# FRM Part I: Topics In Valuation and Risk Models

Valuation and risk models are among the 4 four broad topics tested in FRM Part I. GARP aims to test a candidate’s understanding of valuation techniques and risk models using these topics. 30% of questions in FRM Part I exams originate from these topics, and this can be up to 30 out of 100 exam questions. The Learning Outcomes provided for this section by GARP are computational and non-computational. These are well-balanced in all 16 chapters to be studied in this section. Non-computational LOs usually contain tricky questions as compared to computational LOs.

Some of the points covered in the 16 topics are:

• Value at Risk (VaR)
• Expected Shortfall (ES)
• Estimation of 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

Let us review the contents of the 16 topics and what GARP tests from each.

## Measures of Financial Risk

To determine the suitable risk measure, you must base your assumption on the shape of the primary return distribution. Mean-variance only relates to elliptical distributions such as normal distribution. For non-elliptical distributions, its risk measures are calculated using VaR. However, this measure is unpredictable because it does not approximate the losses incurred.

A better way to estimate risk is using Expected Shortfall. This is because it satisfies all the qualities of a consistent risk measure and has less restrictive presumptions.

For this chapter, the exam might test on:

• Calculating the VaR
• Expected Shortfall methodology
• Properties of a coherent risk measure

## Calculating and Applying VaR

This chapter focuses on the risk evaluation techniques for linear and non-linear derivatives. GARP examines your understanding of the various methods of calculating VaR and Estimated Shortfall under the following techniques:

• Historical simulation technique
• Delta-normal technique
• Full re-valuation technique

GARP might also test on extended VaR approaches, commonly used when correctly measuring risk for complex derivatives and scenarios.  Questions on the following methods may appear in relation to extended VaR techniques:

• Structured Monte Carlo
• Stress testing
• Worst-case scenario analysis

## Measuring and Monitoring Volatility

To understand plausible risk exposure, an accurate estimation of volatility is vital. A normal distribution can be utilized to assess asset value. However, deviations from reality are a common occurrence. Risk managers are frequently challenged by such deviations when measuring volatility and VaR. GARP aims to test your understanding of the following concepts in FRM Part 1 exams:

• Challenges associated with volatility estimation and alternative methods that can be used to determine VaR(parametric and non-parametric)
• The pros and cons of these methods
• The fundamental assumptions associated with these methods
• Why deviations from normality emerge
• The tendency of volatility to revert its mean
• Approximating volatility using the exponentially weighted moving average and generalized autoregressive conditional heteroskedasticity models.

## External and Internal Credit Ratings

Credit ratings provide valuable insight into both individual and company investments. Objectively, there is a significant correlation between ratings and subsequent defaults. Therefore most rating organizations use qualitative and quantitative approaches when determining external ratings.

From this chapter, you are needed to demonstrate your understanding of the following concepts:

• Solving a default probability table and a rating transition matrix
• Value of the hazard rate and the recovery rate and how they relate to expected losses
• How external and internal credit ratings are proven

## Country Risk: Determinants, Measures, and Implications

Sovereign risk frequently varies across countries. Aspects such as a country’s political hazard, legal hazard, or position in the economic market influence the overall risk an investor might face. Rating companies also assess sovereign risks and rating transitions.

GARP might examine your capacity to:

• Analyze and differentiate the benefits of sovereign debt ratings and sovereign default risk spread
• Identify the origins of sovereign risk and illustrate the outcomes of both local and foreign currency defaults

## Measuring Credit Risk

The investment strategy for a financial institution holds a lot of assets. Therefore, you must analyze the expected and unexpected losses from the investment strategy.

During the examination, GARP might test your ability to:

• Compute each asset’s expected loss, unexpected loss, and risk contributions in the investment strategy.
• Calculate risk under Basel II
• Evaluate credit losses using different ways
• Model credit risk using the Gaussian Copula model, the Vasicek model, the credit metrics model, and Euler’s theorem. This includes comprehending the principal rationale and drawbacks of using these methods.

## Operational Risk

This is the direct or indirect loss arising from insufficient or failed internal processes, external risks, people, and the system. This chapter elaborates on the types of operational risk and bank business lines that must be considered when calculating operational risk capital.

## Stress Testing

Stress testing aims to anticipate extreme events with a low possibility of occurrence but a profound effect if they do. An organization is required to have a sufficient amount of liquid assets and capital to endure these events. You might come across questions on the following areas on the exam day:

• Your understanding of the scenarios and how they are chosen.
• How models are regulated
• The basal stress testing principle for banks

The relationship between VaR and ES is paramount to stress testing. Stressed risk metrics have merits and demerits corresponding to traditional risk measures.

## Pricing Conventions, Discounting, and Arbitrage

The chapter outlines the foundations of bond valuation. The value of a bond is equivalent to the current value of its cash flows discounted to the suitable periodic time needed to return. Coupon bonds are priced according to discount factors. This is used to gauge whether the bond trades below or above par.

The law of one price states that securities matching future cash flows should trade at the same price.

## Interest Rates

The future and the present value of an investment are directly impacted by how you compound interest rates. The areas examinable from this topic are:

The different types of rates relevant to debt devices

The relationship between the rates and the influence they have on bond valuations

Yield curves. What causes the flattening and steepening of the curve and the tactics used in these scenarios?

## Bond Yields and Return Calculations

Bond yields and spreads and reinvestment of a coupon are essential in finding the overall return. Using yield to maturity as an indicator of actual returns upon maturity may not be reliable for coupon bonds. If the market goes down, an investor receiving coupon payments is vulnerable to the risk that these cashflows will get reinvested at a rate lower than the initially guaranteed yield. The exams test the calculation and interpretation of YTM(Yield to maturity) and different elements of bond returns.

## Applying Duration, Convexity, and DV01

These are the various ways to determine and secure risk for fixed-income securities. The primary concepts covered in this chapter are:

• DV01 – This is the measure of how much the price of a bond shifts in response to a one basis point change in yield.
• Duration – The change in a bond’s value resulting from a small parallel change in rates can be measured by effective duration.

DV01 and duration can evaluate price volatility but fail to grasp the curvature of the bond yield and price relationship.

• Convexity – This captures the impacts of the price-yield relationship.
• The exams test your ability to draw comparisons and calculate DV01, duration, and convexity.

## Modeling Non-Parallel Term Structure Shifts, and Hedging

This section discusses the term structure of interest by separating it into many regions and assumptions on how the rate of each region changes. Critical rate analysis deduces a portfolio’s exposure to changes in key rates. It is simple and is based on the assumption that rates value in the region of the critical rate selected. The forward-bucket method, however, uses information from a more significant collection of rates, especially those factored into the forward rate curve. The exam tests your knowledge of the following:

• Applying critical rate shift analysis
• Key rate 01 and critical rate duration
• The calculations relating to hedging position given a particular key rate exposure profile

## Binomial Trees

This topic is about the Binomial model for valuing options on the stock. It also introduces the Black-Scholes-Merton model. In the exam, GARP tests your ability to:

• Calculate the value of a European or American option using a one-step or two-step binomial model.
• Use delta concepts to compte hedging.
• Modify the binomial model and lengthen it past modeling for individual, non-dividend-paying stock.

## The Black-Scholes-Merton Model

This option pricing model is based on the assumption that stock prices follow a lognormal distribution. It also discusses how volatility can be measured using the BSM model and current option pricing. The GARP tests your ability to:

• Calculate the value of a call and put the option using the BSM model.
• Factor in dividends, currencies, and futures into the model when required.
• Compute the put-call parity.

## Option Sensitivity Measures: “The Greeks”

Factors affecting the level of risk related to an option position are:

The relationship between the value of a position involving options and the value of the underlying assets.

• Time until expiration.
• Asset value volatility.
• Risk-free rate.
• The metrics that capture the outcomes of these factors are called Greeks because of their names; delta, theta, gamma, vega, and rho.

This is an overview of what to expect from valuation and risk models topics in FRM part I. Are you ready to start studying for your FRM part I? Explore the FRM study options available with AnalaystPrep to ensure you master these concepts adequately for your final exam.

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