“Valuation and Risk Models” is one of the four broad topics that GARP tests in its FRM Part 1 exam. This broad topic has 30% weight in the exam, which means that you may expect 30 out of 100 questions to be asked from this section. This topic tests a candidate’s knowledge of valuation techniques and risk models. The broad knowledge points covered in Valuation and Risk Models include the following:

• Value-at-Risk (VaR)
• Expected shortfall (ES)
• Estimating volatility and correlation
• Economic and regulatory capital
• Stress testing and scenario analysis
• Option valuation
• Fixed income valuation
• Hedging
• Country and sovereign risk models and management
• External and internal credit ratings
• Expected and unexpected losses
• Operational risk

There are sixteen chapters or readings in this section. If you go through the GARP specified learning objectives (LOs) for this section, you will find a good mix of computational and non-computational LOs. As GARP generally asks tricky questions from the non-computational LOs, non-computational LOs are to be equally emphasized to score well in this section.

Let me now take you through the essence of each of the sixteen chapters or readings and identify the concepts that GARP might test on the exam day.

## Chapter 1: Measures of Financial Risk

The assumption on the shape of the underlying return distribution is pivotal in determining a fitting risk measure. The mean-variance framework applies only to an elliptical distribution, such as the normal distribution. The value at risk (VaR) measure may be used for calculating risk measures for nonelliptical return distributions. However, such a measurement is often unreliable and fails to provide an estimate for the amount of loss. Expected shortfall is a better risk measure as it satisfies all the properties of a coherent risk measure and has less restrictive assumptions. On the exam day, GARP might test you on the calculation of VaR, properties of coherent risk measures, and the expected shortfall methodology.

## Chapter 2: Calculating and Applying VaR

This reading discusses the risk measurement approaches for linear and nonlinear derivatives. On the exam day, GARP might test your understanding of different methods for calculating value at risk (VaR) and calculation of expected shortfall (ES) under the historical simulation approach, the delta-normal approach, and the full revaluation approach, including the merits and demerits and underlying assumptions of the various approaches. Also, there could be questions on structured Monte Carlo, stress testing, and worst-case scenario (WSC) analysis, which are often used in extending VaR techniques to measure risk for complex derivatives and scenarios more appropriately.

## Chapter 3: Measuring and Monitoring Volatility

The correct estimation of volatility is vital to understanding potential risk exposure. Asset value can be assessed using a normal distribution; however, deviations from normality are a reality. Such deviations often challenge the risk manager to measure volatility and value at risk (VaR). This reading discusses issues with volatility estimation and different weighting methods that can be used to determine VaR. The merits, demerits, and underlying assumptions of the various methodologies are also discussed. GARP might test your understanding of why deviations from normality arise and different approaches to measuring VaR (parametric and nonparametric) on the exam day. Also, you should be thorough with estimating volatility applying both the exponentially weighted moving average (EWMA) and the generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] models and the mean-reverting nature of volatility.

## Chapter 4: External and Internal Credit Ratings

Credit ratings can be useful for both companies and individual investments. Rating agencies use both qualitative and quantitative methods for determining external ratings. Historically, the relationship between ratings and subsequent defaults is pretty strong. GARP might test your ability to interpret a default probability table and a ratings-transition matrix on the exam day. Also, be thorough with your understanding of the value of the hazard rate and the recovery rate as they relate to expected losses. Banks generate their internal ratings, and they may use an at-the-point approach or a through-the-cycle approach as the agencies do. Additionally, you need to have a general understanding of how external and internal credit ratings are established.

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

Sovereign risks often differ across countries. Factors such as the country’s political risk, legal risk, position in the economic growth cycle, and economic diversity impact the investor’s overall risk. Rating agencies rate sovereign risks and also evaluate rating transitions. Country risk can also be analyzed using sovereign default risk spreads. On the exam day, GARP might test your ability to compare and contrast the advantages of sovereign debt ratings and sovereign default risk spreads and recognize sources of sovereign risk and describe the aftermaths of both local currency and foreign currency sovereign defaults.

## Chapter 6: Measuring Credit Risk

You need to examine the expected and unexpected losses in a portfolio setting for financial institutions because they hold many assets. On the exam day, GARP might test you on the calculations of expected loss, unexpected loss, and the risk contribution of each asset in a portfolio. In addition, be thorough with the two approaches to calculating credit risk capital under Basel II. Also, there could be questions on different ways of measuring credit losses and modelling credit risk, including the Gaussian copula model, the Vasicek model, the CreditMetrics model, and Euler’s theorem. While calculations help understand complex concepts better, GARP generally tests your understanding of the primary rationale and benefits (and limitations) of using these models.

## Chapter 7: Operational Risk

This reading begins by defining operational risk, including internal failures and external events. It then discusses different types of operational risk and bank business lines that must be factored in the calculation for operational risk capital requirements. Collecting data for loss frequency and loss severity distributions is a significant task required to be performed for allocating operational risk capital among various business lines. Methods for obtaining the requisite operational loss data points depend on both internal and external data and historical and forward-looking approaches.

## Chapter 8. Stress Testing

Stress testing is concerned with extreme events, which have a low probability of occurrence but a high bearing if they do occur. Ideally, an institution needs to have enough liquid assets and capital to withstand these events. GARP might test your understanding of how scenarios are selected, models are calibrated, and coverage is tested on exam day. The relationship between the value at risk (VaR) and expected shortfall (ES) is important to stress testing because stressed risk metrics have pros and cons relative to the traditional risk measures. Governance over the stress-testing process and the roles of the board of directors, senior management, and internal audit functions are of paramount importance for a well-functioning stress-testing framework. Policies and procedures, documentation, validation, and the review of the stress-testing process are all crucial components of stress-testing governance. Finally, don’t get surprised if GARP tests you on the Basel stress-testing principles for banks.

## Chapter 9. Pricing Conventions, Discounting, and Arbitrage

This reading offers an overview of the fundamentals of bond valuation. The value of a bond equals the present value of its cash flows discounted at the appropriate periodic required return. Discount factors are used to price coupon bonds and determine whether bonds are trading below or above par. If securities are mispriced, a riskless arbitrage profit can be made from violating the law of one price, which states that securities with matching future cash flows should trade at the same price.

## Chapter 10: Interest Rates

You can compound Interest rates at various frequencies, which will impact the value of an investment in the future and the present value of an investment today. For the exam day, be thorough with the various types of rates applicable to debt instruments, including the spot rate, forward rate, par rate, and swap rate. The relationships between these rates and the impact maturity have on bond valuations are highly critical testable concepts. Also, GARP might test your understanding of yield curves in terms of their slopes, what causes the flattening and steepening of curves, and the strategies used in these situations.

## Chapter 11: Bond Yields and Return Calculations

This reading looks at bond yields and spreads and how reinvestment of a coupon is important in determining the overall return. For coupon bonds, yield to maturity (YTM) may not be a good measure of actual returns to maturity. An investor receiving coupon payments is subject to the risk that these cash flows will get reinvested at a rate of return that is lower than the initially promised yield on the bond if market yields go down. GARP might test you on the calculation and interpretation of YTM on exam day and the various components of bond returns.

## Chapter 12: Applying Duration, Convexity, and DV01

This reading discusses different ways to measure and hedge risk for fixed-income securities. DV01, duration, and convexity are the three main concepts covered in this reading. DV01 is an acronym for the dollar value of a basis point, which measures how much the price of a bond changes in response to a one basis point change in yield. Duration, specifically effective duration, captures the percentage change in a bond’s value caused by small, parallel changes in rates. DV01 and duration can measure price volatility, but they fail to capture the curvature in the relationship between bond yield and price. Convexity captures the curvature effects of the price-yield relationship. GARP might test your ability to compare, contrast, and calculate DV01, duration, and convexity on the exam day.

## Chapter 13: Modeling Non-Parallel Term Structure Shifts and Hedging

This reading discusses the term structure of interest rates by dividing it into several regions and assumptions on how rates change for each region. Key rate analysis captures a portfolio’s exposure to changes in key rates. The key rate method is simple and assumes that rates vary in the region of the key rate selected. The forward-bucket method is akin to the key rate approach but instead uses information from a greater collection of rates, specifically those factored into the forward rate curve. On the exam day, GARP might test your understanding of:

• how to apply key rate shift analysis
• key rate ’01 and key rate duration
• the calculations relating to hedging positions given a specific key rate exposure profile

## Chapter 14: Binomial Trees

This reading talks about the binomial model for valuing options on stock and provides an introduction to the Black-Scholes-Merton model discussed in detail in the next reading. On the exam day, GARP might test your ability to calculate the value of a European or American option using a one-step or two-step binomial model. This requires your understanding of the formulas for the sizes of upward and downward movements, as well as the risk-neutral probabilities in both up and down states. Also, be thorough with the concept of delta and how it is used in hedging. Finally, make sure that you understand how the binomial model can be adjusted to extend beyond just modelling for individual, non-dividend-paying stocks.

## Chapter 15: The Black-Scholes-Merton Model

The Black-Scholes-Merton (BSM) option pricing model is based on the assumption that stock prices follow a lognormal distribution. This reading examines the calculation of calls and puts using the BSM option pricing model. Also, it discusses how volatility can be estimated using both the BSM model and current option prices. On the exam day, GARP might test your understanding of calculating the value of a call option and a put option using the BSM model and your ability to factor in dividends, currencies, and futures into the model if needed. Also, GARP often tests the put-call parity relationship on exam day.

## Chapter 16: Option Sensitivity Measures: The “Greeks”

The level of risk associated with an option position is dependent largely on the relationship between the value of a position involving options and the value of the underlying assets, time until expiration, asset value volatility, and the risk-free rate. Measures that capture the effects of these factors are known as “the Greeks” because of their names: delta, theta, gamma, vega, and rho. Thus, a large part of this reading is devoted to discussing the evaluation of option Greeks. On the exam day, GARP might test your understanding of any of “the Greeks.” Note that once option participants are cognizant of their Greek exposures, they can more effectively hedge their positions to mitigate risk. GARP also likes to test the common hedging concepts of delta-neutral portfolios and portfolio insurance.

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