk Management and Investment Management.........................................................53

Current Issues in Financial Markets ...................................................................................59


FRM PART I—TOPICS AND READINGS

FOUNDATIONS OF RISK MANAGEMENT—Part I Exam Weight | 20%

• The role of risk management
• Basic risk types, measurement and management tools
• Creating value with risk management
• Modern Portfolio Theory (MPT)
• Standard and non-standard forms of the Capital Asset Pricing Model (CAPM)
• Index models
• Risk-adjusted performance measurement
• Enterprise Risk Management
• Financial disasters and risk management failures
• Case studies
• Ethics and the GARP Code of Conduct

Readings for Foundations of Risk Management

1. “Risk Taking: A Corporate Governance Perspective,” (International Finance Corporation, World Bank Group,
June 2012).
Freely available on the GARP Digital Library.

2. Edwin J. Elton, Martin J. Gruber, Stephen J. Brown and William N. Goetzmann, Modern Portfolio Theory and
Investment Analysis, 8th Edition (Hoboken, NJ: John Wiley & Sons, 2009).
• Chapter 5 .............................Delineating Efficient Portfolios
• Chapter 13............................The Standard Capital Asset Pricing Model
• Chapter 14............................Nonstandard Forms of Capital Asset Pricing Models

3. Noel Amenc and Veronique Le Sourd, Portfolio Theory and Performance Analysis (West Sussex, England:
John Wiley & Sons, 2003).
• Chapter 4, Section 4.2 only .............................Applying the CAPM to Performance Measurement: Single-Index
Performance Measurement Indicators

4. Anthony Tarantino and Deborah Cernauskas, Risk Management in Finance: Six Sigma and Other Next Generation
Techniques (Hoboken, NJ: John Wiley & Sons, 2009).
• Chapter 3 .............................Information Risk and Data Quality Management

5. Steve Allen, Financial Risk Management: A Practitioner’s Guide to Managing Market and Credit Risk
(New York: John Wiley & Sons, 2003).
• Chapter 4 .............................Financial Disasters

6. René Stulz, “Risk Management Failures: What are They and When Do They Happen?” Fisher College of Business
Working Paper Series, (Oct 2008).



7. GARP Code of Conduct.

AIMS:
“Risk Taking: A Corporate Governance Perspective,” (International Finance Corporation, World Bank Group,
June 2012).
Candidates, after completing this reading, should be able to:
• Define risk, identify the classifications of risks, and explain the role played by risk in value creation.
• Describe a risk profile and explain how one is created.
• Describe the role of risk governance in a corporation.
• Identify Enterprise Risk Management (ERM) approaches and explain how they address risk management in
an organization.
• Describe how the value of a risky asset or project can be estimated through the development of a risk-adjusted
discount rate, how such a risk-adjusted discount rate can be created, and strengths and weaknesses of this
approach.
• Describe problems which arise when using historical betas and equity risk premiums as inputs into a valuation model.
• Construct a risk-adjusted discount rate for an asset or project and apply that rate to estimate the value of the
asset or project.
• Describe the certainty equivalent approach to estimating value and contrast it with the use of a risk-adjusted
discount rate.
• Identify the four steps in the AIRMIC risk management process and summarize the approach used in each step.
• Identify the four risk treatment strategies a firm can use to manage its risks.
• Compare and contrast the different types of probabilistic approaches used to estimate value and contrast
probabilistic approaches in general with risk-adjusted methods.
• Define hedging, explain the tradeoff between the costs and benefits of hedging, and assess whether it is
appropriate for a firm to hedge in particular cases.
• Identify financial products a firm can use to reduce or eliminate exposure to specific risks.
• Identify the methods a firm can use to exploit risk better than its competitors, and explain how an organization
can create a culture of prudent risk-taking among its employees.
• Summarize the basic steps in building a good risk management system.
• Identify examples of acceptable, desirable, and best practices in corporate risk governance.

Edwin J. Elton, Martin J. Gruber, Stephen J. Brown and William N. Goetzmann, Modern Portfolio Theory and
Investment Analysis, 8th Edition (Hoboken, NJ: John Wiley & Sons, 2009).
Chapter 5 ................................Delineating Efficient Portfolios
• Calculate the expected return and volatility of a portfolio of risky assets.
• Explain how covariance and correlation affect the expected return and volatility of a portfolio of risky assets.
• Describe the shape of the portfolio possibilities curve.
• Define the minimum variance portfolio.
• Define the efficient frontier and describe the impact on it of various assumptions concerning short sales
and borrowing.

4 © 2013 Global Association of Risk Professionals. All rights reserved.


Chapter 13 ...............................The Standard Capital Asset Pricing Model
• Understand the derivation and components of the CAPM.
• Describe the assumptions underlying the CAPM.
• Describe the capital market line.
• Use the CAPM to calculate the expected return on an asset.

Chapter 14...............................Nonstandard Forms of Capital Asset Pricing Models
• Describe the impact on the CAPM of the following:
• Short sales disallowed
• Riskless lending and borrowing
• Personal taxes
• Nonmarketable assets
• Heterogeneous expectations
• Non-price-taking behavior
• Describe the following multi-period versions of CAPM:
• Consumption-oriented CAPM
• CAPM including inflation
• Multi-beta CAPM

Noel Amenc and Veronique Le Sourd, Portfolio Theory and Performance Analysis (West Sussex, England:
John Wiley & Sons, 2003).
Chapter 4, Section 4.2 only ...............................Applying the CAPM to Performance Measurement: Single-Index
Performance Measurement Indicators
• Calculate, compare, and evaluate the Treynor measure, the Sharpe measure, and Jensen’s alpha.
• Compute and interpret tracking error, the information ratio, and the Sortino ratio.
• Define beta and calculate the beta of a portfolio.
• Explain the Morningstar Rating System, VaR based, and management related risk-adjusted return measures.

Anthony Tarantino and Deborah Cernauskas, Risk Management in Finance: Six Sigma and Other Next Generation
Techniques (Hoboken, NJ: John Wiley & Sons, 2009).
Chapter 3 ................................Information Risk and Data Quality Management
• Describe ways in which a business can be negatively impacted by poor quality data.
• Identify the most common issues which result in data errors.
• Identify the key dimensions which characterize acceptable data.
• Define operational data governance and differentiate between data quality inspection and data validation.
• Differentiate between base level and complex metrics in creating data quality scores, and describe the three
different viewpoints by which complex data metrics can be reported.
• Explain the motivation and mechanics of creating a data quality scorecard.



Steve Allen, Financial Risk Management: A Practitioner’s Guide to Managing Market and Credit Risk
Chapter 4 ................................Financial Disasters
• Describe the key factors that led to and the lessons learned from the following risk management case studies:
• Chase Manhattan and their involvement with Drysdale Securities
• Kidder Peabody
• Barings
• Allied Irish Bank
• Union Bank of Switzerland (UBS)
• Long Term Capital Management (LTCM)
• Metallgesellschaft
• Bankers Trust

René Stulz, “Risk Management Failures: What are They and When Do They Happen?” Fisher College of Business
Working Paper Series, (Oct 2008).
• Define the role of risk management and explain why a large financial loss is not necessarily a failure of risk
management.
• Describe how risk management can fail.
• Describe how risk can be mismeasured.
• Explain how a firm can fail to take known and unknown risks into account in making strategic decisions.
• Explain the importance of communication in effective risk management.
• Describe how firms can fail to correctly monitor and manage risk on an ongoing basis.
• Explain the role of risk metrics and describe the shortcomings of existing risk metrics.

GARP Code of Conduct.
• Describe the responsibility of each GARP member with respect to professional integrity, ethical conduct, conflicts
of interest, confidentiality of information and adherence to generally accepted practices in risk management.
• Describe the potential consequences of violating the GARP Code of Conduct.



QUANTITATIVE ANALYSIS—Part I Exam Weight | 20%

• Discrete and continuous probability distributions
• Population and sample statistics
• Statistical inference and hypothesis testing
• Estimating the parameters of distributions
• Graphical representation of statistical relationships
• Linear regression with single and multiple regressors
• The Ordinary Least Squares (OLS) method
• Interpreting and using regression coefficients, the t-statistic, and other output
• Hypothesis testing and confidence intervals
• Heteroskedasticity and multicollinearity
• Monte Carlo Methods
• Estimating correlation and volatility using EWMA and GARCH models
• Volatility term structures

Readings for Quantitative Analysis

8. Michael Miller, Mathematics and Statistics for Financial Risk Management (Hoboken, NJ: John Wiley & Sons, 2012).
• Chapter 2 .............................Probabilities
• Chapter 3 .............................Basic Statistics
• Chapter 4 .............................Distributions
• Chapter 5 .............................Hypothesis Testing & Confidence Intervals

9. James Stock and Mark Watson, Introduction to Econometrics, Brief Edition (Boston: Pearson Education, 2008).
• Chapter 4 .............................Linear Regression with One Regressor
• Chapter 5 .............................Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals
• Chapter 6 .............................Linear Regression with Multiple Regressors
• Chapter 7 .............................Hypothesis Tests and Confidence Intervals in Multiple Regression

10. Philippe Jorion, Value-at-Risk:The New Benchmark for Managing Financial Risk, 3rd Edition.
(New York: McGraw Hill, 2007).
• Chapter 12 ............................Monte Carlo Methods

11. John Hull, Options, Futures, and Other Derivatives, 8th Edition (New York: Pearson Prentice Hall, 2012).
• Chapter 22 ...........................Estimating Volatilities and Correlations



AIMS:
Michael Miller, Mathematics and Statistics for Financial Risk Management (Hoboken, NJ: John Wiley & Sons, 2012).
Chapter 2 ................................Probabilities
• Describe the concept of probability.
• Describe and distinguish between continuous and discrete random variables.
• Define and distinguish between the probability density function, the cumulative distribution function and the
inverse cumulative distribution function, and calculate probabilities based on each of these functions.
• Calculate the probability of an event given a discrete probability function.
• Distinguish between independent and mutually exclusive events.
• Define joint probability, describe a probability matrix and calculate joint probabilities using probability matrices.
• Define and calculate a conditional probability, and distinguish between conditional and unconditional
probabilities.
• Describe Bayes’ Theorem and apply this theorem in the calculation of conditional probabilities.

Chapter 3 ................................Basic Statistics
• Define, calculate, and interpret the mean, standard deviation, and variance of a random variable.
• Define, calculate, and interpret the covariance and correlation between two random variables.
• Interpret and calculate the variance for a portfolio and understand the derivation of the minimum variance
hedge ratio.
• Calculate the mean and variance of sums of larger variables.
• Describe the four central moments of a statistical variable or distribution: mean, variance, skewness and kurtosis.
• Interpret the skewness and kurtosis of a statistical distribution, and interpret the concepts of coskewness and
cokurtosis.
• Define and interpret the best linear unbiased estimator (BLUE).

Chapter 4 ................................Distributions
• Define and distinguish between parametric and nonparametric distributions.
• Describe the key properties of the uniform distribution, Bernoulli distribution, Binomial distribution, Poisson
distribution, normal distribution and lognormal distribution, and identify common occurrences of each distribution.
• Describe and apply the Central Limit Theorem and explain the conditions for the theorem.
• Describe the properties of independent and identically distributed (i.i.d.) variables.
• Describe the properties of linear combinations of normally distributed variables.
• Identify the key properties and parameters of the Chi-squared, Student’s t, and F-distributions.
• Describe a mixture distribution and explain the creation and characteristics of mixture distributions.



Chapter 5 ................................Hypothesis Testing and Confidence Intervals
• Define, calculate and interpret the mean and variance of the sample mean.
• Define and estimate the sample mean and sample variance.
• Define and construct a confidence interval.
• Define and interpret the null hypothesis and the alternative hypothesis, and calculate the test statistics.
• Define, interpret, and calculate the t-statistic.
• Describe the process of selecting and constructing a null hypothesis.
• Differentiate between a one-tailed and a two-tailed test and explain the circumstances in which to use each test.
• Interpret the results of hypothesis tests with a specific level of confidence.
• Describe and apply the principle of Chebyshev’s inequality.

James Stock and Mark Watson, Introduction to Econometrics, Brief Edition (Boston: Pearson Education, 2008).
Chapter 4 ................................Linear Regression with One Regressor
• Explain how regression analysis in econometrics measures the relationship between dependent and
independent variables.
• Define and interpret a population regression function, regression coefficients, parameters, slope and the intercept.
• Define and interpret the stochastic error term.
• Define and interpret a sample regression function, regression coefficients, parameters, slope and the intercept.
• Describe the key properties of a linear regression.
• Describe the method and three key assumptions of ordinary least squares (OLS) for estimation of parameters.
• Summarize the benefits of using OLS estimators.
• Describe the properties of OLS estimators and their sampling distributions, and explain the properties of
consistent estimators in general.
• Define and interpret the explained sum of squares, the total sum of squares, the residual sum of squares,
the standard error of the regression (SER), and the regression R2.
• Interpret the results of an ordinary least squares regression.

Chapter 5 ................................Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals
• Define, calculate, and interpret confidence intervals for regression coefficients.
• Define and interpret the p-value.
• Define and interpret hypothesis tests about regression coefficients.
• Define and differentiate between homoskedasticity and heteroskedasticity.
• Describe the implications of homoskedasticity and heteroskedasticity.
• Explain the Gauss-Markov Theorem and its limitations, and alternatives to the OLS.
• Define, describe, apply, and interpret the t-statistic when the sample size is small.



Chapter 6 ................................Linear Regression with Multiple Regressors
• Define, interpret, and describe methods for addressing omitted variable bias.
• Distinguish between single and multiple regression.
• Define and interpret the slope coefficient in a multiple regression.
• Describe homoskedasticity and heterosckedasticity in a multiple regression.
• Describe the OLS estimator in a multiple regression.
• Define, calculate, and interpret measures of fit in multiple regression.
• Explain the assumptions of the multiple linear regression model.
• Explain the concept of imperfect and perfect multicollinearity and their implications.

Chapter 7 ................................Hypothesis Tests and Confidence Intervals in Multiple Regression
• Construct, perform, and interpret hypothesis tests and confidence intervals for a single coefficient in a multiple
regression.
• Construct, perform, and interpret hypothesis tests and confidence intervals for multiple coefficients in a
multiple regression.
• Define and interpret the F-statistic.
• Define, calculate, and interpret the homoskedasticity-only F-statistic.
• Describe and interpret tests of single restrictions involving multiple coefficients.
• Define and interpret confidence sets for multiple coefficients.
• Define and describe omitted variable bias in multiple regressions.
• Interpret the R2 and adjusted-R2 in a multiple regression.



Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition.
(New York: McGraw Hill, 2007).
Chapter 12 ...............................Monte Carlo Methods
• Describe how to simulate a price path using a geometric Brownian motion model.
• Describe how to simulate various distributions using the inverse transform method.
• Describe the bootstrap method.
• Explain how simulations can be used for computing VaR and pricing options.
• Describe the relationship between the number of Monte Carlo replications and the standard error of the
estimated values.
• Describe and identify simulation acceleration techniques.
• Explain how to simulate correlated random variables using Cholesky factorization.
• Describe deterministic simulations.
• Describe the drawbacks and limitations of simulation procedures.

John Hull, Options, Futures, and Other Derivatives, 8th Edition (New York: Pearson Prentice Hall, 2012).
Chapter 22 ..............................Estimating Volatilities and Correlations
• Explain how historical data and various weighting schemes can be used in estimating volatility.
• Describe the exponentially weighted moving average (EWMA) model for estimating volatility and its properties,
and estimate volatility using the EWMA model.
• Describe the generalized auto regressive conditional heteroscedasticity (GARCH(p,q)) model for estimating
volatility and its properties:
• Estimate volatility using the GARCH(p,q) model
• Explain mean reversion and how it is captured in the GARCH(1,1) model
• Explain how the parameters of the GARCH(1,1) and the EWMA models are estimated using maximum
likelihood methods.
• Explain how GARCH models perform in volatility forecasting.
• Describe how correlations and covariances are calculated, and explain the consistency condition for covariances.



FINANCIAL MARKETS AND PRODUCTS—Part I Exam Weight | 30%

• Mechanics of OTC and exchange markets
• Forwards, futures, swaps and options
• Mechanics
• Pricing and factors that affect it
• Uses in hedging and hedging strategies
• Delivery options
• Interest rates and measures of interest rate sensitivity
• Derivatives on fixed income securities, interest rates, foreign exchange, and equities
• Commodity derivatives
• Foreign exchange risk
• Corporate bonds
• Rating agencies

Readings for Financial Markets and Products

12. Hull, Options, Futures, and Other Derivatives, 8th Edition.
• Chapter 1 ..............................Introduction
• Chapter 2 .............................Mechanics of Futures Markets
• Chapter 3 .............................Hedging Strategies Using Futures
• Chapter 4 .............................Interest Rates
• Chapter 5 .............................Determination of Forward and Futures Prices
• Chapter 6 .............................Interest Rate Futures
• Chapter 7 .............................Swaps
• Chapter 10 ...........................Properties of Stock Options
• Chapter 11 .............................Trading Strategies Involving Options

13. Robert McDonald, Derivatives Markets, 3rd Edition (Boston: Addison-Wesley, 2013).
• Chapter 6 .............................Commodity Forwards and Futures

14. Helyette Geman, Commodities and Commodity Derivatives: Modeling and Pricing for Agriculturals, Metals and
Energy (West Sussex, England: John Wiley & Sons, 2005).
• Chapter 1.....................................Fundamentals of Commodity Spot and Futures Markets: Instruments, Exchanges and Strategies

15. Anthony Saunders and Marcia Millon Cornett, Financial Institutions Management: A Risk Management Approach,
7th Edition (New York: McGraw-Hill, 2011).
• Chapter 14............................Foreign Exchange Risk

16. Frank Fabozzi (editor), The Handbook of Fixed Income Securities, 8th Edition (New York: McGraw-Hill, 2012).
• Chapter 12 ............................Corporate Bonds, by Frank Fabozzi, Steven Mann and Adam Cohen

17. John B. Caouette, Edward I. Altman, Paul Narayanan, and Robert W.J. Nimmo, Managing Credit Risk, 2nd Edition
• Chapter 6 .............................The Rating Agencies



AIMS:
Hull, Options, Futures, and Other Derivatives, 8th Edition.
Chapter 1 .................................Introduction
• Differentiate between an open outcry system and electronic trading.
• Describe the over-the-counter market, how it differs from trading on an exchange, and its advantages and disadvantages.
• Differentiate between options, forwards, and futures contracts.
• Calculate and identify option and forward contract payoffs.
• Describe, contrast, and calculate the payoffs from hedging strategies involving forward contracts and options.
• Describe, contrast, and calculate the payoffs from speculative strategies involving futures and options.
• Calculate an arbitrage payoff and describe how arbitrage opportunities are ephemeral.
• Describe some of the risks that can arise from the use of derivatives.

Chapter 2 ................................Mechanics of Futures Markets
• Define and describe the key features of a futures contract, including the asset, the contract price and size,
delivery and limits.
• Explain the convergence of futures and spot prices.
• Describe the rationale for margin requirements and explain how they work.
• Describe the role of a clearinghouse in futures transactions.
• Describe the role of collateralization in the over-the-counter market and compare it to the margining system.
• Identify and describe the differences between a normal and inverted futures market.
• Describe the mechanics of the delivery process and contrast it with cash settlement.
• Define and demonstrate an understanding of the impact of different order types, including: market, limit,
stop-loss, stop-limit, market-if-touched, discretionary, time-of-day, open, and fill-or-kill.
• Compare and contrast forward and futures contracts.

Chapter 3 ................................Hedging Strategies Using Futures
• Define and differentiate between short and long hedges and identify appropriate uses.
• Describe the arguments for and against hedging and the potential impact of hedging on firm profitability.
• Define the basis and the various sources of basis risk, and explain how basis risks arise when hedging with futures.
• Define cross hedging, and compute and interpret the minimum variance hedge ratio and hedge effectiveness.
• Define, compute, and interpret the optimal number of futures contracts needed to hedge an exposure, and explain
and calculate the “tailing the hedge” adjustment.
• Explain how to use stock index futures contracts to change a stock portfolio’s beta.
• Describe what is meant by “rolling the hedge forward” and describe some of the risks that arise from such
a strategy.



Chapter 4 ................................Interest Rates
• Describe Treasury Rates, LIBOR, Repo Rates, and what is meant by the risk-free rate.
• Calculate the value of an investment using daily, weekly, monthly, quarterly, semiannual, annual, and continuous
compounding. Convert rates based on different compounding frequencies.
• Calculate the theoretical price of a coupon paying bond using spot rates.
• Calculate forward interest rates from a set of spot rates.
• Calculate the value of the cash flows from a forward rate agreement (FRA).
• Describe the limitations of duration and how convexity addresses some of them.
• Calculate the change in a bond’s price given duration, convexity, and a change in interest rates.
• Describe the major theories of the term structure of interest rates.

Chapter 5 ................................Determination of Forward and Futures Prices
• Differentiate between investment and consumption assets.
• Define short-selling and short squeeze.
• Describe the differences between forward and futures contracts and explain the relationship between forward
and spot prices.
• Calculate the forward price, given the underlying asset’s price, with or without short sales and/or consideration to
the income or yield of the underlying asset. Describe an arbitrage argument in support of these prices.
• Explain the relationship between forward and futures prices.
• Calculate a forward foreign exchange rate using the interest rate parity relationship.
• Define income, storage costs, and convenience yield.
• Calculate the futures price on commodities incorporating income/storage costs and/or convenience yields.
• Define and calculate, using the cost-of-carry model, forward prices where the underlying asset either does or
does not have interim cash flows.
• Describe the various delivery options available in the futures markets and how they can influence futures prices.
• Assess the relationship between current futures prices and expected future spot prices, including the impact of
systematic and nonsystematic risk.
• Define contango and backwardation, interpret the effect contango or backwardation may have on the relationship
between commodity futures and spot prices, and relate the cost-of-carry model to contango and backwardation.

Chapter 6 ................................Interest Rate Futures
• Identify the most commonly used day count conventions, describe the markets that each one is typically used in,
and apply each to an interest calculation.
• Calculate the conversion of a discount rate to a price for a U.S. Treasury bill.
• Differentiate between the clean and dirty price for a U.S. Treasury bond; calculate the accrued interest and dirty
price on a U.S. Treasury bond.
• Explain and calculate a U.S. Treasury bond futures contract conversion factor.
• Calculate the cost of delivering a bond into a Treasury bond futures contract.
• Describe the impact of the level and shape of the yield curve on the cheapest-to-deliver bond decision.



• Calculate the theoretical futures price for a Treasury bond futures contract.
• Calculate the final contract price on a Eurodollar futures contract.
• Describe and compute the Eurodollar futures contract convexity adjustment.
• Explain how Eurodollar futures can be used to extend the LIBOR zero curve.
• Calculate the duration-based hedge ratio and describe a duration-based hedging strategy using interest
rate futures.
• Explain the limitations of using a duration-based hedging strategy.

Chapter 7 ................................Swaps
• Explain the mechanics of a plain vanilla interest rate swap and compute its cash flows.
• Explain how a plain vanilla interest rate swap can be used to transform an asset or a liability and calculate the
resulting cash flows.
• Explain the role of financial intermediaries in the swaps market.
• Describe the role of the confirmation in a swap transaction.
• Describe the comparative advantage argument for the existence of interest rate swaps and explain some of
the criticisms of this argument.
• Explain how the discount rates in a plain vanilla interest rate swap are computed.
• Calculate the value of a plain vanilla interest rate swap based on two simultaneous bond positions.
• Calculate the value of a plain vanilla interest rate swap from a sequence of forward rate agreements (FRAs).
• Explain the mechanics of a currency swap and compute its cash flows.
• Describe the comparative advantage argument for the existence of currency swaps.
• Explain how a currency swap can be used to transform an asset or liability and calculate the resulting cash flows.
• Calculate the value of a currency swap based on two simultaneous bond positions.
• Calculate the value of a currency swap based on a sequence of FRAs.
• Describe the role of credit risk inherent in an existing swap position.
• Identify and describe other types of swaps, including commodity, volatility and exotic swaps.

Chapter 10...............................Properties of Stock Options
• Identify the six factors that affect an option’s price and describe how these six factors affect the price for both
European and American options.
• Identify, interpret and compute upper and lower bounds for option prices.
• Explain put-call parity and calculate, using the put-call parity on a non-dividend-paying stock, the value of a
European and American option, respectively.
• Explain the early exercise features of American call and put options on a non-dividend-paying stock and the price
effect early exercise may have.
• Explain the effects of dividends on the put-call parity, the bounds of put and call option prices, and the early
exercise feature of American options.



Chapter 11................................Trading Strategies Involving Options
• Explain the motivation to initiate a covered call or a protective put strategy.
• Describe and explain the use and payoff functions of spread strategies, including bull spread, bear spread, box
spread, calendar spread, butterfly spread, and diagonal spread.
• Calculate the payoffs of various spread strategies.
• Describe and explain the use and payoff functions of combination strategies, including straddles, strangles, strips,
and straps.
• Compute the payoffs of combination strategies.

Robert McDonald, Derivatives Markets, 3rd Edition (Boston: Addison-Wesley, 2013).
Chapter 6 ................................Commodity Forwards and Futures
• Define commodity terminology such as storage costs, carry markets, lease rate, and convenience yield.
• Explain the basic equilibrium formula for pricing commodity forwards.
• Describe an arbitrage transaction in commodity forwards, and compute the potential arbitrage profit.
• Define the lease rate and explain how it determines the no-arbitrage values for commodity forwards and futures.
• Define carry markets, and explain the impact of storage costs and convenience yields on commodity forward
prices and no-arbitrage bounds.
• Compute the forward price of a commodity with storage costs.
• Compare the lease rate with the convenience yield.
• Identify factors that impact gold, corn, electricity, natural gas, and oil forward prices.
• Define and compute a commodity spread.
• Explain how basis risk can occur when hedging commodity price exposure.
• Evaluate the differences between a strip hedge and a stack hedge and explain how these differences impact
risk management.
• Describe examples of cross-hedging, specifically the process of hedging jet fuel with crude oil and using weather
derivatives.
• Explain how to create a synthetic commodity position, and use it to explain the relationship between the forward
price and the expected future spot price.



Helyette Geman, Commodities and Commodity Derivatives: Modeling and Pricing for Agriculturals, Metals and
Energy (West Sussex, England: John Wiley & Sons, 2005).
Chapter 1 .................................Fundamentals of Commodity Spot and Futures Markets: Instruments, Exchanges
and Strategies
• Define “bill of lading.”
• Define the major risks involved with commodity spot transactions.
• Differentiate between ordinary and extraordinary transportation risks.
• Explain the major differences between spot, forward, and futures transactions, markets, and contracts.
• Describe the basic characteristics and differences between hedgers, speculators, and arbitrageurs.
• Describe an “arbitrage portfolio” and explain the conditions for a market to be arbitrage-free.
• Describe the structure of the futures market.
• Define basis risk and the variance of the basis.
• Identify a commonly used measure for determining the effectiveness of hedging a spot position with a futures
contract, and compute and compare the effectiveness of alternative hedges using this measure.
• Define and differentiate between an Exchange for Physical agreement and an Alternative Delivery Procedure.
• Describe volume and open interest and how they relate to liquidity and market depth.

Anthony Saunders and Marcia Millon Cornett, Financial Institutions Management: A Risk Management Approach,
7th Edition (New York: McGraw-Hill, 2011).
Chapter 14...............................Foreign Exchange Risk
• Calculate a financial institution’s overall foreign exchange exposure.
• Explain how a financial institution could alter its net position exposure to reduce foreign exchange risk.
• Calculate a financial institution’s potential dollar gain or loss exposure to a particular currency.
• Identify and describe the different types of foreign exchange trading activities.
• Identify the sources of foreign exchange trading gains and losses.
• Calculate the potential gain or loss from a foreign currency denominated investment.
• Explain balance-sheet hedging with forwards.
• Describe how a non-arbitrage assumption in the foreign exchange markets leads to the interest rate parity
theorem, and use this theorem to calculate forward foreign exchange rates.
• Explain why diversification in multicurrency asset-liability positions could reduce portfolio risk.
• Describe the relationship between nominal and real interest rates.



Frank Fabozzi, The Handbook of Fixed Income Securities, 8th Edition (New York: McGraw-Hill, 2012).
Chapter 12 ...............................Corporate Bonds, by Frank Fabozzi, Steven Mann and Adam Cohen
• Describe a bond indenture and explain the role of the corporate trustee in a bond indenture.
• Explain a bond’s maturity date and how it impacts bond retirements.
• Describe the main types of interest payment classifications.
• Describe zero-coupon bonds, the relationship between original-issue-discount and reinvestment risk, and the
treatment of zeroes in bankruptcy.
• Describe the various security types relevant for corporate bonds, including:
• Mortgage bonds
• Collateral trust bonds
• Equipment trust certificates
• Debenture bonds (including subordinated and convertible debentures)
• Guaranteed bonds
• Describe the mechanisms by which corporate bonds can be retired before maturity, including call provisions,
sinking-fund provisions, maintenance and replacement funds, and tender offers.
• Describe and differentiate between credit default risk and credit spread risk.
• Describe event risk and explain what may cause it in corporate bonds.
• Define high-yield bonds, and describe types of high-yield bond issuers and some of the payment features peculiar
to high yield bonds.
• Define and differentiate between an issuer default rate and a dollar default rate.
• Define recovery rates and describe the relationship between recovery rates and seniority.

John B. Caouette, Edward I. Altman, Paul Narayanan, and Robert W.J. Nimmo, Managing Credit Risk, 2nd Edition
Chapter 6 ................................The Rating Agencies
• Describe the role of rating agencies in the financial markets.
• Explain market and regulatory forces that have played a role in the growth of the rating agencies.
• Describe a rating scale, define credit outlooks, and explain the difference between solicited and unsolicited ratings.
• Describe Standard and Poor’s and Moody’s rating scales and distinguish between investment and noninvestment
grade ratings.
• Describe the difference between an issuer-pay and a subscriber-pay model and describe concerns regarding the
issuer-pay model.
• Describe and contrast the process for rating industrial and sovereign debt and describe how the distributions of
these ratings may differ.
• Describe the ratings performance for corporate bonds.
• Describe the relationship between the rating agencies and regulators and identify key regulations that impact the
rating agencies and the use of ratings in the market.
• Describe some of the trends and issues emerging from the current credit crisis relevant to the rating agencies and
the use of ratings in the market.



VALUATION AND RISK MODELS—Part I Exam Weight | 30%

• Value-at-Risk (VaR)
• Applied to stock, currencies, and commodities
• Applied to linear and non-linear derivatives
• Applied to fixed income securities with embedded options
• Structured Monte Carlo, stress testing, and scenario analysis
• Limitations as a risk measure
• Coherent risk measures
• Volatility Models
• Option valuation
• Pricing options using binomial trees
• The Black-Scholes-Merton Model
• The “Greeks”
• Fixed income valuation
• Discount factors, spot rates, forward rates, and yield to maturity
• Arbitrage and the Law of One Price
• One factor measures of price sensitivity
• Duration, DV01, and convexity
• Key rate exposures
• Hedging and immunization
• Country and sovereign risk models and management
• Fundamental analysis
• External and internal credit ratings
• Expected and unexpected losses
• Operational risk
• Stress testing and scenario analysis

Readings for Valuation and Risk Models

18. Linda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and Operational Risk:
The Value at Risk Approach (Oxford: Blackwell Publishing, 2004).
• Chapter 2 .............................Quantifying Volatility in VaR Models
• Chapter 3 .............................Putting VaR to Work

• Chapter 12 ............................Binomial Trees
• Chapter 14............................The Black-Scholes-Merton Model
• Chapter 18............................The Greek Letters



20. Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011).
• Chapter 1 ..............................Prices, Discount Factors, and Arbitrage
• Chapter 2 .............................Spot, Forward and Par Rates
• Chapter 3 .............................Returns, Spreads and Yields
• Chapter 4 .............................One-Factor Risk Metrics and Hedges
• Chapter 5 .............................Multi-Factor Risk Metrics and Hedges
• Chapter 6 .............................Empirical Approaches to Risk Metrics and Hedging

21. Caouette, Altman, Narayanan, and Nimmo, Managing Credit Risk, 2nd Edition (New York: John Wiley & Sons, 2008).
• Chapter 23...........................Country Risk Models

22. Arnaud de Servigny and Olivier Renault, Measuring and Managing Credit Risk (New York: McGraw-Hill, 2004).
• Chapter 2 .............................External and Internal Ratings

23. Michael Ong, Internal Credit Risk Models: Capital Allocation and Performance Measurement (London: Risk Books, 2003).
• Chapter 4 .............................Loan Portfolios and Expected Loss
• Chapter 5 .............................Unexpected Loss

24. Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley & Sons, 2005).
• Chapter 2 .............................Measures of Financial Risk

25. John Hull, Risk Management and Financial Institutions, 2nd Edition (Boston: Pearson Prentice Hall, 2010).
• Chapter 18............................Operational Risk

26. Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition.
• Chapter 14............................Stress Testing

27. “Principles for Sound Stress Testing Practices and Supervision” (Basel Committee on Banking Supervision
Publication, May 2009).



AIMS:
Linda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and Operational Risk:
The Value at Risk Approach (Oxford: Blackwell Publishing, 2004).
Chapter 2 ................................Quantifying Volatility in VaR Models
• Explain how asset return distributions tend to deviate from the normal distribution.
• Explain potential reasons for the existence of fat tails in a return distribution and describe the implications fat tails
have on analysis of return distributions.
• Distinguish between conditional and unconditional distributions.
• Describe the implications of regime switching on quantifying volatility.
• Explain the various approaches for estimating VaR.
• Compare, contrast and calculate parametric and non-parametric approaches for estimating conditional volatility,
including:
• Historical standard deviation
• Exponential smoothing
• GARCH approach
• Historic simulation
• Multivariate density estimation
• Hybrid methods
• Explain the process of return aggregation in the context of volatility forecasting methods.
• Describe implied volatility as a predictor of future volatility and its shortcomings.
• Explain long horizon volatility/VaR and the process of mean reversion according to an AR(1) model.

Chapter 3 ................................Putting VaR to Work
• Explain and give examples of linear and non-linear derivatives.
• Explain how to calculate VaR for linear derivatives.
• Describe the delta-normal approach to calculating VaR for non-linear derivatives.
• Describe the limitations of the delta-normal method.
• Explain the full revaluation method for computing VaR.
• Compare delta-normal and full revaluation approaches.
• Explain structural Monte Carlo, stress testing and scenario analysis methods for computing VaR, identifying
strengths and weaknesses of each approach.
• Describe the implications of correlation breakdown for scenario analysis.
• Describe worst-case scenario (WCS) analysis and compare WCS to VaR.



Chapter 12 ...............................Binomial Trees
• Calculate the value of a European call or put option using the one-step and two-step binomial model.
• Calculate the value of an American call or put option using a two-step binomial model.
• Describe how volatility is captured in the binomial model.
• Describe how the binomial model value converges as time periods are added.
• Explain how the binomial model can be altered to price options on: stocks with dividends, stock indices,
currencies, and futures.
• Describe how volatility is captured in the binomial model.

Chapter 14...............................The Black-Scholes-Merton Model
• Explain the lognormal property of stock prices, the distribution of rates of return, and the calculation of
expected return.
• Compute the realized return and historical volatility of a stock.
• List and describe the assumptions underlying the Black-Scholes-Merton option pricing model.
• Compute the value of a European option using the Black-Scholes-Merton model on a non dividend paying stock.
• Identify the complications involving the valuation of warrants.
• Define implied volatilities and describe how to compute implied volatilities from market prices of options using
the Black-Scholes-Merton model.
• Explain how dividends affect the early decision for American call and put options.
• Compute the value of a European option using the Black-Scholes-Merton model on a dividend paying stock.
• Use Black’s Approximation to compute the value of an American call option on a dividend-paying stock.

Chapter 18 ...............................The Greek Letters
• Describe and assess the risks associated with naked and covered option positions.
• Explain how naked and covered option positions generate a stop loss trading strategy.
• Describe delta hedging for an option, forward, and futures contracts.
• Compute delta for an option.
• Describe the dynamic aspects of delta hedging.
• Define the delta of a portfolio.
• Define and describe theta, gamma, vega, and rho for option positions.
• Explain how to implement and maintain a gamma neutral position.
• Describe the relationship between delta, theta, and gamma.
• Describe how hedging activities take place in practice, and describe how scenario analysis can be used to
formulate expected gains and losses with option positions.
• Describe how portfolio insurance can be created through option instruments and stock index futures.



Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011).
Chapter 1 .................................Prices, Discount Factors, and Arbitrage
• Define discount factor and use a discount function to compute present and future values.
• Define the “law of one price,” explain it using an arbitrage argument, and describe how it can be applied to
bond pricing.
• Identify the components of a U.S. Treasury coupon bond, and compare and contrast the structure to Treasury
STRIPS, including the difference between P-STRIPS and C-STRIPS.
• Construct a replicating portfolio using multiple fixed income securities to match the cash flows of a given fixed
income security.
• Identify arbitrage opportunities for fixed income securities with certain cash flows.
• Differentiate between “clean” and “dirty” bond pricing and explain the implications of accrued interest with
respect to bond pricing.
• Describe the common day-count conventions used in bond pricing.

Chapter 2 ................................Spot, Forward and Par Rates
• Calculate and describe the impact of different compounding frequencies on a bond’s value.
• Calculate discount factors given interest rate swap rates.
• Compute spot rates given discount factors.
• Define and interpret the forward rate, and compute forward rates given spot rates.
• Define par rate and describe the equation for the par rate of a bond.
• Interpret the relationship between spot, forward and par rates.
• Assess the impact of maturity on the price of a bond and the returns generated by bonds.
• Define the “flattening” and “steepening” of rate curves and construct a hypothetical trade to reflect expectations
that a curve will flatten or steepen.

Chapter 3 ................................Returns, Spreads and Yields
• Distinguish between gross and net realized returns, and calculate the realized return for a bond over a holding
period including reinvestments.
• Define and interpret the spread of a bond, and explain how a spread is derived from a bond price and a term
structure of rates.
• Define, interpret, and apply a bond’s yield-to-maturity (YTM) to bond pricing.
• Compute a bond's YTM given a bond structure and price.
• Calculate the price of an annuity and a perpetuity.
• Explain the relationship between spot rates and YTM.
• Define the coupon effect and explain the relationship between coupon rate, YTM, and bond prices.
• Explain the decomposition of P&L for a bond into separate factors including carry roll-down, rate change and
spread change effects.
• Identify the most common assumptions in carry roll-down scenarios, including realized forwards, unchanged term
structure, and unchanged yields.



Chapter 4 ................................One-Factor Risk Metrics and Hedges
• Describe an interest rate factor and identify common examples of interest rate factors.
• Define and compute the DV01 of a fixed income security given a change in yield and the resulting change in price.
• Calculate the face amount of bonds required to hedge an option position given the DV01 of each.
• Define, compute, and interpret the effective duration of a fixed income security given a change in yield and the
resulting change in price.
• Compare and contrast DV01 and effective duration as measures of price sensitivity.
• Define, compute, and interpret the convexity of a fixed income security given a change in yield and the resulting
change in price.
• Explain the process of calculating the effective duration and convexity of a portfolio of fixed income securities.
• Explain the impact of negative convexity on the hedging of fixed income securities.
• Construct a barbell portfolio to match the cost and duration of a given bullet investment, and explain the
advantages and disadvantages of bullet versus barbell portfolios.

Chapter 5 ................................Multi-Factor Risk Metrics and Hedges
• Describe and assess the major weakness attributable to single-factor approaches when hedging portfolios or
implementing asset liability techniques.
• Define key rate exposures and know the characteristics of key rate exposure factors including partial ‘01s and
forward-bucket ‘01s.
• Describe key-rate shift analysis.
• Define, calculate, and interpret key rate ‘01 and key rate duration.
• Describe the key rate exposure technique in multi-factor hedging applications and summarize its advantages
and disadvantages.
• Calculate the key rate exposures for a given security, and compute the appropriate hedging positions given a
specific key rate exposure profile.
• Describe the relationship between key rates, partial '01s and forward-bucket ‘01s, and calculate the forward-
bucket ‘01 for a shift in rates in one or more buckets.
• Construct an appropriate hedge for a position across its entire range of forward bucket exposures.
• Explain how key rate and multi-factor analysis may be applied in estimating portfolio volatility.

Chapter 6 ................................Empirical Approaches to Risk Metrics and Hedging
• Explain the drawbacks to using a DV01-neutral hedge for a bond position.
• Describe a regression hedge and explain how it improves on a standard DV01-neutral hedge.
• Calculate the regression hedge adjustment factor, beta.
• Calculate the face value of an offsetting position needed to carry out a regression hedge.
• Calculate the face value of multiple offsetting swap positions needed to carry out a two-variable regression hedge.
• Compare and contrast between level and change regressions.
• Describe principal component analysis and explain how it is applied in constructing a hedging portfolio.



Caouette, Altman, Narayanan, and Nimmo, Managing Credit Risk, 2nd Edition. (New York: John Wiley & Sons, 2008).
Chapter 23 ..............................Country Risk Models
• Define and differentiate between country risk and transfer risk and describe some of the factors that might lead
to each.
• Describe country risk in a historical context.
• Identify and describe some of the major risk factors that are relevant for sovereign risk analysis.
• Compare and contrast corporate and sovereign historical default rate patterns.
• Explain approaches for and challenges in assessing country risk.
• Describe how country risk ratings are used in lending and investment decisions.
• Describe some of the challenges in country risk analysis.

Arnaud de Servigny and Olivier Renault, Measuring and Managing Credit Risk (New York: McGraw-Hill, 2004).
Chapter 2 ................................External and Internal Ratings
• Describe external rating scales, the rating process, and the link between ratings and default.
• Describe the impact of time horizon, economic cycle, industry, and geography on external ratings.
• Review the results and explanation of the impact of ratings changes on bond and stock prices.
• Compare external and internal ratings approaches.
• Explain and compare the through-the-cycle and at-the-point internal ratings approaches.
• Define and explain a ratings transition matrix and its elements.
• Describe the process for and issues with building, calibrating and backtesting an internal rating system.
• Identify and describe the biases that may affect a rating system.

Michael Ong, Internal Credit Risk Models: Capital Allocation and Performance Measurement
(London: Risk Books, 2003).
Chapter 4 ................................Loan Portfolios and Expected Loss
• Describe the objectives of measuring credit risk for a bank’s loan portfolio.
• Define, calculate and interpret the expected loss for an individual credit instrument.
• Distinguish between loan and bond portfolios.
• Explain how a credit downgrade or loan default affects the return of a loan.
• Distinguish between expected and unexpected loss.
• Define exposures, adjusted exposures, commitments, covenants, and outstandings:
• Explain how drawn and undrawn portions of a commitment affect exposure
• Explain how covenants impact exposures
• Define usage given default and how it impacts expected and unexpected loss.
• Explain the concept of credit optionality.
• Describe the process of parameterizing credit risk models and its challenges.



Chapter 5 ................................Unexpected Loss
• Explain the objective for quantifying both expected and unexpected loss.
• Describe factors contributing to expected and unexpected loss.
• Define, calculate and interpret the unexpected loss of an asset.
• Explain the relationship between economic capital, expected loss and unexpected loss.

Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley & Sons, 2005).
Chapter 2 ................................Measures of Financial Risk
• Describe the mean-variance framework and the efficient frontier.
• Explain the limitations of the mean-variance framework with respect to assumptions about the return distributions.
• Define the Value-at-Risk (VaR) measure of risk, describe assumptions about return distributions and holding
period, and explain the limitations of VaR.
• Define the properties of a coherent risk measure and explain the meaning of each property.
• Explain why VaR is not a coherent risk measure.
• Explain and calculate expected shortfall (ES), and compare and contrast VaR and ES.
• Describe spectral risk measures, and explain how VaR and ES are special cases of spectral risk measures.
• Describe how the results of scenario analysis can be interpreted as coherent risk measures.

John Hull, Risk Management and Financial Institutions, 2nd Edition (Boston: Pearson Prentice Hall, 2010).
Chapter 18 ...............................Operational Risk
• Calculate the regulatory capital using the basic indicator approach and the standardised approach.
• Explain the Basel Committee’s requirements for the advanced measurement approach (AMA) and their seven
categories of operational risk.
• Explain how to get a loss distribution from the loss frequency distribution and the loss severity distribution using
Monte Carlo simulations.
• Describe the common data issues that can introduce inaccuracies and biases in the estimation of loss frequency
and severity distributions.
• Describe how to use scenario analysis in instances when there is scarce data.
• Describe how to identify causal relationships and how to use risk and control self assessment (RCSA) and
key risk indicators (KRIs) to measure and manage operational risks.
• Describe the allocation of operational risk capital and the use of scorecards.
• Explain how to use the power law to measure operational risk.
• Explain the risks of moral hazard and adverse selection when using insurance to mitigate operational risks.



Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition.
Chapter 14...............................Stress Testing
• Describe the purposes of stress testing and the process of implementing a stress testing scenario.
• Contrast between event-driven scenarios and portfolio-driven scenarios.
• Identify common one-variable sensitivity tests.
• Describe the Standard Portfolio Analysis of Risk (SPAN®) system for measuring portfolio risk.
• Describe the drawbacks to scenario analysis.
• Explain the difference between unidimensional and multidimensional scenarios.
• Compare and contrast various approaches to scenario analysis.
• Define and distinguish between sensitivity analysis and stress testing model parameters.
• Explain how the results of a stress test can be used to improve our risk analysis and risk management systems.

“Principles for Sound Stress Testing Practices and Supervision” (Basel Committee on Banking Supervision
Publication, May 2009).
• Describe the rationale for the use of stress testing as a risk management tool.
• Describe weaknesses identified and recommendations for improvement in:
• The use of stress testing and integration in risk governance
• Stress testing methodologies
• Stress testing scenarios
• Stress testing handling of specific risks and products.
• Describe stress testing principles for banks within:
• Use of stress testing and integration in risk governance
• Stress testing methodology and scenario selection
• Principles for supervisors



FRM PART II—TOPICS AND READINGS

MARKET RISK MEASUREMENT AND MANAGEMENT—Part II Exam Weight | 25%

• Fixed income securities
• Risk-neutral pricing
• Term structure models
• Mortgages and mortgage-backed securities (MBS)
• Structure, markets, and valuation
• VaR and other risk measures
• VaR mapping
• Backtesting VaR
• Expected shortfall (ES) and other coherent risk measures
• Parametric and non-parametric methods of estimation
• Modeling dependence: correlations and copulas
• Extreme value theory (EVT)
• Volatility: smiles and term structures
• Exotic options

Readings for Market Risk Measurement and Management

• Chapter 19............................Volatility Smiles
• Chapter 25...........................Exotic Options

29. Tuckman, Fixed Income Securities, 3rd Edition.
• Chapter 7 .............................The Science of Term Structure Models
• Chapter 8 .............................The Evolution of Short Rates and the Shape of the Term Structure
• Chapter 9 .............................The Art of Term Structure Models: Drift
• Chapter 10 ...........................The Art of Term Structure Models: Volatility and Distribution

30. Pietro Veronesi, Fixed Income Securities (Hoboken, NJ: John Wiley & Sons, 2010).
• Chapter 8 .............................Basics of Residential Mortgage Backed Securities

31. Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition.
• Chapter 6 .............................Backtesting VaR
• Chapter 11 .............................VaR Mapping



32. Kevin Dowd, Measuring Market Risk, 2nd Edition.
• Chapter 3 .............................Estimating Market Risk Measures
• Chapter 4 .............................Non-parametric Approaches
• Chapter 5 .............................Appendix—Modeling Dependence: Correlations and Copulas
• Chapter 7 .............................Parametric Approaches (II): Extreme Value

33. Frank Fabozzi, Anand Bhattacharya, William Berliner, Mortgage-Backed Securities, 3rd Edition
(Hoboken, NJ: John Wiley & Sons, 2011).
• Chapter 1 ..............................Overview of Mortgages and the Consumer Mortgage Market
• Chapter 2 .............................Overview of the Mortgage-Backed Securities Market
• Chapter 10 ...........................Techniques for Valuing MBS

34. “Messages from the Academic Literature on Risk Measurement for the Trading Book,” Basel Committee on
Banking Supervision, Working Paper, No. 19, Jan 2011.

AIMS:
Chapter 19...............................Volatility Smiles
• Define volatility smile and volatility skew.
• Explain how put-call parity indicates that the implied volatility used to price call options is the same used to price
put options.
• Compare the shape of the volatility smile (or skew) to the shape of the implied distribution of the underlying asset
price and to the pricing of options on the underlying asset.
• Explain why foreign exchange rates are not necessarily lognormally distributed and the implications this can have
on option prices and implied volatility.
• Describe the volatility smile for equity options and give possible explanations for its shape.
• Describe alternative ways of characterizing the volatility smile.
• Describe volatility term structures and volatility surfaces and how they may be used to price options.
• Explain the impact of the volatility smile on the calculation of the “Greeks.”
• Explain the impact of asset price jumps on volatility smiles.

Chapter 25 ..............................Exotic Options
• Define and contrast exotic derivatives and plain vanilla derivatives.
• Describe some of the factors that drive the development of exotic products.
• Explain how any derivative can be converted into a zero-cost product.
• Identify and describe how various option characteristics can transform standard American options into
nonstandard American options.



• Identify and describe the characteristics and pay-off structure of:
• Forward start options
• Compound options
• Chooser and barrier options
• Binary options
• Lookback options
• Shout options
• Asian options
• Exchange options
• Rainbow options
• Basket options
• Describe and contrast volatility and variance swaps.
• Explain the basic premise of static option replication and how it can be applied to hedging exotic options.

Tuckman, Fixed Income Securities, 3rd Edition.
Chapter 7 ................................The Science of Term Structure Models
• Calculate the expected discounted value of a zero-coupon security using a binomial tree.
• Construct and apply an arbitrage argument to price a call option on a zero-coupon security using replicating
portfolios.
• Explain why a call option on a zero-coupon security cannot be properly priced using expected discounted values.
• Explain the role of up-state and down-state probabilities in the valuation of a call option on a zero-coupon security
• Define risk-neutral pricing and explain how it is used in option pricing.
• Explain the difference between true and risk-neutral probabilities, and apply this difference to interest rate drift.
• Explain how the principles of arbitrage pricing of derivatives on fixed income securities can be extended over
multiple periods.
• Describe the rationale behind the use of non-recombining trees in option pricing.
• Calculate the value of a constant maturity Treasury swap, given an interest rate tree and the risk‐neutral probabilities.
• Describe the advantages and disadvantages of reducing the size of the time steps on the pricing of derivatives on
fixed income securities.
• Explain why the Black‐Scholes‐Merton model used in valuing equity derivatives is not appropriate to value
derivatives on fixed income securities.
• Describe the impact of embedded options on the value of fixed income securities.

Chapter 8 ................................The Evolution of Short Rates and the Shape of the Term Structure
• Explain the role of interest rate expectations in determining the shape of the term structure.
• Apply a risk-neutral interest rate tree to assess the effect of volatility on the shape of the term structure.
• Calculate the convexity effect using Jensen’s inequality.
• Calculate the price and return of a zero coupon bond incorporating a risk premium.



Chapter 9 ................................The Art of Term Structure Models: Drift
• Describe the process and effectiveness of the following models, and construct a tree for a short-term rate using
the following models:
• A model with normally distributed rates and no drift (Model 1)
• A model incorporating drift (Model 2)
• Calculate the short-term rate change and standard deviation of the change of the rate using a model with
normally distributed rates and no drift.
• Describe methods for handling negative short-term rates for term structure models.
• Describe the process of and construct a tree for a short-term rate under the Ho-Lee Model with time-
dependent drift.
• Describe uses and benefits of the arbitrage-free models and assess the issue of fitting models to market prices.
• Describe the process of and construct a simple and recombining tree for a short-term rate under the Vasicek
Model with mean reversion.
• Calculate the Vasicek Model rate change, standard deviation of the change of the rate, expected rate in T years,
and half life.
• Describe the effectiveness of the Vasicek Model.

Chapter 10...............................The Art of Term Structure Models: Volatility and Distribution
• Describe the short-term rate process under a model with time-dependent volatility (Model 3).
• Calculate the short-term rate change and describe the behavior of the standard deviation of the change of the
rate using a model with time dependent volatility.
• Describe the effectiveness of time-dependent volatility models.
• Describe the short-term rate process under the Cox-Ingersoll-Ross (CIR) and Lognormal models.
• Calculate the short-term rate change and describe the basis point volatility using the CIR and Lognormal models.
• Summarize the application of a lognormal model with deterministic drift and a lognormal model with
mean reversion.

Pietro Veronesi, Fixed Income Securities (Hoboken, NJ: John Wiley & Sons, 2010).
Chapter 8 ................................Basics of Residential Mortgage Backed Securities
• Summarize the securitization process of residential mortgage backed securities (MBS).
• Differentiate between agency and non-agency MBS and describe the major participants in the residential
MBS market.
• Describe the mortgage prepayment option and the factors that influence prepayments.
• Describe the impact on a MBS of the weighted average maturity, the weighted average coupon, and the speed of
prepayments of the mortgages underlying the MBS.
• Identify, describe, and contrast different standard prepayment measures.
• Describe the effective duration and effective convexity of standard MBS instruments and the factors that affect them.
• Describe collateralized mortgage obligations (CMOs) and contrast them with MBSs.
• Describe and work through a simple cash flow example for the following types of MBS:
• Pass-through securities
• CMOs, both sequential and planned amortization class
• Interest only and principal only strips



Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition.
Chapter 6 ................................Backtesting VaR
• Define backtesting and exceptions and explain the importance of backtesting VaR models.
• Explain the significant difficulties in backtesting a VaR model.
• Explain the framework of backtesting models with the use of exceptions or failure rates.
• Define and identify type I and type II errors.
• Explain why it is necessary to consider conditional coverage in the backtesting framework.
• Describe the Basel rules for backtesting.

Chapter 11................................VaR Mapping
• Explain the principles underlying VaR Mapping, list and describe the mapping process.
• Explain how the mapping process captures general and specific risks.
• List and describe the three methods of mapping portfolios of fixed income securities.
• Map a fixed income portfolio into positions of standard instruments.
• Describe how mapping of risk factors can support stress testing.
• Explain how VaR can be used as a performance benchmark.
• Describe the method of mapping forwards, commodity forwards, forward rate agreements, and interest rate swaps.
• Describe the method of mapping options.

Kevin Dowd, Measuring Market Risk, 2nd Edition.
Chapter 3 ................................Estimating Market Risk Measures
• Calculate VaR using a historical simulation approach.
• Calculate VaR using a parametric estimation approach assuming that the return distribution is either normal
or lognormal.
• Calculate the expected shortfall given P/L or return data.
• Define coherent risk measures.
• Describe the method of estimating coherent risk measures by estimating quantiles.
• Describe the method of estimating standard errors for estimators of coherent risk measures.
• Describe the use of QQ plots for identifying the distribution of data.

Chapter 4 ................................Non-parametric Approaches
• Describe the bootstrap historical simulation approach to estimating coherent risk measures.
• Describe historical simulation using non-parametric density estimation.
• Describe the following weighted historic simulation approaches:
• Age-weighted historic simulation
• Volatility-weighted historic simulation
• Correlation-weighted historic simulation
• Filtered historical simulation
• Describe the advantages and disadvantages of non-parametric estimation methods.



Chapter 5 ................................Appendix—Modeling Dependence: Correlations and Copulas
• Explain the drawbacks of using correlation to measure dependence.
• Describe how copulas provide an alternative measure of dependence.
• Identify basic examples of copulas.
• Explain how tail dependence can be investigated using copulas.

Chapter 7 ................................Parametric Approaches (II): Extreme Value
• Explain the importance and challenges of extreme values for risk management.
• Describe extreme value theory (EVT) and its use in risk management.
• Describe the peaks-over-threshold (POT) approach.
• Compare generalized extreme value and POT.
• Describe the parameters of a generalized Pareto (GP) distribution.
• Explain the tradeoffs in setting the threshold level when applying the GP distribution.
• Compute VaR and expected shortfall using the POT approach, given various parameter values.
• Explain the importance of multivariate EVT for risk management.

Frank Fabozzi, Anand Bhattacharya, William Berliner, Mortgage-Backed Securities, 3rd Edition
(Hoboken, NJ: John Wiley & Sons, 2011).
Chapter 1 .................................Overview of Mortgages and the Consumer Mortgage Market
• Describe the key attributes that define mortgages.
• Calculate the mortgage payment factor.
• Understand the allocation of loan principal and interest over time for various loan types.
• Define prepayment risk, reasons for prepayment, and the negative convexity of mortgages.
• Explain credit and default risk analysis of mortgages, including metrics for delinquencies, defaults, and loss severity.

Chapter 2 ................................Overview of the Mortgage-Backed Securities Market
• Describe the evolution of the MBS market.
• Explain the creation of agency (fixed rate and adjustable rate) and private-label MBS pools, pass-throughs, CMOs,
and mortgage strips.
• Explain how a loan progresses from application to agency pooling.
• Describe MBS market structure and the ways that fixed rate pass-through securities trade.
• Explain a dollar roll transaction, how to value a dollar roll, and what factors can cause a roll to trade “special.”
• Compare the pricing of mortgage products to developments in MBS markets.
• Explain the purpose of cash flow structuring of mortgage backed securities.


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