Chapter 6

Global Bond Investing

7 - 2

Introduction

In this chapter we look at: Global bond market statistics Major differences among bond markets Bond quotations, conventions and valuation

7 - 3

World Market Size

Size of world bond market is estimated to be $66 trillion at the start of 2007.

The world market capitalization is higher than that of the equity market.

The relative share of each currency market depends not only on new issues and repaid bonds, but also on exchange rate movements.

7 - 4

Exhibit 7.1: Market Capitalization of Domestic Bond Markets Total $48.7 trillion

7 - 5

The Eurobond Market//International Bond Market The major types of instruments are:

Straight bonds with fixed coupons Floating-rate notes (FRNs) with a coupon

indexed on a short-term interest rate Bonds with some equity feature (convertibles).

7 - 6

Exhibit 7.2: Market Capitalization of International Bonds Total $17.6 trillion

7 - 7

Instead the global bond market may be classified into three categories: Domestic bond market

Issued by domestic borrower in local currency

Foreign bonds e.g. Yankee, Samurai, dragon, Rembrandt, Matador

bonds, Caravel， Bulldog bonds

International bonds Underwritten by a multinational syndicate

Global bond market

7 - 8

Domestic bonds:

Issued locally by a domestic borrower and are usually denominated in the local currency

Usually make up the bulk of the national bond market

Issuers include government, semi-government and corporate agencies

7 - 9

Foreign bond market Issued on a local market by a foreign borrower and are

usually denominated in the local currency. Foreign bond issues and trading are under the

supervision of local market authorities. Foreign bonds include:

Yankee bonds (in the U.S) Samurai bonds (in Japan) Bulldog bonds (in the UK) Matador bonds (in Spain) Rembrandt bonds (in the Netherlands)

7 - 10

International bond market Underwritten by a multinational syndicate of

banks and are placed mainly in countries other than the one in whose currency the bond is denominated.

International bonds (Eurobonds) are not traded on a specific national market. Avoids most national regulations and constraints

Developed in the 1960s and was early recognized as an efficient, low-cost and innovative market.

7 - 11

A note on terminology…

In 1999, all bonds denominated in one of the former currencies of Euroland were translated into euros.

This new denomination could create confusion between “Eurobonds” and “bonds issued in euros”.

So to avoid this… From this point on, the term “international bond” is

used in lieu of “Eurobond”.

7 - 12

Exhibit 7.3

International Bond Tombstone

7 - 13

1. International bond market - Characteristics The underwriting syndicate is made up of banks

from numerous countries. Underwriting banks tend to use subsidiaries

established in London or a foreign country with a favorable tax situation.

Corporate borrowers use a subsidiary incorporated in a country with a favorable tax and regulatory treatment.

For fixed-rate Eurobonds, the frequency of coupon payments is usually annual.

7 - 14

2.Issuance Process Issuing syndicate is organized by an international

bank called a lead manager. Timetable of New Issue (total time: 5 to 6 weeks):

discussion between lead manager and borrower (2 weeks or more).

Announcement of international bond issue (1 to 2 weeks of preplacement).

offering day with final terms (2 week public placement) Closing day: selling group pays for bonds After closing day, the bonds can be publicly traded.

7 - 15

Exhibit 7.4: Timetable of a New International Bond Issue

7 - 16

3.Dealing in international bonds:

Eurobond dealers created an around-the-clock market among financial institutions across the world, forming the International Capital Market Association (ICMA).

Eurobond Clearing System:

A trade is settled in three business days and the transactions are cleared through either Euroclear or Clearstream (formerly Cedel).

Euroclear and Clearstream collect a transaction fee for each book entry as well as a custody fee for holding the security.

7 - 17

Emerging Markets

Several alternatives are available: Domestic bonds

Various restrictions and liquidity problems reduce the amount available to foreign investors.

Foreign bonds International bonds Brady bonds

In 1990, the Brady plan allowed emerging countries to transform nonperforming debt into Brady bonds.

7 - 18

Brady Bonds

Formulated in 1990, as a solution to the emerging market debt crisis of the 1980s.

A Brady plan is a debt-reduction program whereby sovereign debt is repackaged into tradable Brady bonds, generally with collateral.

Close to 20 countries have issued Brady bonds and the total market capitalization is close to $100 billion.

7 - 19

1. Characteristics

The basic idea is to replace existing government debt with Brady BONDS, whose market value is less than the par value of the original debt, but are more attractive because of the guarantees provided and their tradability.

Three main types of guarantees can be put in place: principal collateral rolling-interest guarantee value recovery rights

7 - 20

2.Types of Brady Bonds

Two major types of Brady bonds have been issued: par bonds (PARS) discount bonds (DISCS)

Other types of Brady bonds include: Front-loaded interest reduction bonds (FLIRBs) New-money bonds (NMBs) and debt-

conversion bonds(DCBs) Past-due interest bonds (PDIs)

7 - 21

Major Differences Among Bond Markets

Quotation

Bonds are quoted on a price plus accrued interest in percentage of face value

The full price (or value) of a bond is the sum of its clean price plus accrued interest. Or, P = Q +AI

Where P = full price, Q = quoted price and AI = accrued interest

Accrued interest = Coupon (days since last coupon date/days in coupon period).

7 - 22

Full Price and Clean Price – An example

Question: The clean price of a Eurobond is quoted at Q=96%. The annual coupon is 5 percent, and we are exactly four months from the past coupon payment. What is the full price of the bond?

Solution:

P = Q + accrued interest

= 96% + (120/360) x 5%

= 97.67%

7 - 23

1.Coupon Frequency and Day Count The day count convention known as “30/360” is

commonly used in the USA, Germany, Scandinavia, Switzerland and the Netherlands. In the USA it is used for agency, municipal, corporate

and foreign bonds.

The day count on US Treasury bonds is actual number of days in a year of 365 or 366 days. The day count convention known as “actual/actual”

BY contrast, Canada and Japan use a day count based on the actual number of days in a 365-day year

7 - 24

Straight Eurobonds usually pay an annual coupon and use the U.S.30/360 DAY-COUNT convention

Euro- FRNs use a actual days in a 360-day year an pay quarterly or semiannual coupons.

7 - 25

Exhibit 7.5: Coupon Characteristics of Major Bond Markets

7 - 26

Yield to Maturity The yield to maturity (YTM) is the average

promised yield over the life of the bond. The convention used to calculate YTM varies

across markets. In the U.S, YTM is calculated at a semiannual rate

and the result is multiplied by 2 to report an annualized rate.

Most Europeans calculate an annual, actuarial YTM. （ compounding of the two semiannual coupons ）

The simple interest yield approach is also used in Japan.

7 - 27

Simple yield calculation - example

Question:

A four year bond has exactly four years till maturity and the last coupon has just been paid. The coupon is annual and equal to 5.5 percent. The bond price is 96 percent. Calculate its simple yield.

7 - 28

Simple yield calculation - example

Solution:

%77.64

1

96

)96100(

96

5.5

1)100(

yieldSimple

xyieldSimple

maturitytoYearsx

priceCurrent

priceCurrent

priceCurrent

CouponyieldSimple

7 - 29

2. Legal and Fiscal Aspects legal aspects

Bearer form (e.g., Eurobonds and in many European countries). The bearer of the bond is assumed to be its legal

owner. Provide confidentiality of ownership.

Registered form (e.g., In the United States, owners must be registered in the issuer’s books) Allows for easier transfer of interest payments and

amortization.

7 - 30

Tax aspects Avoiding double taxation was a major impetus

behind the development of the international (Eurobond) market.

To attract foreign investors in their government bonds, most countries eliminate withholding taxes on foreign investment in their domestic bond markets.

7 - 31

Bond ValuationBond Valuation

Zero coupon bonds

They are bonds that do not pay a coupon but pay only a fixed cash flow at their maturity.

Yield to maturity

The YTM is defined as the interest rate at which P should be invested today in order to realize Ct t year from now.

7 - 32

There exists an inverse relationship between market yield and bond price.

7 - 33

Coupon Bonds

The theoretical value of a coupon-paying bonds may be considered the present value of a stream of cash flows consisting of each coupon payment and the principal reimbursement.

Yield to maturity:

nnrnC

r

C

r

CP

12

21

21

11

1

如果票面金额为 1000元的两年期债券，第一年支付 60元利息，第二年支付 50元利息，现在的市场价格为 950元，求该债券的到期收益率为多少？

7 - 34

Bonds traders often refers to the European, or ICMA method.

The U.S. YTM is a mixture of an internal rate of return calculation to obtain the semiannual yield, and of a multiplication to transform it into an annualized yield. (p279)

n

n

trtC

trtC

tr

CP

111t

2

2

1

1

7 - 35

European YTM versus U.S. YTM

the difference between r and r’ comes from the difference between compounding and linearizing semiannual yields to get annual yields

7 - 36

Coupon Bonds - example

Question: A six-year bond has exactly six years till maturity, and the last coupon has just been paid. The coupon is annual and equal to 5 percent. The bond price is 104 percent. What is its European YTM and U.S. YTM?

7 - 37

Solution: The European YTM is r, given by the formula

We find r = 4.23%

The U.S. YTM is r1, given by the formula

Hence r1 = 4.186%

612111

5104 1055

rrr

122/'1

42/'1

22/'1

104 10555

rrr

7 - 38

Duration and Interest Rate Sensitivity

1. Duration

Duration is a measure of interest risk for a specific bond.

Mathematically, duration, D, can be written as:

The Macaulary duration is a weighted-average maturity

rDP

P

7 - 39

Frederick R. Macaulay在 1938年发表的一篇研究文章中提出久期，他在现值的基础上，衡量了与金融工具 (如附息债券 )有关的现金流的平均期限 (the average of the stream of payment)

“久期”是债券的各期支付 (包括息票的支付与本金的偿还 )所需时间长度的加权平均数。

Pr

nM

r

nc

r

c

r

cnn

1

)1()1()1(

2

1

1MD

2

MDrPdr

dP

1

11

7 - 40

2. For larger movements in yield, the convexity can be used.

The bond return can be approximated as:

Return = Yield – D (yield)

Return = Cash rate +

( Yield - Cash rate) - D * ( yield)

risk premium

7 - 41

The expected return on a bond is equal to the risk-free cash rate plus a risk premium:

E (return) = Cash rate + Risk premium

7 - 42

Duration - Example

Question:

You hold a government bond with a duration of 12. Its yield is 6 percent. You expect yields to move down by 20 basis points in the next few minutes. Calculate a rough estimate of expected return.

7 - 43

Duration - Example

Solution:

Given the very short horizon, the only component of return is the expected capital gain:

Return = -12 x (-0.2%) = +2.4%

7 - 44

Duration – Example 2

Question: You hold a government bond with a duration of 12. Its yield is 6 percent, although the cash (one-year) rate is 2.5 percent. You expect yields to move down by 20 basis points over the next year. Calculate a rough estimate of expected return. What is the risk premium on this bond?

7 - 45

Duration – Example 2

Solution:

Return = Yield – D x (Δyield)

= 6% - 12 x (-0.2%)

= 8.4%

Risk premium is obtained by deducting the short-term interest rate = 5.9%

7 - 46

Credit Spreads

The credit spread captures three components:

An expected loss component

A credit-risk premium.

A liquidity premium.

7 - 47

Multicurrency Approach

A higher yield in one currency is often compensated for, ex post, by a depreciation in this currency and, in turn, an offsetting currency loss on the bond

Implied forward exchange rates: (break-even point)

The formula is:

By comparing the yield curves in two currencies, we can derive the term structure of implied forward exchange rates and therefore, implied currency appreciation or depreciation.

ttr

ttrStF

1

1

7 - 48

Exhibit 7.7: Yield Curves in Different Currencies in 2007

7 - 49

The risk on a foreign bond investment has two major sources: Interest rate risk: the risk that foreign yields

will rise. Currency risk: the risk that a foreign currency

will depreciate.

Credit risk should be taken into account for nongovernmental bonds.

Return and Risk on Foreign Bond Investments

7 - 50

The return from investing in a foreign bond has three components:

During the investment period, the bondholder receives the foreign yield.

A change in the foreign yield (Δforeign) induces a percentage capital gain/loss on the price of the bond.

A currency movement induces a currency gain or loss on the position.

Return = Foreign yield – D (foreign yield) + % currency movement

7 - 51

The expected return on a foreign bond is equal to the domestic cash rate plus a risk premium.

The risk premium equals the sum of:

The spread of the foreign bond yield over the domestic cash rate.

The percentage capital gain/loss due to an expected foreign yield movement, and

The expected percentage currency movement.

7 - 52

Currency-Hedging Strategies

Foreign investments can be hedged against currency risk by selling forward currency contracts for an amount equal to the capital invested.

The decision to hedge depends on return and risk considerations. Hedging will turn out to improve return on a foreign bond if the percentage currency movement is less than the cash rate differential (domestic minus foreign); otherwise hedging will not be advantageous, ex-post.

7 - 53

Hedged Return = Foreign yield – D (foreign yield) + Domestic cash rate

– Foreign cash rate

7 - 54

a risk premium equal to: Spread of the foreign bond yield over the

foreign cash rate, and Percentage gain/loss due to an expected foreign

yield movement

7 - 55

Currency-Hedging Strategies - Example

You are British and hold a U.S. Treasury bond with a full price of 100 and duration of 15. Its yield is 6 percent. The dollar cash rate is 3 percent and the pound cash rate is 4 percent. You expect U.S. yields to move down by 15 basis points over the year. Give a rough estimate of your expected return if you decide to hedge the currency risk.

7 - 56

Currency-Hedging Strategies - Example

SolutionHedged Return = Foreign yield – D (foreign yield)

+ Domestic cash rate – Foreign cash rate

Hedged Return = 6 – 15 (-0.15) + 4 – 3 = 9.25%

Risk premium = 9.25 – 4% = 5.25%

7 - 57

Floating Rate Notes (FRNs) FRNs are a major segment of the international

bond market.

FRNs represent a quarter of all Eurobonds, with issues in euros and dollars playing a dominant role.

Major issuers are financial institutions.

FRNs are generally indexed to LIBOR. The rate is called EURIBOR for euros.

The coupon on Eurobond FRNs is generally reset every semester or every quarter.

Structured Notes and FRNs

7 - 58

The coupon to be paid the next period is then set equal to the LIBOR plus a spread that has been fixed at the time of issue.

In other words, the coupon, C, that will be paid at time t is set at time t - 1(the previous coupon date) equal to the LIBOR rate, plus a fixed spread, m0

7 - 59

1.Motivation FRN prices behave quite differently from fixed-interest

straight bond prices, which adjust to fluctuations in the market interest rate. The price of a straight bond must go down if the market interest rate goes up, in order to maintain a competitive YTM.

This means that FRNs exhibit great price stability when compared with straight bonds.

The motivation for an investor to buy FRNs is to avoid interest rate risk

7 - 60

2. Valuing FRNs

(1) No Default Risk On Reset Date: we can show that the price of

the bond should always be 100 percent Between Reset Dates: Once the coupon is fixed

on a reset date, the bond tends to behave like a short-term fixed-coupon bond until the next reset date. FRN prices are more volatile just after the reset date

7 - 61

Exhibit 7.9: FRNs: The Stability of Reset Date Prices Midland Bank, May 1987

7 - 62

A company without default risk has issued a 10-year FRN at LIBOR. The coupon is paid and reset semiannually. It is certain that the issuer will never have default risk and will always be able to borrow at LIBOR. The FRN is issued on November 1, 2005, when the six-month LIBOR is at 5 percent. On May 1, 2006, the six-month LIBOR is at 5.5 percent.

1. What is the coupon paid on May 1,2006, per $1,000 bond?

2. What is the new value of the coupon set on the bond? 3. On May 2, 2006, the six-month LIBOR has dropped

to 5.4 percent. What is the new value of the FRN? (neglecting the past day)

7 - 63

(2) Default Risk FRNs cannot be valued as if they were fixed-

coupon bonds. Their future cash flows are uncertain

7 - 64

FRN - example

A perpetual bond is issued by a corporation rated A with an annual coupon set at yearly LIBOR plus a spread of 0.30 percent. Some time later, LIBOR is equal to 6 percent, and the market requires a spread of 0.60 percent for such an A corporation. Give an estimate of the bond value on the rest date using the “freezing” method.

7 - 65

FRN - example

With the “freezing” method,

The coupon is supposed to be fixed at:

C = 6% + 0.30% = 6.30%

The market-required yield is supposed to be fixed at

r = 6% + 0.6% = 6.6%

An approximation of the value of this perpetual FRN is:

%455.9560.6

30.6P

7 - 66

A structured note is a bond (note) issued with some unusual clause, often an option-like clause.

Issued by a name of good credit standing.

Can be purchased as investment grade bonds by most institutional investors.

Offer long-term options that are not publicly traded.

Structured Notes

7 - 67

Bull FRNBull FRN

Bull FRNs strongly benefit investors if interest rates drop.

An example of a bull FRN is a reverse (inverse) floater, set at a fixed rate minus LIBOR.

Motivation: For Investor, he can benefit markedly from a drop in market interest rates, which is very attractive,

7 - 68

Bear FRNBear FRN Description

Bear FRNs are notes that benefit investors if interest rates rise.

An example of a bear bond is a note with a coupon set at twice LIBOR minus 7%. Again, the coupon has a floor of 0%, which is attractive to the investor if LIBOR goes below 3.5%.

Motivation: The coupon will increase rapidly with a rise in LIBOR.

7 - 69

Exhibit 7.11: Characteristics of Bonds, Assuming a Drop in Market Interest Rates

7 - 70

Dual Currency Bonds A dual currency bond is a bond issued with

coupons in one currency and principal redemption in another.

Valuation: The value of a yen/dollar dual-currency bond can be broken down into two parts as follows: A stream of fixed coupon payments in yen: A dollar zero-coupon bond for the final dollar

principal repayment

7 - 71

Let’s consider the NKK bond described in Exhibit 7.3. It promise annual coupons of 8% on 20 billion yen and is redeemed in 10 years for $110.480 million. The current spot exchange is ￥ 181.02824 per dollar, so that $110.480 million is exactly equal to ￥ 20 billion. The yen yield curve is flat at 4%, and the dollar yield curve is flat at 12%.

What is the theoretical value of this dual-currency bond?

7 - 72

Currency Option BondsCurrency Option Bonds A currency option bond is one for which the coupons

and/or the principal can be paid in two, or more currencies, as chosen by the bondholder.

a British company issues a five-year pound/euro bond. Each bond is issued at 100 pounds and is repaid 100 pounds or 160 Euros. The annual coupon is 3 pounds, or 4.8 Euros.

7 - 73

It benefits the investor who can always select the stronger currency.

The interest rate set at issue is always lower than the yields paid on a single currency straight bond denominated in either currency.

7 - 74

Motivation:

They offer long-term currency play with limited risk

Institutional investors are often prohibited from directly buying derivatives. On the other hand, currency-option bonds are usually issued by good-quality issues and are therefore available to institutional investors who are attracted by the implicit currency play. Investors are willing to receive a lower yield in order to get the currency play.

7 - 75

Valuation: the value of this bond is the sum of The value of a straight bond The value of currency options.

7 - 76

TATA issues a one-year euro/pound currency-option bond with a coupon rate of 3%, It is issued for 100 pounds, pays a coupon of either 3 pounds or 4.8 euros, and is redeemed for either 100 pounds or 160 euros, at the option of the bondholder. Of course, the bondholder will require payment in euros if the exchange rate is below 1.6 at maturity of the one-year bond. The current spot exchange rate is 1.6 euros/pound, and the one-year interest rates are 6% in euros and 5% in British pounds. A one-year put pound, with a strike price of 1.6 euros per pound, is quoted at 0.015 pound. In other words, investor have to pay a premium of 0.015 pound to get the right to sell one pound at 1.6 euros. What is the fair market value of this currency-option

bond?

7 - 77

Collateralized debt obligation (CDO) A special type of structured note that allows

structuring the credit risk assumed on a portfolio of bonds.

A bank bundle together a set of bonds and sell the portfolio of bonds to a special purpose vehicle (SPV).

In turn the SPV securitizes the portfolio and issues a set of structured notes called “tranches” or “slices”.

7 - 78

Exhibit 7.12: Example of a CDO

7 - 79

标准 · 普尔（ S&P’s)公司的评级标准

级别 说明AAAAAABBBBBBCCCCCCD

还本付息能力极强还本付息能力很强还本付息能力强还本付息能力充分不断发生一些可能导致不安全的事件具有可能损害付息或还本能力的不利情况现时就有可能违约次于 CCC级次于 CCC级，即将被清算要违约的债券

7 - 80

穆迪（Moody’s)公司的评级标准

级别 说明

AaaAaABaBCaaCaC

判定为最高，风险程度小还本付息能力很强，但低于 Aaa还本付息能力强不断发生一些可能导致不安全的事件具有可能损害付息或还本能力的不利情况现时就有可能违约次于 CCC级次于 CCC级，即将被清算

7 - 81

我国债券信用级别设置

级别分类

级别划分 级别 说明

投资级

投机级

一等

二等

三等

AAAAAA

BBB

BBB

CCCCCC

有极高的还本付息能力 ,投资者没有风险很高的还本付息能力 ,投资者基本没有风险有一定的还本付息能力 ,经采取保护措施后有可能按期还本付息 ,投资者风险较低

还本付息资金来源不足 ,发债企业对经济形势变化的应变能力差 ,有可能延期支付 ,有一定风险还本付息能力脆弱 ,投资风险较大还本付息能力差 ,投资风险大

还本付息能力很低 ,投资风险极大还本付息能力极低 ,投资风险最大濒临破产 ,到期没有还本付息能力 ,绝对有风险

7 - 82

日计法

半年付息一次的债券每年的付息日为 4月 7 日和 10月 7 日。假设某一个投资者购买该债券结算日为 10月 15 日，该年不是闰年，请用日计法中的两种方法分别计算剩余计息期商数。

久期和凸度的推导nn i

M

i

c

i

c

i

cP

)1()1(....

)1()1( 21

)1()1()1(

....)1(

2

)1()1(

1

)1()1(....

)1(

2

)1( 211132

nnnn i

nM

i

nc

i

c

i

c

ii

nM

i

nc

i

c

i

c

i

P

Pi

nMi

ncic

ic

iM

ic

ic

ic

inM

inc

ic

ic

Dnn

nn

nn )1()1(....

)1(2

)1(

)1()1(....

)1()1(

)1()1(....

)1(2

)1( 21

21

21

)2()1()1(

....)1(

2

)1( 21 nn i

nM

i

nc

i

c

i

cDP

DP

ii

P

)1(

1

久期（未来各期现金流与 P的比值作为权数）

债券价格

7 - 84

久期D

ii

PP

)1(

iPP

i

DD

1)1(

久期修正久期

i

债券价格对利率微小变化时的敏感度—利率弹性？

债券价格对利率微小变化 时，债券价格变化

P

P

P

修正久期价格久期 Di

PD

7 - 85

误差项

22

2

2

1i

i

Pi

i

PdP

Pi

pi

Pi

pi

P

p

dP 误差项

22

2 1

2

11

0,02

2

i

P

i

P凸性定义

-1*价格久期

价格凸性函数

-1*修正久期

凸性系数

7 - 86

时债券价格变化情况利率变化 i

2

2

iiD1

iiD1

凸性系数债券价格变动比例

价格凸性系数债券价格变动金额

修正久期

价格久期