Financial Risk Manager Handbook

Philippe Jorion

• Publisher: Wiley
• Year: 2009
• ISBN:
  9780470521991
• Edition: 5
• Topic: Business
• Subtopic: Finance
• Index: Business

The essential reference for financial risk management Filled with in-depth insights and practical advice, theFinancial Risk Manager Handbook is the core text for riskmanagement training programs worldwide. Presented in a clear andconsistent fashion, this completely updated FifthEdition-which comes with an interactive CD-ROM containinghundreds of multiple-choice questions from previous FRM exams-isone of the best ways to prepare for the Financial Risk Manager(FRM) exam. Financial Risk Manager Handbook, Fifth Edition supportscandidates studying for the Global Association of RiskProfessional's (GARP) annual FRM exam and prepares you to assessand control risk in today's rapidly changing financial world.Authored by renowned risk management expert Philippe Jorion-withthe full support of GARP-this definitive guide summarizes the corebody of knowledge for financial risk managers.
* Offers valuable insights on managing market, credit, operational, and liquidity risk
* Examines the importance of structured products, futures, options, and other derivative instruments
* Identifies regulatory and legal issues
* Addresses investment management and hedge fund risk Financial Risk Manager Handbook is the most comprehensiveguide on this subject, and will help you stay current on bestpractices in this evolving field. The FRM Handbook is the officialreference book for GARP's FRM® certification program. Note: CD-ROM/DVD and other supplementary materials arenot included as part of eBook file.

PART One

Quantitative Analysis

CHAPTER 1

Bond Fundamentals

Risk management starts with the pricing of assets. The simplest assets to study are regular, fixed-coupon bonds. Because their cash flows are predetermined, we can translate their stream of cash flows into a present value by discounting at a fixed interest rate. Thus the valuation of bonds involves understanding compounded interest, discounting, as well as the relationship between present values and interest rates.

Risk management goes one step further than pricing, however. It examines potential changes in the price of assets as the interest rate changes. In this chapter, we assume that there is a single interest rate, or yield, that is used to price the bond. This will be our fundamental risk factor. This chapter describes the relationship between bond prices and yields and presents indispensable tools for the management of fixed-income portfolios.

This chapter starts our coverage of quantitative analysis by discussing bond fundamentals. Section 1.1 reviews the concepts of discounting, present values, and future values. Section 1.2 then plunges into the price-yield relationship. It shows how the Taylor expansion rule can be used to relate movements in bond prices to those in yields. This Taylor expansion rule, however, covers much more than bonds. It is a building block of risk measurement methods based on local valuation, as we shall see later. Section 1.3 then presents an economic interpretation of duration and convexity.

The reader should be forewarned that this chapter, like many others in this handbook, is rather compact. This chapter provides a quick review of bond fundamentals with particular attention to risk measurement applications. By the end of this chapter, however, the reader should be able to answer advanced FRM questions on bond mathematics.

1.1 DISCOUNTING, PRESENT, AND FUTURE VALUE

An investor considers a zero-coupon bond that pays $100 in 10 years. Assume that the investment is guaranteed by the U.S. government, and that there is no credit risk. So, this is a default-free bond, which is exposed to market risk only. Because the payment occurs at a future date, the current value of the investment is surely less than an up-front payment of $100.

To value the payment, we need a discounting factor. This is also the interest rate, or more simply the yield. Define C_t as the cash flow at time t and the discounting factor as y. We define T as the number of periods until maturity, e.g., number of years, also known as tenor. The present value (P V) of the bond can be computed as

(1.1)

For instance, a payment of C_T = $100 in 10 years discounted at 6 percent is only worth $55.84 now. So, all else fixed, the market value of zero-coupon bonds decreases with longer maturities. Also, keeping T fixed, the value of the bond decreases as the yield increases.

Conversely, we can compute the future value (FV ) of the bond as

(1.2)

For instance, an investment now worth P V = $100 growing at 6 percent will have a future value of F V = $179.08 in 10 years.

Here, the yield has a useful interpretation, which is that of an internal rate of return on the bond, or annual growth rate. It is easier to deal with rates of returns than with dollar values. Rates of return, when expressed in percentage terms and on an annual basis, are directly comparable across assets. An annualized yield is sometimes defined as the effective annual rate (EAR).

It is important to note that the interest rate should be stated along with the method used for compounding. Annual compounding is very common. Other conventions exist, however. For instance, the U.S. Treasury market uses semiannual compounding. Define in this case y^S as the rate based on semiannual compounding. To maintain comparability, it is expressed in annualized form, i.e., after multiplication by 2. The number of periods, or semesters, is now 2T. The formula for finding y^S is

(1.3)

For instance, a ...

Table of contents

• Title Page
• Copyright Page
• Preface
• About the Author
• About GARP
• Introduction
• PART One - Quantitative Analysis
• PART Two - Capital Markets
• PART Three - Market Risk Management
• PART Four - Investment Risk Management
• PART Five - Credit Risk Management
• PART Six - Legal, Operational, and Integrated Risk Management
• PART Seven - Regulation and Compliance
• About the CD-ROM
• Index