### Got any Questions Query Inquisition

#### LOS

- Foundations of Risk Management
- Quantitative Analysis
- Financial Markets and Products
- Valuation and Risk Models

**a.** Distinguish between expected loss and unexpected loss and provide examples of each.

**b.** Evaluate, compare and apply tools and procedures used to measure and manage risk, including quantitative measures, qualitative risk assessment techniques, and enterprise risk management.

**c. **Distinguish between expected loss and unexpected loss and provide examples of each.

**d.** Interpret the relationship between risk and reward, and explain how conflicts of interest can impact risk management.

**e.** 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 organization.

**f.** Explain how risk factors can interact with each other and describe challenges in aggregating risk exposures.

**a.** Compare different strategies a firm can use to manage its risk exposures and explain situations in which a firm would want to use each strategy.

**b.** Explain the relationship between risk appetite and a firm’s risk management decisions.

**c.** Evaluate some advantages and disadvantages of hedging risk exposures, and explain challenges that can arise when implementing a hedging strategy.

**d. **Apply appropriate methods to hedge operational and financial risks, including pricing, foreign currency, and interest rate risk.

**e. **Assess the impact of risk management tools and instruments, including risk limits and derivatives.

**a. **Explain changes in regulations and corporate risk governance that occurred as a result of the 2007-2009 financial crisis.

**b. **Describe best practices for the governance of a firm’s risk management processes.

**c. **Explain the risk management roles and responsibilities of a firm’s board of directors.

**d. **Evaluate the relationship between a firm’s risk appetite and its business strategy, including the role of incentives.

**e. **Illustrate the interdependence of functional units within a firm as it relates to risk management.

**f. **Assess the role and responsibilities of a firm’s audit committee.

**a. **Compare different types of credit derivatives, explain their applications, and describe their advantages.

**b. **Explain different traditional approaches or mechanisms that firms can use to help mitigate credit risk.

**c. **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 crisis.

**d. **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.

**a. **Explain MPT and interpret the Markowitz efficient frontier.

**b. **Understand the derivation and components of the CAPM.

**c. **Describe the assumptions underlying the CAPM.

**d. **Interpret and compare the capital market line and the security market line.

**e. **Apply the CAPM in calculating the expected return on an asset.

**f. **Interpret beta and calculate the beta of a single asset or portfolio.

**g. **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 Sorting ratio.

**a.** Explain the Arbitrage Pricing Theory (APT), describe its assumptions, and compare the APT to the CAPM.

**b.** Describe the inputs (including factor betas) to a multifactor model and explain the challenges of using multifactor models in hedging.

**c.** Calculate the expected return of an asset using a single-factor and a multifactor model.

**d.** Explain how to construct a portfolio to hedge exposure to multiple factors.

**e.** Describe and apply the Fama-French three-factor model in estimating asset returns.

**a.** Explain the potential benefits of having effective risk data aggregation and reporting.

**b.** Explain challenges to the implementation of a strong risk data aggregation and reporting process and the potential impacts of using poor quality data.

**c.** Describe key governance principles related to risk data aggregation and risk reporting.

**d.** Describe characteristics of effective data architecture, IT infrastructure, and risk-reporting practices.

**a.** Describe ERM and compare an ERM program with a traditional silo-based risk management program.

**b.** Describe the motivations for a firm to adopt an ERM initiative.

**c.** Explain best practices for the governance and implementation of an ERM program.

**d.** 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 firm.

**e.** Explain the role of scenario analysis in the implementation of an ERM program and describe its

advantages and disadvantages.

**f.** Explain the use of scenario analysis in stress testing programs and capital planning.

**a.** Analyze the key factors that led to and derive the lessons learned from case studies involving the following risk factors.

**b.** Interest rate risk, including the 1980s savings and loan crisis in the U.S.

**c.** Funding liquidity risk, including Lehman Brothers, Continental Illinois, and Northern Rock.

**d.** Implementing hedging strategies, including the Metallgesellschaft case.

**e.** Model risk, including the Niederhoffer case, Long Term Capital Management, and the London Whale case.

**f.** Rogue trading and misleading reporting, including the Barings case.

**g.** Financial engineering and complex derivatives, including Bankers Trust, the Orange County case, and Sachsen Landesbank.

**h.** Reputational risk, including the Volkswagen case.

**i.** Corporate governance, including the Enron case.

**j.** Cyber risk, including the SWIFT case.

**a.** Describe the historical background and provide an overview of the 2007-2009 financial crisis.

**b.** Describe the build-up to the financial crisis and the factors that played an important role.

**c.** Explain the role of subprime mortgages and collateralized debt obligations (CDOs) in the crisis.

**d.** Compare the roles of different types of institutions in the financial crisis, including banks, financial

intermediaries, mortgage brokers and lenders, and rating agencies.

**e.** Describe trends in the short-term wholesale funding markets that contributed to the financial crisis, including their impact on systemic risk.

**f.** Describe responses made by central banks in response to the crisis.

**a.** Describe the responsibility of each GARP Member with respect to professional integrity, ethical conduct, conflicts of interest, confidentiality of information, and adherence to generally accepted practices in risk management.

**b.** Describe the potential consequences of violating the GARP Code of Conduct.

**a.** Describe an event and an event space.

**b.** Describe independent events and mutually exclusive events.

**c.** Explain the difference between independent events and conditionally independent events.

**d.** Calculate the probability of an event for a discrete probability function.

**e.** Define and calculate a conditional probability.

**f.** Distinguish between conditional and unconditional probabilities.

**g.** Explain and apply Bayes’ rule.

**a.** Describe and distinguish a probability mass function from a cumulative distribution function, and explain the relationship between these two.

**b.** Understand and apply the concept of a mathematical expectation of a random variable.

**c.** Describe the four common population moments.

**d.** Explain the differences between a probability mass function and a probability density function.

**e.** Characterize the quantile function and quantile-based estimators.

**f.** Explain the effect of a linear transformation of a random variable on the mean, variance, standard deviation, skewness, kurtosis, median and interquartile range.

**a.** 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.

**b.** Describe a mixture distribution and explain the creation and characteristics of mixture distributions.

**a.** Explain how a probability matrix can be used to express a probability mass function.

**b.** Compute the marginal and conditional distributions of a discrete bivariate random variable.

**c.** Explain how the expectation of a function is computed for a bivariate discrete random variable.

**d.** Define covariance and explain what it measures.

**e.** Explain the relationship between the covariance and correlation of two random variables, and how these are related to the independence of the two variables.

**f.** Explain the effects of applying linear transformations on the covariance and correlation between two random variables.

**g.** Compute the variance of a weighted sum of two random variables.

**h.** Compute the conditional expectation of a component of a bivariate random variable.

**i.** Describe the features of an independent and identically distributed (iid) sequence of random variables.

**j.** Explain how the iid property is helpful in computing the mean and variance of a sum of iid random variables.

**a.** Estimate the mean, variance, and standard deviation using sample data.

**b.** Explain the difference between a population moment and a sample moment.

**c.** Distinguish between an estimator and an estimate.

**d.** Describe the bias of an estimator and explain what the bias measures.

**e.** Explain what is meant by the statement that the mean estimator is BLUE.

**f.** Describe the consistency of an estimator and explain the usefulness of this concept.

**g.** Explain how the Law of Large Numbers (LLN) and Central Limit Theorem (CLT) apply to the sample mean.

**h.** Estimate and interpret the skewness and kurtosis of a random variable.

**i.** Use sample data to estimate quantiles, including the median.

**j.** Estimate the mean of two variables and apply the CLT.

**k.** Estimate the covariance and correlation between two random variables.

**l.** Explain how coskewness and cokurtosis are related to skewness and kurtosis.

**a.** Construct an appropriate null hypothesis and alternative hypothesis, and distinguish between the two.

**b.** Differentiate between a one-sided and a two-sided test and identify when to use each test.

**c.** Explain the difference between Type I and Type II errors and how these relate to the size and power of a test.

**d.** Understand how a hypothesis test and a confidence interval are related.

**e.** Explain what the p-value of a hypothesis test measures.

**f.** Construct and apply confidence intervals for one-sided and two-sided hypothesis tests, and interpret the results of hypothesis tests with a specific confidence level.

**g.** Identify the steps to test a hypothesis about the difference between two population means.

**h.** Explain the problem of multiple testing and how it can lead to biased results.

**a.** Describe the models which can be estimated using linear regression and differentiate them from those which cannot.

**b.** Interpret the results of an ordinary least squares (OLS) regression with a single explanatory variable.

**c.** Describe the key assumptions of OLS parameter estimation.

**d.** Characterize the properties of OLS estimators and their sampling distributions.

**e.** Construct, apply, and interpret hypothesis tests and confidence intervals for a single regression coefficient in a regression.

**f.** Explain the steps needed to perform a hypothesis test in a linear regression.

**g.** Describe the relationship among a t-statistic, its p-value, and a confidence interval.

**a.** Distinguish between the relative assumptions of single and multiple regression.

**b.** Interpret regression coefficients in a multiple regression.

** c.** Interpret goodness-of-fit measures for single and multiple regressions, including R2 and adjusted-R2.

**d.** Construct, apply, and interpret joint hypothesis tests and confidence intervals for multiple coefficients in a regression.

**a.** Explain how to test whether a regression is affected by heteroskedasticity.

**b.** Describe approaches to using heteroskedastic data.

**c.** Characterize multicollinearity and its consequences; distinguish between multicollinearity and perfect collinearity.

**d.** Describe the consequences of excluding a relevant explanatory variable from a model and contrast those with the consequences of including an irrelevant regressor.

**e.** Explain two model selection procedures and how these relate to the bias-variance trade off.

**f.** Describe the various methods of visualizing residuals and their relative strengths.

**g.** Describe methods for identifying outliers and their impact.

**h.** Determine the conditions under which OLS is the best linear unbiased estimator.

**a.** Describe the requirements for a series to be covariance stationary.

**b.** Define the autocovariance function and the autocorrelation function.

**c.** Define white noise, and describe independent white noise and normal (Gaussian) white noise.

**d.** Define and describe the properties of autoregressive (AR) processes.

**e.** Define and describe the properties of moving average (MA) processes.

**f.** Explain how a lag operator works.

**g.** Explain mean reversion and calculate a mean-reverting level.

**h.** Define and describe the properties of autoregressive moving average (ARMA) processes.

**i.** Describe the application of AR, MA, and ARMA processes.

**j.** Describe sample autocorrelation and partial autocorrelation.

**k.** Describe the Box-Pierce Q statistic and the Ljung-Box Q statistic.

**l.** Explain how forecasts are generated from ARMA models.

**m.** Describe the role of mean reversion in long-horizon forecasts.

**n.** Explain how seasonality is modeled in a covariance-stationary ARMA.

**a.** Describe linear and nonlinear time trends.

**b.** Explain how to use regression analysis to model seasonality.

**c.** Describe a random walk and a unit root.

**d.** Explain the challenges of modeling time series containing unit roots.

**e.** Describe how to test if a time series contains a unit root.

**f.** Explain how to construct an h-step-ahead point forecast for a time series with seasonality.

**g.** Calculate the estimated trend value and form an interval forecast for a time series.

**a.** Calculate, distinguish, and convert between simple and continuously compounded returns.

**b.** Define and distinguish between volatility, variance rate, and implied volatility.

**c.** Describe how the first two moments may be insufficient to describe non-normal distributions.

**d.** Explain how the Jarque-Bera test is used to determine whether returns are normally distributed.

**e.** Describe the power law and its use for non-normal distributions.

**f.** Define correlation and covariance and differentiate between correlation and dependence.

**g.** Describe properties of correlations between normally distributed variables when using a one-factor model.

**a.** Describe the basic steps to conduct a Monte Carlo simulation.

**b.** Describe ways to reduce Monte Carlo sampling error.

**c.** Explain the use of antithetic and control variates in reducing Monte Carlo sampling error.

**d.** Describe the bootstrapping method and its advantage over Monte Carlo simulation.

**e.** Describe pseudo-random number generation.

**f.** Describe situations where the bootstrapping method is ineffective.

**g.** Describe the disadvantages of the simulation approach to financial problem-solving.

**a.** Identify the major risks faced by banks and explain ways in which these risks can arise.

**b.** Distinguish between economic capital and regulatory capital.

**c.** Summarize the Basel Committee regulations for regulatory capital and their motivations.

**d.** Explain how deposit insurance gives rise to a moral hazard problem.

**e.** Describe investment banking financing arrangements including private placement, public offering, best efforts, firm commitment, and Dutch auction approaches.

**f.** 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 problems.

**g.** Describe the distinctions between the banking book and the trading book of a bank.

**h.** Explain the originate-to-distribute banking model and discuss its benefits and drawbacks.

**a.** Describe the key features of the various categories of insurance companies and identify the risks facing insurance companies.

**b.** Describe the use of mortality tables and calculate the premium payment for a policy holder.

**c.** Distinguish between mortality risk and longevity risk and describe how to hedge these risks.

**d.** Describe defined benefit plans and defined contribution plans and explain the differences between them.

**e.** Compare the various types of life insurance policies.

**f.** Calculate and interpret loss ratio, expense ratio, combined ratio, and operating ratio for a property-casualty insurance company.

**g.** Describe moral hazard and adverse selection risks facing insurance companies, provide examples of each, and describe how to overcome these problems.

**h.** Evaluate the capital requirements for life insurance and property-casualty insurance companies.

**i.** Compare the guaranty system and the regulatory requirements for insurance companies with those for banks.

**a.** Differentiate among open-end mutual funds, closed-end mutual funds, and exchange-traded funds (ETFs).

**b.** Identify and describe potential undesirable trading behaviors at mutual funds.

**c.** Explain the concept of net asset value (NAV) of an open-end mutual fund and how it relates to share price.

**d.** Explain the key differences between hedge funds and mutual funds.

**e.** 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 clawback.

**f.** 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 funds.

**g.** Describe characteristics of mutual fund and hedge fund performance and explain the effect of measurement biases on performance measurement.

**a.** Define derivatives, describe the features and uses of derivatives, and compare linear and nonlinear derivatives.

**b.** Describe the specifics of exchange-traded and over-the-counter markets, and evaluate the advantages and disadvantages of each.

**c.** Differentiate between options, forwards, and futures contracts.

**d.** Identify and calculate option and forward contract payoffs.

**e.** Differentiate among the broad categories of traders: hedgers, speculators, and arbitrageurs.

**f.** Calculate and compare the payoffs from hedging strategies involving forward contracts and options.

**g.** Calculate and compare the payoffs from speculative strategies involving futures and options.

**h.** Describe arbitrageurs’ strategy and calculate an arbitrage payoff.

**i.** Describe some of the risks that can arise from the use of derivatives.

**a.** Describe how exchanges can be used to alleviate counterparty risk.

**b.** Explain the developments in clearing that reduce risk.

**c.** Define netting and describe a netting process.

**d.** Describe the implementation of a margining process; by central counterparty (CCP); explain the determinants of and calculate initial and variation margin requirements.

**e.** Describe process of buying stock on margin without using CCP and calculate margin requirements.

**f.** Compare exchange-traded and OTC markets and describe their uses.

**g.** Identify risks associated with OTC markets and explain how these risks can be mitigated.

**h.** Describe the role of collateralization in the OTC market and compare it to the margining system.

**i.** Explain the use of special purpose vehicles (SPVs) in the OTC derivatives market.

**a.** Provide examples of the mechanics of a CCP.

**b.** Describe the role of CCPs and distinguish between bilateral and centralized clearing.

**c.** Describe advantages and disadvantages of central clearing of OTC derivatives.

**d.** Explain regulatory initiatives for the OTC derivatives market and their impact on central clearing.

**e.** Compare margin requirements in centrally cleared and bilateral markets, and explain how margin can mitigate risk.

**f.** Compare netting in bilateral markets vs centrally cleared.

**g.** Assess the impact of central clearing on the broader financial markets.

**h.** Identify and explain the types of risks faced by CCPs.

**i.** Identify and distinguish between the risks to clearing members and to non-members.

**a.** 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 limits.

**b.** Explain the convergence of futures and spot prices.

**c.** Describe the role of an exchange in futures transactions.

**d.** Explain the differences between a normal and inverted futures market.

**e.** Describe the mechanics of the delivery process and contrast it with cash settlement.

**f.** Describe and compare different trading order types.

**g.** Describe the application of marking to market and hedge accounting for futures.

**h.** Compare and contrast forward and futures contracts.

**a.** Define and differentiate between short and long hedges and identify their appropriate uses.

**b.** Describe the arguments for and against hedging and the potential impact of hedging on firm profitability.

**c.** Define and calculate the basis, discuss various sources of basis risk, and explain how basis risks arise when hedging with futures.

**d.** Define cross hedging and compute and interpret hedge ratio and hedge effectiveness.

**e.** Calculate the profit and loss on a short or long hedge.

**f.** Compute the optimal number of futures contracts needed to hedge an exposure and explain, and calculate the “tailing the hedge” adjustment.

**g.** Explain how to use stock index futures contracts to change a stock portfolio’s beta.

**h.** 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.

**a.** Explain and describe the mechanics of spot quotes, forward quotes, and futures quotes in the foreign exchange markets; distinguish between bid and ask exchange rates.

**b.** 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 quotes.

**c.** Compare outright (forward) and swap transactions.

**d.** Define, compare, and contrast transaction risk, translation risk, and economic risk.

**e.** Describe examples of transaction, translation, and economic risks and explain how to hedge these risks.

**f.** Describe the rationale for multi-currency hedging using options.

**g.** Identify and explain the factors that determine exchange rates.

**h.** Calculate and explain the effect of an appreciation/depreciation of one currency relative to another.

**i.** Explain the purchasing power parity theorem and use this theorem to calculate the appreciation or depreciation of a foreign currency.

**j.** Describe the relationship between nominal and real interest rates.

**k.** Describe how a non-arbitrage assumption in the foreign exchange markets leads to the interest rate parity theorem and use this theorem to calculate forward foreign exchange rates.

**l.** Distinguish between covered and uncovered interest rate parity conditions.

**a.** Define and describe financial assets.

**b.** Define short-selling and calculate the net profit of a short sale of a dividend-paying stock.

**c.** Describe the differences between forward and futures contracts and explain the relationship between forward and spot prices.

**d.** Calculate the forward price given the underlying asset’s spot price and describe an arbitrage argument between spot and forward prices.

**e.** Distinguish between the forward price and the value of a forward contract.

**f.** Calculate the value of a forward contract on a financial asset that does or does not provide income or yield.

**g.** Explain the relationship between forward and futures prices.

**h.** Calculate the value of a stock index futures contract and explain the concept of index arbitrage.

**a.** Explain the key differences between commodities and financial assets.

**b.** Define and apply commodity concepts such as storage costs, carry markets, lease rate, and convenience yield.

**c.** Identify factors that impact prices on agricultural commodities, metals, energy, and weather derivatives.

**d.** Explain the formula for pricing commodity forwards.

**e.** Describe an arbitrage transaction in commodity forwards and compute the potential arbitrage profit.

**f.** Define the lease rate and explain how it determines the no-arbitrage values for commodity forwards and futures.

**g.** Describe the cost of carry model and determine the impact of storage costs and convenience yields on commodity forward prices and no-arbitrage bounds.

**h.** Compute the forward price of a commodity with storage costs.

**i.** Explain how to create a synthetic commodity position and use it to explain the relationship between the forward price and the expected future spot price.

**j.** Explain the impact of systematic and nonsystematic risk on current futures prices and expected future spot prices.

**k.** Define and interpret normal backwardation and contango.

**a.** Describe the various types and uses of options; define moneyness.

**b.** Explain the payoff function and calculate the profit and loss from an options position.

**c.** Explain the specification of exchange-traded stock option contracts, including that of nonstandard products.

**d.** Explain how dividends and stock splits can impact the terms of a stock option.

**e.** Describe the application of commissions, margin requirements, and exercise procedures to exchange-traded options and explain the trading characteristics of these options.

**f.** Define and describe warrants, convertible bonds, and employee stock options.

**a.** Identify the six factors that affect an option’s price.

**b.** Identify and compute upper and lower bounds for option prices on non-dividend and dividend paying stocks.

**c.** 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 prices.

**d.** Explain and assess potential rationales for using the early exercise features of American call and put options.

**a.** Explain the motivation to initiate a covered call or a protective put strategy.

**b.** Describe principal protected notes (PPNs) and explain necessary conditions to create a PPN.

**c.** Describe the use and calculate the payoffs of various spread strategies.

**d.** Describe the use and explain the payoff functions of combination strategies.

**a.** Define and contrast exotic derivatives and plain vanilla derivatives.

**b.** Describe some of the reasons that drive the development of exotic derivative products.

**c.** Explain how any derivative can be converted into a zero-cost product.

** **Describe how standard American options can be transformed into nonstandard American options.

**e.** 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 options.

**f.** Describe and contrast volatility and variance swaps.

**g.** Explain the basic premise of static option replication and how it can be applied to hedging exotic options.

**a.** Describe Treasury rates, LIBOR, Secured Overnight Financing Rate (SOFR), and repo rates, and explain what is meant by the “risk-free” rate.

**b.** Calculate the value of an investment using different compounding frequencies.

**c.** Convert interest rates based on different compounding frequencies.

**d.** Calculate the theoretical price of a bond using spot rates.

**e.** Calculate the Macaulay duration, modified duration, and dollar duration of a bond.

**f.** Evaluate the limitations of duration and explain how convexity addresses some of them.

**g.** Calculate the change in a bond’s price given its duration, its convexity, and a change in interest rates.

**h.** Derive forward interest rates from a set of spot rates.

**i.** Derive the value of the cash flows from a forward rate agreement (FRA).

**j.** Calculate zero-coupon rates using the bootstrap method.

**k.** Compare and contrast the major theories of the term structure of interest rates.

**a.** Describe features of bond trading and explain the behavior of bond yield.

**b.** Describe a bond indenture and explain the role of the corporate trustee in a bond indenture.

**c.** Define high-yield bonds and describe types of high-yield bond issuers and some of the payment features unique to high-yield bonds.

**d.** Differentiate between credit default risk and credit spread risk.

**e.** Describe event risk and explain what may cause it to manifest in corporate bonds.

**f.** Describe different characteristics of bonds such as issuer, maturity, interest rate, and collateral.

**g.** Describe the mechanisms by which corporate bonds can be retired before maturity.

**h.** Define recovery rate and default rate, and differentiate between an issue default rate and a dollar default rate.

**i.** Evaluate the expected return from a bond investment and identify the components of the bond’s expected return.

**a.** Describe the various types of residential mortgage products.

**b.** Calculate a fixed-rate mortgage payment and its principal and interest components.

**c.** Summarize the securitization process of mortgage-backed securities (MBS), particularly the formation of mortgage pools, including specific pools and to-be-announceds (TBAs).

**d.** Calculate the weighted average coupon, weighted average maturity, single monthly mortality rate (SMM), and conditional prepayment rate (CPR) for a mortgage pool.

**e.** Describe the process of trading pass-through agency MBS.

**f.** Explain the mechanics of different types of agency MBS products, including collateralized mortgage obligations (CMOs), interest-only securities (IOs), and principal-only securities (POs).

**g.** Describe a dollar roll transaction and how to value a dollar roll.

**h.** Describe the mortgage prepayment option and factors that affect it; explain prepayment modeling and its four components: refinancing, turnover, defaults, and curtailments.

**i.** Describe the steps in valuing an MBS using Monte Carlo simulation.

**j.** Define Option-Adjusted Spread (OAS) and explain its challenges and its uses.

**a.** Identify the most commonly used day count conventions, describe the markets that each one is typically used in, and apply each to an interest calculation.

**b.** Calculate the conversion of a discount rate to a price for a U.S. Treasury bill.

**c.** Differentiate between the clean and dirty price for a U.S. Treasury bond; calculate the accrued interest and dirty price on a US Treasury bond.

**d.** Explain and calculate a US Treasury bond futures contract conversion factor.

**e.** Calculate the cost of delivering a bond into a Treasury bond futures contract.

**f.** Describe the impact of the level and shape of the yield curve on the cheapest-to-deliver Treasury bond decision.

**g.** Calculate the theoretical futures price for a Treasury bond futures contract.

**h.** Calculate the final contract price on a Eurodollar futures contract and compare Eurodollar futures to FRAs.

**i.** Describe and compute the Eurodollar futures contract convexity adjustment.

**j.** Calculate the duration-based hedge ratio and create a duration-based hedging strategy using interest rate futures.

**k.** Explain the limitations of using a duration-based hedging strategy.

**a.** Explain the mechanics of a plain vanilla interest rate swap and compute its cash flows.

**b.** Explain how a plain vanilla interest rate swap can be used to transform an asset or a liability and calculate the resulting cash flows.

**c.** Explain the role of financial intermediaries in the swaps market.

**d.** Describe the role of the confirmation in a swap transaction.

**e.** Describe the comparative advantage argument for the existence of interest rate swaps and evaluate some of the criticisms of this argument.

**f.** Explain how the discount rates in a plain vanilla interest rate swap are computed.

**g.** Calculate the value of a plain vanilla interest rate swap based on two simultaneous bond positions.

**h.** Calculate the value of a plain vanilla interest rate swap from a sequence of FRAs.

**i.** Explain the mechanics of a currency swap and compute its cash flows.

**j.** Explain how a currency swap can be used to transform an asset or liability and calculate the resulting cash flows.

**k.** Calculate the value of a currency swap based on two simultaneous bond positions.

**l.** Calculate the value of a currency swap based on a sequence of forward exchange rates.

**m.** Identify and describe other types of swaps, including commodity, volatility, credit default, and exotic swaps.

**n.** Describe the credit risk exposure in a swap position.

**a.** Describe the mean-variance framework and the efficient frontier.

**b.** Compare the normal distribution with the typical distribution of returns of risky financial assets such as equities.

**c.** Define the VaR measure of risk, describe assumptions about return distributions and holding periods, and explain the limitations of VaR.

**d.** Explain and calculate ES and compare and contrast VaR and ES.

**e.** Define the properties of a coherent risk measure and explain the meaning of each property.

**f.** Explain why VaR is not a coherent risk measure.

**a.** Explain and give examples of linear and non-linear portfolios.

**b.** Describe and explain the historical simulation approach for computing VaR and ES.

**c.** Describe the delta-normal approach and use it to calculate VaR for non-linear derivatives.

**d.** Describe and calculate VaR for linear derivatives.

**e.** Describe the limitations of the delta-normal method.

**f.** Explain the structured Monte Carlo method for computing VaR and identify its strengths and weaknesses.

**g.** Describe the implications of correlation breakdown for scenario analysis.

**h.** Describe worst-case scenario (WCS) analysis and compare WCS to VaR.

**a.** Explain how asset return distributions tend to deviate from the normal distribution.

**b.** Explain reasons for fat tails in a return distribution and describe their implications.

**c.** Distinguish between conditional and unconditional distributions, and describe the implications of regime switching on quantifying volatility.

**d.** Compare and contrast different approaches for estimating conditional volatility.

**e.** Apply the exponentially weighted moving average (EWMA) approach and the GARCH (1,1) model to estimate volatility, and describe alternative approaches to weighting historical return data.

**f.** Apply the GARCH (1,1) model to estimate volatility.

**g.** Explain and apply approaches to estimate long horizon volatility/VaR and describe the process of mean reversion according to a GARCH (1,1) model.

**h.** Evaluate implied volatility as a predictor of future volatility and its shortcomings.

**i.** Describe an example of updating correlation estimates.

**a.** Describe external rating scales, the rating process, and the link between ratings and default.

**b.** Define conditional and unconditional default probabilities and explain the distinction between the two.

**c.** Define and use the hazard rate to calculate the unconditional default probability of a credit asset.

**d.** Define recovery rate and calculate the expected loss from a loan.

**e.** Explain and compare the through-the-cycle and point-in-time internal ratings approaches.

**f.** Describe alternative methods to credit ratings produced by rating agencies.

**g.** Compare external and internal ratings approaches.

**h.** Describe and interpret a ratings transition matrix and explain its uses.

**i.** Describe the relationships between changes in credit ratings and changes in stock prices, bond prices, and credit default swap spreads.

**j. **Explain historical failures and potential challenges to the use of credit ratings in making investment decisions.

**a.** Explain how a country’s position in the economic growth life cycle, political risk, legal risk, and economic structure affects its risk exposure.

**b.** Evaluate composite measures of risk that incorporate all major types of country risk.

**c.** Compare instances of sovereign default in both foreign currency debt and local currency debt and explain common causes of sovereign defaults.

**d.** Describe the consequences of sovereign default.

**e.** Describe factors that influence the level of sovereign default risk; explain and assess how rating agencies measure sovereign default risks.

**f.** Describe the characteristics of sovereign credit spreads and sovereign credit default swaps (CDS) and compare the use of sovereign spreads to credit ratings.

**a.** Explain the distinctions between economic capital and regulatory capital and describe how economic capital is derived.

**b.** Describe the degree of dependence typically observed among the loan defaults in a bank’s loan portfolio, and explain the implications for the portfolio’s default rate.

**c.** Define and calculate expected loss (EL).

**d.** Define and explain unexpected loss (UL).

**e.** Estimate the mean and standard deviation of credit losses assuming a binomial distribution.

**f.** Describe the Gaussian copula model and its application.

**g.** Describe and apply the Vasicek model to estimate default rate and credit risk capital for a bank.

**h.** Describe the CreditMetrics model and explain how it is applied in estimating economic capital.

**i.** Describe and use Euler’s theorem to determine the contribution of a loan to the overall risk of a portfolio.

**j.** Explain why it is more difficult to calculate credit risk capital for derivatives than for loans.

**k.** Describe challenges to quantifying credit risk.

**a.** Describe the different categories of operational risk and explain how each type of risk can arise.

**b.** Compare the basic indicator approach, the standardized approach, and the advanced measurement approach for calculating operational risk regulatory capital.

**c.** Describe the standardized measurement approach and explain the reasons for its introduction by the Basel Committee.

**d.** Explain how a loss distribution is derived from an appropriate loss frequency distribution and loss severity distribution using Monte Carlo simulation.

**e.** Describe the common data issues that can introduce inaccuracies and biases in the estimation of loss frequency and severity distributions.

**f.** Describe how to use scenario analysis in instances when data are scarce.

**g.** Describe how to identify causal relationships and how to use Risk and Control Self-assessment (RCSA), Key Risk Indicators (KRIs), and education to understand and manage operational risks.

**h.** Describe the allocation of operational risk capital to business units.

**i.** Explain how to use the power law to measure operational risk.

**j.** Explain how the moral hazard and adverse selection problems faced by insurance companies relate to insurance against operational risk.

**a.** Describe the rationale for the use of stress testing as a risk management tool.

**b.** Explain key considerations and challenges related to stress testing, including choice of scenarios, regulatory specifications, model building, and reverse stress testing.

**c.** Describe the relationship between stress testing and other risk measures, particularly in

enterprise-wide stress testing.

**d.** Describe stressed VaR and stressed ES, including their advantages and disadvantages, and compare the process of determining stressed VaR and ES to that of traditional VaR and ES.

**e.** Describe the responsibilities of the board of directors, senior management, and the internal audit function in stress testing governance.

**f.** Describe the role of policies and procedures, validation, and independent review in stress testing governance.

**g.** Describe the Basel stress testing principles for banks regarding the implementation of stress testing.

**a.** Define discount factor and use a discount function to compute present and future values.

**b.** Define the “law of one price,” explain it using an arbitrage argument, and describe how it can be applied to bond pricing.

**c.** Identify arbitrage opportunities for fixed-income securities with certain cash flows.

**d.** 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.

**e.** Construct a replicating portfolio using multiple fixed income securities to match the cash flows of a given fixed-income security.

**f.** Differentiate between “clean” and “dirty” bond pricing and explain the implications of accrued interest with respect to bond pricing.

**g.** Describe the common day-count conventions used in bond pricing.

**a.** Calculate and interpret the impact of different compounding frequencies on a bond’s value.

**b.** Define spot rate and compute discount factors given spot rates.

**c.** Interpret the forward rate and compute forward rates given spot rates.

**d.** Define par rate and describe the equation for the par rate of a bond.

**e.** Interpret the relationship between spot, forward, and par rates.

**f.** Assess the impact of maturity on the price of a bond and the returns generated by bonds.

**g.** Define the “flattening” and “steepening” of rate curves and describe a trade to reflect expectations that a curve will flatten or steepen.

**h.** Describe a swap transaction and explain how a swap market defines par rates.

**i.** Describe overnight indexed swaps (OIS) and distinguish OIS rates from LIBOR swap rates.

**a.** Distinguish between gross and net realized returns and calculate the realized return for a bond over a holding period including reinvestments.

**b.** 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.

**c.** Define, interpret, and apply a bond’s yield-to-maturity (YTM) to bond pricing.

**d.** Compute a bond’s YTM given a bond structure and price.

**e.** Calculate the price of an annuity and a perpetuity.

**f.** Explain the relationship between spot rates and YTM.

**g.** Define the coupon effect and explain the relationship between coupon rate, YTM, and bond prices.

**h.** 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 effects.

**i.** 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.

**a.** Describe a one-factor interest rate model and identify common examples of interest rate factors.

**b.** Define and compute the DV01 of a fixed income security given a change in yield and the resulting change in price.

**c.** Calculate the face amount of bonds required to hedge an option position given the DV01 of each.

**d.** Define, compute, and interpret the effective duration of a fixed income security given a change in yield and the resulting change in price.

**e.** Compare and contrast DV01 and effective duration as measures of price sensitivity.

**f.** Define, compute, and interpret the convexity of a fixed income security given a change in yield and the resulting change in price.

**g.** Explain the process of calculating the effective duration and convexity of a portfolio of fixed income securities.

**h.** Describe an example of hedging based on effective duration and convexity.

**i.** Construct a barbell portfolio to match the cost and duration of a given bullet investment and explain the advantages and disadvantages of bullet versus barbell portfolios.

**a.** Describe principal components analysis and explain its use in understanding term structure movements.

**b.** Define key rate exposures and know the characteristics of key rate exposure factors, including partial 01s and forward bucket 01s.

**c.** Describe key-rate shift analysis.

**d.** Define, calculate, and interpret key rate 01 and key rate duration.

**e.** Compute the positions in hedging instruments necessary to hedge the key rate risks of a portfolio.

**f.** Relate key rates, partial 01s, and forward-bucket 01s and calculate the forward-bucket 01 for a shift in rates in one or more buckets.

**g.** Apply key rate and multi-factor analysis to estimating portfolio volatility.

**a.** Calculate the value of an American and a European call or put option using a one-step and two-step binomial model.

**b.** Describe how volatility is captured in the binomial model.

**c.** Describe how the value calculated using a binomial model converges as time periods are added.

**d.** Define and calculate delta of a stock option.

**e.** Explain how the binomial model can be altered to price options on stocks with dividends, stock indices, currencies, and futures.

**a.** Explain the lognormal property of stock prices, the distribution of rates of return, and the calculation of expected return.

**b.** Compute the realized return and historical volatility of a stock.

**c.** Describe the assumptions underlying the Black-Scholes-Merton option pricing model.

**d.** Compute the value of a European option on a non-dividend-paying stock using the Black-Scholes-Merton model.

**e.** Define implied volatilities and describe how to compute implied volatilities from market prices of options using the Black-Scholes-Merton model.

**f.** Explain how dividends affect the decision to exercise early for American call and put options.

**g.** Compute the value of a European option using the Black-Scholes-Merton model on a dividend-paying stock, futures, and exchange rates.

**h.** Describe warrants, calculate the value of a warrant, and calculate the dilution cost of the warrant to existing shareholders. FRM.

**a.** Describe and assess the risks associated with naked and covered option positions.

**b.** 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 positions.

**c.** Describe delta hedging for options as well as for forward and futures contracts.

**d.** Compute the delta of an option.

**e.** Describe the dynamic aspects of delta hedging and distinguish between dynamic hedging and hedge-and-forget strategies.

**f.** Define and calculate the delta of a portfolio.

**g.** Define and describe theta, gamma, vega, and rho for option positions and calculate the gamma and vega for a portfolio.

**h.** Explain how to implement and maintain a delta-neutral and a gamma-neutral position.

**i.** Describe the relationship between delta, theta, gamma, and vega.

**j.** Describe how to implement portfolio insurance and how this strategy compares with delta hedging.