## 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.