FRM Part I Learning Objectives 2021

FRM Part I Learning Objectives 2021

Chapter 1. The Building Blocks of Risk Management

After completing this reading, you should be able to:

  • Explain the concept of risk and compare risk management with risk
  • Evaluate, compare and apply tools and procedures used to measure and manage risk, including quantitative measures, qualitative risk assessment techniques, and enterprise risk
  • Distinguish between expected loss and unexpected loss and provide examples of
  • Interpret the relationship between risk and reward and explain how conflicts of interest can impact risk
  • Describe and differentiate between the key classes of risks, explain how each type of risk can arise, and assess the potential impact of each type of risk on an
  • Explain how risk factors can interact with each other and describe challenges in aggregating risk

Chapter 2. How Do Firms Manage Financial Risk?

After completing this reading, you should be able to:

  • Compare different strategies a firm can use to manage its risk exposures and explain situations in which a firm would want to use each
  • Explain the relationship between risk appetite and a firm’s risk management
  • Evaluate some advantages and disadvantages of hedging risk exposures and explain challenges that can arise when implementing a hedging
  • Apply appropriate methods to hedge operational and financial risks, including pricing, foreign currency, and interest rate
  • Assess the impact of risk management tools and instruments, including risk limits and derivatives.

Chapter 3. The Governance of Risk Management

After completing this reading, you should be able to:

  • Explain changes in regulations and corporate risk governance that occurred as a result of the 2007-2009 financial crisis.
  • Describe best practices for the governance of a firm’s risk management
  • Explain the risk management role and responsibilities of a firm’s board of
  • Evaluate the relationship between a firm’s risk appetite and its business strategy, including the role of
  • Illustrate the interdependence of functional units within a firm as it relates to risk
  • Assess the role and responsibilities of a firm’s audit committee.

Chapter 4. Credit Risk Transfer Mechanisms

After completing this reading, you should be able to:

  • Compare different types of credit derivatives, explain their applications, and describe their
  • Explain different traditional approaches or mechanisms that firms can use to help mitigate credit
  • Evaluate the role of credit derivatives in the 2007-2009 financial crisis and explain changes in the credit derivative market that occurred as a result of the
  • Explain the process of securitization, describe a special purpose vehicle (SPV), and assess the risk of different business models that banks can use for securitized products.

Chapter 5. Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

After completing this reading, you should be able to:

  • Explain Modern Portfolio Theory and interpret the Markowitz efficient
  • Understand the derivation and components of the
  • Describe the assumptions underlying the
  • Interpret and compare the capital market line and the security market
  • Apply the CAPM in calculating the expected return on an
  • Interpret beta and calculate the beta of a single asset or
  • Calculate, compare, and interpret the following performance measures: the Sharpe performance index, the Treynor performance index, the Jensen performance index, the tracking error, information ratio, and Sortino ratio.

Chapter 6. The Arbitrage Pricing Theory and Multifactor Models of Risk and Return

After completing this reading, you should be able to:

  • Explain the Arbitrage Pricing Theory (APT), describe its assumptions, and compare the APT to the
  • Describe the inputs (including factor betas) to a multifactor model and explain the challenges of using multifactor models in
  • Calculate the expected return of an asset using a single-factor and a multifactor
  • Explain how to construct a portfolio to hedge exposure to multiple factors.
  • Describe and apply the Fama-French three-factor model in estimating asset returns.

Chapter 7. Principles for Effective Data Aggregation and Risk Reporting 

After completing this reading, you should be able to:

  • Explain the potential benefits of having effective risk data aggregation and
  • Explain challenges to the implementation of a strong risk data aggregation and reporting process and the potential impacts of using poor quality
  • Describe key governance principles related to risk data aggregation and risk reporting.
  • Describe characteristics of effective data architecture, IT infrastructure, and risk reporting practices.

Chapter 8. Enterprise Risk Management and Future Trends 

After completing this reading, you should be able to:

  • Describe Enterprise Risk Management (ERM) and compare an ERM program with a traditional silo-based risk management
  • Describe the motivations for a firm to adopt an ERM
  • Explain best practices for the governance and implementation of an ERM
  • Describe risk culture, explain the characteristics of a strong corporate risk culture, and describe challenges to the establishment of a strong risk culture at a
  • Explain the role of scenario analysis in the implementation of an ERM program and describe its advantages and
  • Explain the use of scenario analysis in stress testing programs and capital planning.

Chapter 9. Learning from Financial Disasters

After completing this reading, you should be able to:

  • Analyze the key factors that led to and derive the lessons learned from case studies involving the following risk factors:
    • Interest rate risk, including the 1980s savings and loan crisis in the US.
    • Funding liquidity risk, including Lehman Brothers, Continental Illinois, and Northern
    • Implementing hedging strategies, including the Metallgesellschaft
    • Model risk, including the Niederhoffer case, Long Term Capital Management, and the London Whale
    • Rogue trading and misleading reporting, including the Barings
    • Financial engineering and complex derivatives, including Bankers Trust, the Orange County case, and Sachsen
    • Reputational risk, including the Volkswagen
    • Corporate governance, including the Enron
    • Cyber risk, including the SWIFT case.

Chapter 10. Anatomy of the Great Financial Crisis of 2007-2009

After completing this reading, you should be able to:

  • Describe the historical background and provide an overview of the 2007-2009 financial
  • Describe the build-up to the financial crisis and the factors that played an important
  • Explain the role of subprime mortgages and collateralized debt obligations (CDOs) in the
  • Compare the roles of different types of institutions in the financial crisis, including banks, financial intermediaries, mortgage brokers and lenders, and rating
  • Describe trends in the short-term wholesale funding markets that contributed to the financial crisis, including their impact on systemic
  • Describe responses made by central banks in response to the crisis.

Chapter 11. GARP Code of Conduct

After completing this reading, you should be able to:

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

Chapter 1: Fundamentals of Probability

After completing this reading, you should be able to:

  • Describe an event and an event
  • Describe independent events and mutually exclusive
  • Explain the difference between independent events and conditionally independent
  • Calculate the probability of an event for a discrete probability
  • Define and calculate a conditional
  • Distinguish between conditional and unconditional
  • Explain and apply Bayes’ rule.

Chapter 2: Random Variables

After completing this reading, you should be able to:

  • Describe and distinguish a probability mass function from a cumulative distribution function and explain the relationship between these
  • Understand and apply the concept of a mathematical expectation of a random
  • Describe the four common population
  • Explain the differences between a probability mass function and a probability density
  • Characterize the quantile function and quantile-based
  • Explain the effect of a linear transformation of a random variable on the mean, variance, standard deviation, skewness, kurtosis, median and interquartile range.

Chapter 3: Common Univariate Random Variables

After completing this reading, you should be able to:

  • Distinguish the key properties and identify the common occurrences of the following distributions: uniform distribution, Bernoulli distribution, binomial distribution, Poisson distribution, normal distribution, lognormal distribution, Chi-squared distribution, Student’s t and F-distributions.
  • Describe a mixture distribution and explain the creation and characteristics of mixture distributions.

Chapter 4: Multivariate Random Variables

After completing this reading, you should be able to:

  • Explain how a probability matrix can be used to express a probability mass
  • Compute the marginal and conditional distributions of a discrete bivariate random
  • Explain how the expectation of a function is computed for a bivariate discrete random
  • Define covariance and explain what it measures.
  • Explain the relationship between the covariance and correlation of two random variables and how these are related to the independence of the two
  • Explain the effects of applying linear transformations on the covariance and correlation between two random
  • Compute the variance of a weighted sum of two random
  • Compute the conditional expectation of a component of a bivariate random
  • Describe the features of an independent and identically distributed (iid) sequence of random
  • Explain how the iid property is helpful in computing the mean and variance of a sum of iid random variables.

Chapter 5: Sample Moments

After completing this reading, you should be able to:

  • Estimate the mean, variance and standard deviation using sample
  • Explain the difference between a population moment and a sample
  • Distinguish between an estimator and an
  • Describe the bias of an estimator and explain what the bias
  • Explain what is meant by the statement that the mean estimator is
  • Describe the consistency of an estimator and explain the usefulness of this
  • Explain how the Law of Large Numbers (LLN) and Central Limit Theorem (CLT) apply to the sample
  • Estimate and interpret the skewness and kurtosis of a random
  • Use sample data to estimate quantiles, including the
  • Estimate the mean of two variables and apply the
  • Estimate the covariance and correlation between two random
  • Explain how coskewness and cokurtosis are related to skewness and kurtosis.

Chapter 6: Hypothesis Testing 

After completing this reading, you should be able to:

  • Construct an appropriate null hypothesis and alternative hypothesis and distinguish between the
  • Differentiate between a one-sided and a two-sided test and identify when to use each
  • Explain the difference between Type I and Type II errors and how these relate to the size and power of a
  • Understand how a hypothesis test and a confidence interval are
  • Explain what the p-value of a hypothesis test
  • Construct and apply confidence intervals for one-sided and two-sided hypothesis tests and interpret the results of hypothesis tests with a specific level of
  • Identify the steps to test a hypothesis about the difference between two population
  • Explain the problem of multiple testing and how it can bias results.

Chapter 7: Linear Regression

After completing this reading, you should be able to:

  • Describe the models which can be estimated using linear regression and differentiate them from those which
  • Interpret the results of an ordinary least squares (OLS) regression with a single explanatory
  • Describe the key assumptions of OLS parameter
  • Characterize the properties of OLS estimators and their sampling
  • Construct, apply and interpret hypothesis tests and confidence intervals for a single regression coefficient in a
  • Explain the steps needed to perform a hypothesis test in a linear
  • Describe the relationship between a t-statistic, its p-value and a confidence interval.

Chapter 8: Regression with Multiple Explanatory Variables

After completing this reading, you should be able to:

  • Distinguish between the relative assumptions of single and multiple
  • Interpret regression coefficients in a multiple
  • Interpret goodness of fit measures for single and multiple regressions, including R2 and adjusted-R2.
  • Construct, apply and interpret joint hypothesis tests and confidence intervals for multiple coefficients in a regression.

Chapter 9: Regression Diagnostics

After completing this reading, you should be able to:

  • Explain how to test whether a regression is affected by heteroskedasticity
  • Describe approaches to using heteroskedastic
  • Characterize multicollinearity and its consequences; distinguish between multicollinearity and perfect
  • Describe the consequences of excluding a relevant explanatory variable from a model and contrast those with the consequences of including an irrelevant
  • Explain two model selection procedures and how these relate to the bias-variance trade-off.
  • Describe the various methods of visualizing residuals and their relative
  • Describe methods for identifying outliers and their
  • Determine the conditions under which OLS is the best linear unbiased estimator.

Chapter 10: Stationary Time Series 

After completing this reading, you should be able to:

  • Describe the requirements for a series to be covariance
  • Define the autocovariance function and the autocorrelation
  • Define white noise; describe independent white noise and normal (Gaussian) white
  • Define and describe the properties of autoregressive (AR)
  • Define and describe the properties of moving average (MA)
  • Explain how a lag operator
  • Explain mean reversion and calculate a mean-reverting
  • Define and describe the properties of autoregressive moving average (ARMA)
  • Describe the application of AR, MA and ARMA
  • Describe sample autocorrelation and partial
  • Describe the Box-Pierce Q-statistic and the Ljung-Box Q
  • Explain how forecasts are generated from ARMA
  • Describe the role of mean reversion in long-horizon
  • Explain how seasonality is modeled in a covariance-stationary ARMA.

Chapter 11: Non-Stationary Time Series

After completing this reading, you should be able to:

  • Describe linear and nonlinear time
  • Explain how to use regression analysis to model
  • Describe a random walk and a unit
  • Explain the challenges of modeling time series containing unit
  • Describe how to test if a time series contains a unit
  • Explain how to construct an h-step-ahead point forecast for a time series with
  • Calculate the estimated trend value and form an interval forecast for a time series.

Chapter 12: Measuring Returns, Volatility, and Correlation

After completing this reading, you should be able to:

  • Calculate, distinguish and convert between simple and continuously compounded
  • Define and distinguish between volatility, variance rate and implied
  • Describe how the first two moments may be insufficient to describe non-normal
  • Explain how the Jarque-Bera test is used to determine whether returns are normally
  • Describe the power law and its use for non-normal
  • Define correlation and covariance and differentiate between correlation and
  • Describe properties of correlations between normally distributed variables when using a one-factor model.

Chapter 13: Simulation and Bootstrapping

After completing this reading, you should be able to:

  • Describe the basic steps to conduct a Monte Carlo
  • Describe ways to reduce Monte Carlo sampling
  • Explain the use of antithetic and control variates in reducing Monte Carlo sampling
  • Describe the bootstrapping method and its advantage over Monte Carlo
  • Describe pseudo-random number
  • Describe situations where the bootstrapping method is
  • Describe the disadvantages of the simulation approach to financial problem solving.

 

Chapter 1. Banks

After completing this reading, you should be able to:

  • Identify the major risks faced by banks and explain ways in which these risks can
  • Distinguish between economic capital and regulatory
  • Summarize the Basel Committee regulations for regulatory capital and their
  • Explain how deposit insurance gives rise to a moral hazard
  • Describe investment banking financing arrangements including private placement, public offering, best efforts, firm commitment, and Dutch auction
  • Describe the potential conflicts of interest among commercial banking, securities services, and investment banking divisions of a bank, and recommend solutions to these conflict of interest
  • Describe the distinctions between the banking book and the trading book of a
  • Explain the originate-to-distribute banking model and discuss its benefits and drawbacks.

Chapter 2. Insurance Companies and Pension Plans

After completing this reading, you should be able to:

  • Describe the key features of the various categories of insurance companies and identify the risks facing insurance
  • Describe the use of mortality tables and calculate the premium payment for a policy
  • Distinguish between mortality risk and longevity risk and describe how to hedge these
  • Describe defined benefit plans and defined contribution plans and explain the differences between
  • Compare the various types of life insurance policies
  • Calculate and interpret loss ratio, expense ratio, combined ratio, and operating ratio for a property-casualty insurance
  • Describe moral hazard and adverse selection risks facing insurance companies, provide examples of each, and describe how to overcome these
  • Evaluate the capital requirements for life insurance and property-casualty insurance
  • Compare the guaranty system and the regulatory requirements for insurance companies with those for banks.

Chapter 3. Fund Management

After completing this reading, you should be able to:

  • Differentiate among open-end mutual funds, closed-end mutual funds, and exchange-traded funds (ETFs).
  • Identify and describe potential undesirable trading behaviors at mutual
  • Calculate the net asset value (NAV) of an open-end mutual
  • Explain the key differences between hedge funds and mutual
  • Calculate the return on a hedge fund investment and explain the incentive fee structure of a hedge fund, including the terms hurdle rate, high-water mark, and
  • Describe various hedge fund strategies including long/short equity, dedicated short, distressed securities, merger arbitrage, convertible arbitrage, fixed income arbitrage, emerging markets, global macro, and managed futures, and identify the risks faced by hedge
  • Describe characteristics of mutual fund and hedge fund performance and explain the effect of measurement biases on performance measurement.

Chapter 4. Introduction to Derivatives

After completing this reading, you should be able to:

  • Define derivatives, describe the features and uses of derivatives, and compare linear and non-linear
  • Describe exchange-traded and over-the-counter markets, and evaluate the advantages and disadvantages of
  • Differentiate between options, forwards, and futures
  • Identify and calculate option and forward contract
  • Differentiate among the broad categories of traders: hedgers, speculators, and
  • Calculate and compare the payoffs from hedging strategies involving forward contracts and
  • Calculate and compare the payoffs from speculative strategies involving futures and
  • Calculate an arbitrage payoff and describe how arbitrage opportunities are
  • Describe some of the risks that can arise from the use of derivatives.

Chapter 5. Exchanges and OTC Markets

After completing this reading, you should be able to:

  • Describe how exchanges can be used to alleviate counterparty
  • Explain the developments in clearing that reduce
  • Describe netting and describe a netting
  • Describe the implementation of a margining process; explain the determinants of and calculate initial and variation margin
  • Compare exchange-traded and OTC markets and describe their
  • Identify the classes of derivative securities and explain the risk associated with
  • Identify risks associated with OTC markets and explain how these risks can be
  • Describe the role of collateralization in the OTC market and compare it to the margining
  • Explain the use of special purpose vehicles (SPVs) in the OTC derivatives market.

Chapter 6. Central Clearing

After completing this reading, you should be able to:

  • Provide examples of the mechanics of a central counterparty (CCP).
  • Describe the role of CCPs and distinguish between bilateral and centralized
  • Describe advantages and disadvantages of central clearing of OTC
  • Explain regulatory initiatives for the OTC derivatives market and their impact on central
  • Compare margin requirements in centrally cleared and bilateral markets and explain how margin can mitigate risk.
  • Compare and contrast bilateral markets to the use of novation and
  • Assess the impact of central clearing on the broader financial
  • Identify and explain the types of risks faced by
  • Identify and distinguish between the risks to clearing members and to non-members.

Chapter 7. Futures Markets

After completing this reading, you should be able to:

  • Define and describe the key features and specifications of a futures contract, including the underlying asset, the contract price and size, trading volume, open interest, delivery, and
  • Explain the convergence of futures and spot
  • Describe the role of an exchange in futures
  • Explain the differences between a normal and inverted futures
  • Describe the mechanics of the delivery process and contrast it with cash
  • Evaluate the impact of different trading order
  • Describe the application of marking to market and hedge accounting for
  • Compare and contrast forward and futures contracts.

Chapter 8. Using Futures for Hedging

After completing this reading, you should be able to:

  • Define and differentiate between short and long hedges and identify their appropriate
  • Describe the arguments for and against hedging and the potential impact of hedging on firm
  • Define the basis and explain the various sources of basis risk and explain how basis risks arise when hedging with
  • Define cross hedging and compute and interpret the minimum variance hedge ratio and hedge
  • Calculate the profit and loss on a short or long hedge
  • Compute the optimal number of futures contracts needed to hedge an exposure and explain and calculate the “tailing the hedge”
  • Explain how to use stock index futures contracts to change a stock portfolio’s
  • Explain how to create a long-term hedge using a stack and roll strategy and describe some of the risks that arise from this strategy.

Chapter 9. Foreign Exchange Markets

After completing this reading, you should be able to:

  • Explain and describe the mechanics of spot quotes, forward quotes, and futures quotes in the foreign exchange markets; distinguish between bid and ask exchange
  • Calculate a bid-ask spread and explain why the bid-ask spread for spot quotes may be different from the bid- ask spread for forward
  • Compare outright (forward) and swap
  • Define, compare, and contrast transaction risk, translation risk, and economic
  • Describe examples of transaction, translation, and economic risks and explain how to hedge these
  • Describe the rationale for multi-currency hedging using
  • Identify and explain the factors that determine exchange
  • Calculate and explain the effect of an appreciation/depreciation of one currency relative to
  • Explain the purchasing power parity theorem and use this theorem to calculate the appreciation or depreciation of a foreign
  • Describe the relationship between nominal and real interest
  • 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
  • Distinguish between covered and uncovered interest rate parity conditions.

Chapter 10. Pricing Financial Forwards and Futures

After completing this reading, you should be able to:

  • Differentiate between investment and consumption
  • Define short-selling and calculate the net profit of a short sale of a dividend-paying
  • Describe the differences between forward and futures contracts and explain the relationship between forward and spot
  • Calculate the forward price given the underlying asset’s spot price and describe an arbitrage argument between spot and forward
  • Distinguish between the forward price and the value of a forward
  • Calculate the value of a forward contract on a financial asset that does or does not provide income or
  • Explain the relationship between forward and futures
  • Calculate a forward foreign exchange rate using the interest rate parity
  • Calculate the value of a stock index futures contract and explain the concept of index arbitrage.

Chapter 11. Commodity Forwards and Futures

After completing this reading, you should be able to:

  • Explain the key differences between commodities and financial
  • Define and apply commodity concepts such as storage costs, carry markets, lease rate, and convenience
  • Identify factors that impact prices on agricultural commodities, metals, energy, and weather
  • Explain the basic equilibrium formula for pricing commodity
  • Describe an arbitrage transaction in commodity forwards and compute the potential arbitrage
  • Define the lease rate and explain how it determines the no-arbitrage values for commodity forwards and
  • Describe the cost of carry model and determine the impact of storage costs and convenience yields on commodity forward prices and no-arbitrage
  • Compute the forward price of a commodity with storage
  • Compare the lease rate with the convenience
  • Explain how to create a synthetic commodity position and use it to explain the relationship between the forward price and the expected future spot
  • Explain the relationship between current futures prices and expected future spot prices, including the impact of systematic and nonsystematic
  • Define and interpret normal backwardation and contango.

Chapter 12. Options Markets

After completing this reading, you should be able to:

  • Describe the various types, uses, and typical underlying assets of
  • Explain the payoff function and calculate the profit and loss from an options
  • Explain the specification of exchange-traded stock option contracts, including that of nonstandard
  • Explain how dividends and stock splits can impact the terms of a stock
  • Describe the application of commissions, margin requirements, and exercise procedures to exchange-traded options and explain the trading characteristics of these
  • Define and describe warrants, convertible bonds, and employee stock options.

Chapter 13. Properties of Options

After completing this reading, you should be able to:

  • Identify the six factors that affect an option’s
  • Identify and compute upper and lower bounds for option prices on non-dividend and dividend paying
  • Explain put-call parity and apply it to the valuation of European and American stock options, with dividends and without dividends, and express it in terms of forward
  • Explain and assess potential rationales for using the early exercise features of American call and put options.

Chapter 14. Trading Strategies

After completing this reading, you should be able to:

  • Explain the motivation to initiate a covered call or a protective put
  • Describe principal protected notes (PPNs) and explain necessary conditions to create a
  • Describe the use and calculate the payoffs of various spread
  • Describe the use and explain the payoff functions of combination strateigies.

Chapter 15. Exotic Options

After completing this reading, you should be able to:

  • Define and contrast exotic derivatives and plain vanilla
  • Describe some of the factors that drive the development of exotic derivative
  • Explain how any derivative can be converted into a zero-cost
  • Describe how standard American options can be transformed into nonstandard American
  • Identify and describe the characteristics and payoff structures of the following exotic options: gap, forward start, compound, chooser, barrier, binary, lookback, Asian, exchange, and basket
  • Describe and contrast volatility and variance
  • Explain the basic premise of static option replication and how it can be applied to hedging exotic options.

 

Chapter 16. Properties of Interest Rates

After completing this reading, you should be able to:

  • Describe Treasury rates, LIBOR, Secured Overnight Financing Rate (SOFR), and repo rates, and explain what is meant by the “risk-free”
  • Calculate the value of an investment using different compounding
  • Convert interest rates based on different compounding
  • Calculate the theoretical price of a bond using spot
  • Calculate the Macaulay duration, modified duration, and dollar duration of a
  • Evaluate the limitations of duration and explain how convexity addresses some of
  • Calculate the change in a bond’s price given its duration, its convexity, and a change in interest
  • Derive forward interest rates from a set of spot
  • Derive the value of the cash flows from a forward rate agreement (FRA).
  • Calculate zero-coupon rates using the bootstrap
  • Compare and contrast the major theories of the term structure of interest rates.

Chapter 17. Corporate Bonds

After completing this reading, you should be able to:

  • Describe features of bond trading and explain the behavior of bond
  • Describe a bond indenture and explain the role of the corporate trustee in a bond
  • Define high-yield bonds and describe types of high-yield bond issuers and some of the payment features unique to high-yield
  • Differentiate between credit default risk and credit spread
  • Describe event risk and explain what may cause it to manifest in corporate
  • Describe the different classifications of bonds characterized by issuer, maturity, interest rate, and
  • Describe the mechanisms by which corporate bonds can be retired before maturity.
  • Define recovery rate and default rate, and differentiate between an issue default rate and a dollar default
  • Evaluate the expected return from a bond investment and identify the components of the bond’s expected return.

Chapter 18. Mortgages and Mortgage-Backed Securities

After completing this reading, you should be able to:

  • Describe the various types of residential mortgage
  • Calculate a fixed-rate mortgage payment and its principal and interest
  • Describe the mortgage prepayment option and the factors that influence
  • Summarize the securitization process of mortgage-backed securities (MBS), particularly the formation of mortgage pools, including specific pools and to-be-announceds (TBAs).
  • Calculate the weighted average coupon, weighted average maturity, single monthly mortality rate (SMM), and conditional prepayment rate (CPR) for a mortgage
  • Describe the process of trading pass-through agency
  • Explain the mechanics of different types of agency MBS products, including collateralized mortgage obligations (CMOs), interest-only securities (IOs), and principal-only securities (POs).
  • Describe a dollar roll transaction and how to value a dollar
  • Explain prepayment modeling and its four components: refinancing, turnover, defaults, and
  • Describe the steps in valuing an MBS using Monte Carlo
  • Define Option Adjusted Spread (OAS) and explain its challenges and its uses.

Chapter 19. Interest Rate Futures

After completing this reading, you should be able to:

  • Identify the most commonly used day count conventions, describe the markets that each one is typically used in, and apply each to an interest
  • Calculate the conversion of a discount rate to a price for a US Treasury
  • Differentiate between the clean and dirty price for a US Treasury bond; calculate the accrued interest and dirty price on a US Treasury
  • Explain and calculate a US Treasury bond futures contract conversion
  • Calculate the cost of delivering a bond into a Treasury bond futures
  • Describe the impact of the level and shape of the yield curve on the cheapest-to-deliver Treasury bond
  • Calculate the theoretical futures price for a Treasury bond futures
  • Calculate the final contract price on a Eurodollar futures contract and compare Eurodollar futures to
  • Describe and compute the Eurodollar futures contract convexity
  • Explain how Eurodollar futures can be used to extend the LIBOR zero
  • Calculate the duration-based hedge ratio and create a duration-based hedging strategy using interest rate futures.

Chapter 20. Swaps

After completing this reading, you should be able to:

  • Explain the mechanics of a plain vanilla interest rate swap and compute its cash
  • 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
  • Describe the role of the confirmation in a swap
  • Describe the comparative advantage argument for the existence of interest rate swaps and evaluate some of the criticisms of this
  • Explain how the discount rates in a plain vanilla interest rate swap are
  • Calculate the value of a plain vanilla interest rate swap based on two simultaneous bond
  • Calculate the value of a plain vanilla interest rate swap from a sequence of
  • Explain the mechanics of a currency swap and compute its cash
  • 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
  • Calculate the value of a currency swap based on a sequence of forward exchange
  • Identify and describe other types of swaps, including commodity, volatility, credit default, and exotic
  • Describe the credit risk exposure in a swap position.
  • Explain the limitations of using a duration-based hedging strategy.

Chapter 1. Measures of Financial Risk

After completing this reading, you should be able to:

  • Describe the mean-variance framework and the efficient
  • Explain the limitations of the mean-variance framework with respect to assumptions about return
  • Compare the normal distribution with the typical distribution of returns of risky financial assets such as
  • Define the VaR measure of risk, describe assumptions about return distributions and holding periods, and explain the limitations of
  • Explain and calculate ES and compare and contrast VaR and
  • Define the properties of a coherent risk measure and explain the meaning of each
  • Explain why VaR is not a coherent risk measure.

Chapter 2. Calculating and Applying VaR

After completing this reading, you should be able to:

  • Explain and give examples of linear and non-linear
  • Describe and calculate VaR for linear
  • Describe and explain the historical simulation approach for computing VaR and
  • Describe the delta-normal approach for calculating VaR for non-linear
  • Describe the limitations of the delta-normal
  • Explain the structured Monte Carlo method for computing VaR and identify its strengths and
  • Describe the implications of correlation breakdown for scenario
  • Describe worst-case scenario (WCS) analysis and compare WCS to VaR.

Chapter 3. Measuring and Monitoring Volatility

After completing this reading, you should be able to:

  • Explain how asset return distributions tend to deviate from the normal
  • Explain reasons for fat tails in a return distribution and describe their
  • Distinguish between conditional and unconditional
  • Describe the implications of regime switching on quantifying
  • Compare and contrast different parametric and non-parametric approaches for estimating conditional
  • Calculate conditional volatility using parametric and non-parametric
  • Evaluate implied volatility as a predictor of future volatility and its
  • Apply the exponentially weighted moving average (EWMA) approach and the GARCH (1,1) model to estimate
  • Explain and apply approaches to estimate long horizon volatility/VaR and describe the process of mean reversion according to a GARCH (1,1) model.
  • Calculate conditional volatility with and without mean
  • Describe the impact of mean reversion on long horizon conditional volatility
  • Describe an example of updating correlation estimation.

Chapter 4. External and Internal Credit Ratings

After completing this reading, you should be able to:

  • Describe external rating scales, the rating process, and the link between ratings and
  • Describe the impact of time horizon, economic cycle, industry, and geography on external
  • Define and use the hazard rate to calculate the unconditional default probability of a credit
  • Define recovery rate and calculate the expected loss from a
  • Explain and compare the through-the-cycle and point-in-time internal ratings
  • Describe alternative methods to credit ratings produced by rating
  • Compare external and internal ratings
  • Describe and interpret a ratings transition matrix and explain its
  • Describe the relationships between changes in credit ratings and changes in stock prices, bond prices, and credit default swap
  • Explain historical failures and potential challenges to the use of credit ratings in making investment decisions.

Chapter 5. Country Risk: Determinants, Measures, and Implications

After completing this reading, you should be able to:

  • Identify sources of country
  • Explain how a country’s position in the economic growth life cycle, political risk, legal risk, and economic structure affects its risk exposure.
  • Evaluate composite measures of risk that incorporate all major types of country
  • Compare instances of sovereign default in both foreign currency debt and local currency debt and explain common causes of sovereign
  • Describe the consequences of sovereign default.
  • Describe factors that influence the level of sovereign default risk; explain and assess how rating agencies measure sovereign default
  • Describe the characteristics of sovereign credit spreads and sovereign credit default swaps (CDS) and compare the use of sovereign spreads to credit ratings.

Chapter 6. Measuring Credit Risk

After completing this reading, you should be able to:

  • Evaluate a bank’s economic capital relative to its level of credit
  • Explain the distinctions between economic capital and regulatory capital and describe how economic capital is
  • Identify and describe important factors used to calculate economic capital for credit risk: probability of default, exposure, and loss
  • Define and calculate expected loss (EL).
  • Define and explain unexpected loss (UL).
  • Estimate the mean and standard deviation of credit losses assuming a binomial
  • Describe the Gaussian copula model and its
  • Describe and apply the Vasicek model to estimate default rate and credit risk capital for a
  • Describe the CreditMetrics model and explain how it is applied in estimating economic
  • Describe and use the Euler’s theorem to determine the contribution of a loan to the overall risk of a
  • Explain why it is more difficult to calculate credit risk capital for derivatives than for
  • Describe challenges to quantifying credit risk.

Chapter 7. Operational Risk

After completing this reading, you should be able to:

  • Describe the different categories of operational risk and explain how each type of risk can
  • Compare the basic indicator approach, the standardized approach, and the advanced measurement approach for calculating operational risk regulatory
  • Describe the standardized measurement approach and explain the reasons for its introduction by the Basel
  • Explain how a loss distribution is derived from an appropriate loss frequency distribution and loss severity distribution using Monte Carlo
  • Describe the common data issues that can introduce inaccuracies and biases in the estimation of loss frequency and severity
  • Describe how to use scenario analysis in instances when data are
  • Describe how to identify causal relationships and how to use Risk and Control Self-assessment (RCSA), Key Risk Indicators (KRIs), and education to measure and manage operational
  • Describe the allocation of operational risk capital to business
  • Explain how to use the power law to measure operational
  • Explain how the moral hazard and adverse selection problems faced by insurance companies relate to insurance against operational risk.

Chapter 8. Stress Testing

After completing this reading, you should be able to:

  • Describe the rationale for the use of stress testing as a risk management
  • Explain key considerations and challenges related to stress testing, including choice of scenarios, regulatory specifications, model building, and reverse stress
  • Describe the relationship between stress testing and other risk measures, particularly in enterprise-wide stress
  • Describe stressed VaR and stressed ES and compare the process of determining stressed VaR and ES to that of traditional VaR and
  • Identify the advantages and disadvantages of stressed risk
  • Describe the responsibilities of the board of directors, senior management, and the internal audit function in stress testing governance
  • Identify elements of clear and comprehensive policies, procedures, and documentations for stress
  • Identify areas of validation and independent review for stress tests that require attention from a governance
  • Describe the Basel stress testing principles for banks regarding the implementation of stress testing.

Chapter 9. Pricing Conventions, Discounting, and Arbitrage

After completing this reading, you should be able to:

  • Define discount factor and use a discount function to compute present and future
  • Define the “law of one price,” explain it using an arbitrage argument, and describe how it can be applied to bond
  • Identify arbitrage opportunities for fixed income securities with certain cash
  • Identify the components of a US Treasury coupon bond and compare 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
  • Differentiate between “clean” and “dirty” bond pricing and explain the implications of accrued interest with respect to bond
  • Describe the common day-count conventions used in bond pricing.

Chapter 10. Interest Rates

After completing this reading, you should be able to:

  • Calculate and interpret the impact of different compounding frequencies on a bond’s
  • Define spot rate and compute discount factors given spot rates .
  • Interpret the forward rate and compute forward rates given spot
  • Define par rate and describe the equation for the par rate of a
  • Interpret the relationship between spot, forward, and par
  • Assess the impact of maturity on the price of a bond and the returns generated by
  • Define the “flattening” and “steepening” of rate curves and describe a trade to reflect expectations that a curve will flatten or
  • Describe a swap transaction and explain how a swap market defines par
  • Describe overnight indexed swaps (OIS) and distinguish OIS rates from LIBOR swap rates.

Chapter 11. Bond Yields and Return Calculations

After completing this reading, you should be able to:

  • Distinguish between gross and net realized returns and calculate the realized return for a bond over a holding period including
  • 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
  • Compute a bond’s YTM given a bond structure and
  • Calculate the price of an annuity and a
  • Explain the relationship between spot rates and
  • Define the coupon effect and explain the relationship between coupon rate, YTM, and bond
  • Explain the decomposition of the profit and loss (P&L) for a bond position or portfolio into separate factors including carry roll-down, rate change, and spread change
  • Explain the following four common assumptions in carry roll-down scenarios: realized forwards, unchanged term structure, unchanged yields, and realized expectations of short-term rates; and calculate carry roll down under these assumptions.

Chapter 12. Applying Duration, Convexity, and DV01

After completing this reading, you should be able to:

  • Describe a one-factor interest rate model and identify common examples of interest rate
  • Define and compute the DV01 of a fixed income security given a change in yield and the resulting change in
  • 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
  • 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
  • Explain the process of calculating the effective duration and convexity of a portfolio of fixed income
  • Describe an example of hedging based on effective duration and
  • 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 portfolio.

Chapter 13. Modeling Non-Parallel Term Structure Shifts and Hedging 

After completing this reading, you should be able to:

  • Describe principal components analysis and explain its use in understanding term structure
  • Define key rate exposures and know the characteristics of key rate exposure factors, including partial ‘01s and forward-bucket ‘01s.
  • Describe key-rate shift
  • Define, calculate, and interpret key rate ‘01 and key rate duration.
  • Compute the positions in hedging instruments necessary to hedge the key rate risks of a
  • Relate key rates, partial ‘01s, and forward-bucket ‘01s and calculate the forward-bucket ‘01 for a shift in rates in one or more
  • Apply key rate and multi-factor analysis to estimating portfolio volatility.

Chapter 14. Binomial Trees

After completing this reading, you should be able to:

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

Chapter 15. The Black-Scholes-Merton Model

After completing this reading, you should be able to:

  • Explain the lognormal property of stock prices, the distribution of rates of return, and the calculation of expected
  • Compute the realized return and historical volatility of a
  • Describe the assumptions underlying the Black-Scholes-Merton option pricing
  • Compute the value of a European option on a non-dividend-paying stock using the Black-Scholes- Merton
  • Define implied volatilities and describe how to compute implied volatilities from market prices of options using the Black-Scholes-Merton
  • Explain how dividends affect the decision to exercise early for American call and put
  • Compute the value of a European option using the Black-Scholes-Merton model on a dividend-paying stock, futures, and exchange rates.
  • Describe warrants, calculate the value of a warrant, and calculate the dilution cost of the warrant to existing shareholders.

Chapter 16. Option Sensitivity Measures: The “Greeks”

After completing this reading, you should be able to:

  • Describe and assess the risks associated with naked and covered option
  • Describe the use of a stop loss hedging strategy, including its advantages and disadvantages, and explain how this strategy can generate naked and covered option
  • Describe delta hedging for options as well as for forward and futures
  • Compute the delta of an
  • Describe the dynamic aspects of delta hedging and distinguish between dynamic hedging and hedge-and- forget
  • Define and calculate the delta of a
  • Define and describe theta, gamma, vega, and rho for option positions and calculate the gamma and vega for a
  • Explain how to implement and maintain a delta-neutral and a gamma-neutral
  • Describe the relationship between delta, theta, gamma, and
  • Describe how portfolio insurance can be created through option instruments and stock index futures.

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