The Capital Markets: Bonds Prof. Ian Giddy New York University New York University/ING Barings

The Capital Markets:Bonds

Prof. Ian GiddyNew York University

New York University/ING Barings

Copyright ©1998 Ian H. Giddy Bonds 2

The Bond Markets

Treasuries Corporates International Bonds Market Risk Credit risk


Fixed-Income Benchmarks

02/13/97 - 11:06 PM ET

Money rates

Treasury securities

Thu. 6-mos. ago Yr. ago3-mo. T-bill discount 4.98% -0.02 5.05% 4.77%6-mo. T-bill discount 4.99% -0.05 5.12% 4.71%10-yr. note 6.31% -0.10 6.60% 5.70%30-yr. bond 6.62% -0.08 6.80% 6.16%

Savings rates, latest 7-day averages

Thu. 6-mos. ago Yr. agoMoney mut. funds 4.81% 4.79% 4.84%Tax-free money funds 2.83% 2.96% 2.82%Bank money market 2.60% 2.64% 2.74%6-mo. CDs 4.76% 4.73% 4.59%1-yr. CDs 5.05% 5.07% 4.69%5-yr. CDs 5.57% 5.67% 5.02%

Mortgage rates

Thu. 6-mos. ago Yr. ago30-yr. fixed (FHLMC) 7.65% 7.88% 6.94%15-yr. fixed (FHLMC) 7.14% 7.39% 6.44%Adj. rate (FHLMC) 5.52% 5.81% 5.19%1-yr. Treas. ARM index(*) 5.53% 5.60% 4.85%11th dist. ARM index 4.842% 4.809% 5.059%Fannie Mae 30 year commitments 30 days, 7.77 60 days, 7.84

Other rates

Thu. 6-mos. ago Yr. agoPrime lending 8.25% 8.25% 8.25%Fed. discount 5.00% 5.00% 5.00%Federal funds 5.06% 5.63% 5.38%


Money Market Instruments

Treasury bills Certificates of deposit Commercial Paper Bankers Acceptances Eurodollars Repurchase Agreements (RPs) and Reverse

RPs Federal Funds


The Eurocurrency Market and its Linkages

US Domestic German

Market EUR0CURRENCY MARKET Domestic Market

Euro-Deutsche Mark

Eurodollar Market

Market Foreign

Exchange

Market Japanese

Euro-Yen Domestic

Market Market

Euro-Commercial Euro-Floating Rate Straight

Paper Market Note Market Eurobond Market


Instruments and Markets

BondsBonds

GovernmentsGovernments CorporatesCorporates



GovernmentsGovernments

TreasuriesTreasuries Agencies, Mortgage-backed

Securities

Agencies, Mortgage-backed

Securities


Benchmark Bonds


The Yield

Yield to maturity combines coupons and capital gains - all cash flows.

The yield to maturity on any bond, is the rate that will make the present value of the cash flows from the investment equal to the price of the investment.


Prices and Yields in the Wall Street Journal

Rate Mat.Mo/yr

Bid Asked Chg AskYld

5 1/85...7 7/88 1/2...7 1/86 1/4

May 94nJun 94n

Feb 95-00Feb 00n

Feb 23Aug 23

100:01100:04

101:14107:11

95:0685:21

100:03100:06

101:16107:13

95:0885:23

...+1

+1+7

+16+14

2.443.35

5.716.92

7.537.46

Monday, May 16, 1994


Yield To Maturity (YTM)

YTM is the rate of return investors earn if they buy a bond at a specific price and hold it until maturity

YTM is also the discount rate that causes the bond’s current price to just equal the present value of its interest payments and par value.

Find y such that LHS=RHS:

PC

yCy

My n0 1 21 1 1

( ) ( )

...( )


The Yield Curve

Maturity(years)

Yield toMaturity

12345678910

5.426.026.426.696.826.927.077.167.247.23


Yield Curves

Yields

Maturity

Upward Upward SlopingSloping

Downward Downward SlopingSloping


Theories of Term Structure

Expectations Liquidity Preference

Upward bias over expectations Market Segmentation

Preferred Habitat


Yield Has Problems

Reinvestment assumption: YTM assumes we reinvest at the same yield.

Coupon effect: different bonds with the same maturity, all fairly priced, have different yields.

Callable bonds have no defined maturity.


Yield of a Zero

Zero-coupon bonds simply pay the principal at maturity, no interest, so find k such that:

Example: 10-year US Treasury zero with face value $1,000 priced at $399.85: k=9.60%

BM

k n0 1

( )


Better Bond Pricing

The method used previously discounts all the bond's cash flows at a single rate, the yield to maturity.

But as the yield curve shows, different yields apply to different maturities. The best way to look at the yield for a particular maturity is to find out the yield on a zero-coupon bond for that maturity.

Then we can find the PV of each cash flow (coupons & principal) by discounting each cash flow at the corresponding zero-coupon rate. (Or, equivalently, by multiplying by the corresponding discount factor.)


Better Bond Pricing

So we need to find out the z's: the zero-coupon bond yields. There are two ways of doing this.

B o n d V a l u e = 1C

( 1 + 1z 1) + 2C

( 1 + 2z 2) + 3C

( 1 + 3z 3) + + nM

( 1 + nz n)

Let us call the zero-coupon rate for each maturity zt. Then the value of a bond should be the sum of the PVs of each of the cash flows.


The Zero Approach

Use zero-coupon rates to value each cash flow - then add them!

Where can we get the z’s? One place is from the Treasury strip market.

BCz

Cz

Mzn

n0

1

1

2

21 1 1

( ) ( )...

( )


Treasury Strips in the Wall Street Journal

Mat. Type Bid Asked Chg AskYld

Aug 94Nov 94

...May 20May 20

...Aug 23Aug 23

cici

cibp

cibp

98:3197:21

13:2213:25

11:3112:07

98:3197:22

13:2513:29

12:0212:10

+1+1

+4+4

+4+4

4.424:83

7.777.74

7.367.29

Monday, May 16, 1994


Bond Lego

To value this bond, break it up into its component cash flows - e.g. 1st coupon of (5 3/4)/2 in Feb 1996, and so on...

Then use zero’s to see what each is worth, and add the total.

In general, breaking up a security into its component parts is an excellent path to valuation.

R ate6

M aturity, M o/YrD ec 97

B id Asked99:29 99:31

Ask Y ld.6.01

A Treasury Noteas quoted in the W all Street Journal M onday, July 24, 1995


Identifying Undervalued Securities

BondsBonds

Spot

Rates

Spot

Rates“Correct”

pricing

“Correct”

pricingCompare

with actual

Compare

with actual



BondsBonds

GovernmentsGovernments CorporatesCorporates


Corporate Bonds: Spread over Benchmark


Corporate Bonds

Legal Aspects Of Corporate BondsA Bond Indenture is a contract between the

borrowing corporation and the bondholders, stating the conditions under which a bond has been issued

Common features of bond indentures include: Sinking-Fund Requirements Security Interest

A Trustee is a third party paid to protect the bondholders' interest


Provisions of Bonds

Secured or unsecured Call provision Convertible provision Put provision (putable bonds) Floating rate bonds Sinking funds


Default Risk and Ratings

Rating companiesMoody’s Investor ServiceStandard & Poor’sDuff and PhelpsFitch

Rating CategoriesInvestment gradeSpeculative grade


Bond Credit Ratings

Moody’sStandard &Poor’s Interpretation

AaaAa

AAAAA

High-quality debt instruments

ABaa

ABBB

Strong to adequate ability topay principal and interest

BaBCaaCaC

BBBCCCCCC

Ability to pay interest andprincipal speculative

D In default


Factors Used by Rating Companies

Coverage ratios Leverage ratios Liquidity ratios Profitability ratios Cash flow to debt


Protection Against Default

Sinking funds Subordination of future debt Dividend restrictions Collateral


AT&T’s Cost of Debt

After the divestiture of AT&T analysts lowered the corporation's bond rating due to the uncertainty of the outcome of the massive breakup. While AT&T eventually regained its former top rating, for the interim period AT&T bond prices fell... and its cost of debt was higher as a result of investors increasing their required rates of return on AT&T bonds.



Corporate BondsCorporate Bonds

DomesticDomestic InternationalInternational


International Capital Markets The Eurobond Market is the market for bonds issued

outside the country of the currency The Foreign Bond Market is one in which a foreign

corporation or government issues bonds in a domestic market in the local currency

An International Equity Market has emerged that allows corporations to sell large blocks of shares simultaneously to investors in several different countries

Major Securities Markets


International Bond Markets are Linked

Issuers and investors compare terms in the domestic and Eurobond markets, which are linked across currencies via currency swaps

BONDMARKETSWITHINCOUNTRYOFCURRENCY

BONDMARKETSOUTSIDECOUNTRYOFCURRENCY

CurrencySwaps

Long-datedForwardExchange

Domestic US

- Gov't- Corporate

ForeignBonds

"Yankee"

DomesticJapanese

- Gov't- Corporate

ForeignBonds

"Samurai"

EurodollarBond Market

EuroyenBond Market


Foreign Bonds

A foreign bond is a bond issued in a host country's financial market, in the host country's currency, by a foreign borrower

The three largest foreign bond markets are Japan, Switzerland, and the U.S., representing issuance of about $40 billion in bonds annually


Private Placements and Rule 144A

The private placement exemption from registration and disclosure is extended to Eurobonds as long as the U.S. investors meet the following requirements:They are large and sophisticatedThere are only a few investorsThey have access to information and analysis similar

to that which would ordinarily be contained in a registered offering prospectus

They are capable of sustaining the risk of losses, andThey intend to purchase the bonds for their own

investment portfolios, and not for resale.


Characteristics of Eurobonds

Issued outside country of currency Not subject to domestic registration or disclosure

requirements In most cases take form of private placements Placed through syndicates in many countries who sell

principally to nonresidents Bonds are structured so as to be free of withholding

tax Bearer form

But... Eurobonds usually influenced de facto by government

and banks of country of currency


Key Dates in the Issuance of a Eurobond

Issuance need oropportunity identified

Announcement ofEurobond issue

Offering day:Eurobond issued

Closing day:Eurobonds delivered,

Issuer gets money

Issuerdiscussesdeal withleadmanager

Syndicateformed,bonds"presold"prior tofinal terms

Finalterms,bonds soldby sellinggroup toinvestors


Key Players in the Issuance of a Eurobond

MANAGERSUNDER-

WRITERS

SELLING

GROUP


A Day in the Life...

NEW INTER NA TIONAL BO ND ISSUES

Bo rrowerBo rrower Amou nt m .Amou nt m . Cou pon %Cou pon % Pr icePr ice Mat ur ityMat ur ity FeesFees Boo k ru nn erBoo k ru nn er

Celworks Trust 1990-1¶ (b) US$250 9 1/4 99.80 1998 1 7/8-1 5/8 Credit Suisse

Marui Corp* US$500 (4 3/ 8) 100 1995 2 1/4-1 1/2 Nomura

Holderbank (a) US$150 9 3/4 101 1994 1 3/8-1 CSFB

Battle Mountaingold US$100 7 1/2 100 2006 2 1/2-1 1/2 Merrill Lynch

SN CF FFr750 9 1/4 98.55 1997 1 7/8-1 1/4 CCF

Viennische Stadtsbank (a) L100bn 13 101 3/8 1994 1 3/8-7/8 BN L

Eurofima (a ) P ta10bn 12 5/8 101 1/8 1996 1 5/8-1 Deutsche Bank

Ir ish Bldg Soc . (a ) ¥15bn 7.4 101 5/8 1995 1 5/8-1 1/8 IBJ

Bank of Montreal (c ) ¥2.8bn 7 1/4 101 1/8 1993 1 1/8-5/8 Nippon Credit

¶Final te rms. *With equity warrants. Private placement. Convertible. (a) Non-callable. (b) Callable at par af ter 5 years. I f call notexercised, bond pays 50bp over Libor in last year . (c) Redemption linked to Nikkei stock index .

NEW INTER NA TIONAL BO ND ISSUES

Bo rrowerBo rrower Amou nt m .Amou nt m . Cou pon %Cou pon % Pr icePr ice Mat ur ityMat ur ity FeesFees Boo k ru nn erBoo k ru nn er

Celworks Trust 1990-1¶ (b) US$250 9 1/4 99.80 1998 1 7/8-1 5/8 Credit Suisse

Marui Corp* US$500 (4 3/ 8) 100 1995 2 1/4-1 1/2 Nomura

Holderbank (a) US$150 9 3/4 101 1994 1 3/8-1 CSFB

Battle Mountaingold US$100 7 1/2 100 2006 2 1/2-1 1/2 Merrill Lynch

SN CF FFr750 9 1/4 98.55 1997 1 7/8-1 1/4 CCF

Viennische Stadtsbank (a) L100bn 13 101 3/8 1994 1 3/8-7/8 BN L

Eurofima (a ) P ta10bn 12 5/8 101 1/8 1996 1 5/8-1 Deutsche Bank

Ir ish Bldg Soc . (a ) ¥15bn 7.4 101 5/8 1995 1 5/8-1 1/8 IBJ

Bank of Montreal (c ) ¥2.8bn 7 1/4 101 1/8 1993 1 1/8-5/8 Nippon Credit

¶Final te rms. *With equity warrants. Private placement. Convertible. (a) Non-callable. (b) Callable at par af ter 5 years. I f call notexercised, bond pays 50bp over Libor in last year . (c) Redemption linked to Nikkei stock index .

The Bond Markets:Risk

Prof. Ian GiddyNew York University

New York University/ING Barings


Risk and ReturnA positive relationship exists between risk and nominal

or expected return The actual return earned on a security will affect the

subsequent actions of investors Investors must be compensated for accepting greater

risk with the expectation of greater return

Return

Risk

Interest Ratesand Required Returns


FEMSA, the Mexican brewing company, recently borrowed 5-year US$ funds at 16% from American International Insurance Co.

On the same day, Heineken was able to issue a 3-year Eurobond at 8%.

Meanwhile, US government securities were paying the following interest rates: 1-year bills: 5% 3-year notes: 5.5% 30-year bonds: 6.5%

To what do you attribute these differences?

Why do Interest Rates Differ?


Risk

Bond RiskBond Risk

Market RiskMarket Risk Credit RiskCredit Risk


A $1 Investment in Different Types of Portfolios: 1926-1996

0.1

1

10

100

1000

10000

1925 1935 1945 1955 1965 1975 1985 1995

Index ($)

$4,495.99

$33.73

$13.54$8.85

$1,370.95

Small Company Stocks

Large Company Stocks

Long-Term Government Bonds

Treasury BillsInflation Year-End


Average Annual Returns and Risk Premiums: 1926-1996

Investment Average Return Risk Premium

Large company stocks 12.7% 8.9%

Small company stocks 17.7 13.9

Long-term corporate bonds 6.0 2.2

Long-term government bonds 5.4 1.6

U.S. Treasury bills 3.8 0.0

Source: © Stocks, Bonds, Bills and Inflation 1997 Yearbook™, Ibbotson Associates, Inc. Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved


Price Risk of Treasuries

Treasuries differ: Liquidity - traders quote wider bid-ask

spreads for illiquid bonds Duration - sensitivity of price to a change in

interest rates - is based on the bond’s coupon levels and maturity date (low duration means less risky)

Convexity - measures how duration changes with a change in rates (high convexity is desirable)


The Price-Yield Relationship

Bond prices and interest rates have an inverse relationship:

PRICE

YIELD(RATE)9%

100


The Price-Yield Relationship

But plotting price vs yield shows that the relationship is non-linear:

100

9%

Price of a 9% bond


Maturity

In general, the longer the maturity, the more sensitive is a bond’s price to interest-rate changes, other things being equal:

PriceRequiredyield

9%,5 year

9%,25 year

8%9%10%

104.0554100.000096.1391

110.7510100.000090.8720


The Coupon Effect...

But three bonds with the same maturity can have very different sensitivities, depending on their coupon levels:

PriceRequiredyield

9%,5 year

6%,5 year

0%,5 year

8%9%10%

104.05100.0096.13

91.8888.1384.56

67.5664.3961.39


Duration as a Measure of Price Sensitivity

Duration measures the % price change for a given change in yield:

PRICE

YIELD9%

100

The steeper the line, the more the price falls for a given rise in yield


Uses of Duration

Summary measure of length or effective maturity for a portfolio

Immunization of interest rate risk (passive management)Net worth immunizationTarget date immunization

Measure of price sensitivity for changes in interest rate


Managing Fixed Income Securities: Basic Strategies

Active strategyTrade on interest rate predictionsTrade on market inefficiencies

Passive strategyControl riskBalance risk and return


Active Bond Management: Swapping Strategies

Substitution swap Intermarket swap Rate anticipation swap Pure yield pickup Tax swap


Frequency Distribution of Returns on Common Stocks, 1926-1996

0

2

4

6

8

10

12

14

16

18

-55 -45 -35 -25 -15 -5 5 15 25 35 45 55

2

16

1

8

11

6

10

13

1 3

Number of Years

Return (%)


Returns, Standard Deviations, and Frequency Distributions: 1926-1996

Source: © Stocks, Bonds, Bills, and Inflation 1997 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.

– 90% + 90%0%

Average Standard Series Annual Return Deviation Distribution

Large Company Stocks 12.7% 20.3%

Small Company Stocks 17.7 34.1

Long-Term Corporate Bonds 6.0 8.7

Long-Term Government Bonds 5.4 9.2

U.S. Treasury Bills 3.8 3.3

Inflation 3.2 4.5


The Normal Distribution

Probability

Return onlarge companystocks

68%

95%

> 99%

– 3 – 48.2%

– 2 – 27.9%

– 1 – 7.6%

012.7%

+ 1 33.0%

+ 2 53.3%

+ 3 73.6%


Risk and Return of Stocks, Bonds and a Diversified Portfolio

Rate of Return

State Prob. Equity Bond Portfolio

Recession 1/3 -7% +17% +5%

Normal 1/3 +12% +7% +9.5%Boom 1/3 +28% -3% +12.5%

Expected Return 11% 7.0% 9.0%Variance 204.7% 66.7% 9.5%Standard Deviation 14.3% 8.2% 3.1%


The Correlation Between Stock and Bond Returns Covariance

= 0.3333(-7-11)(17-7) + 0.3333(12-11)(7-7) +0.3333(28-11)(-3-7)

= -116.67

Correlation

= -116.66 / 14.3(8.2) = -0.99

p R E R R E Rss

n

s e e s b b1

, ,( ) ( )

cov ,e b

e b


Portfolio Return and Standard DeviationGiven:

WS = 0.5 RS = 12% S = 25%

WB = 0.5 RB = 9% B = 12%

and S,B = 0.2

Rp = 0.5(12)+0.5(9) = 10.5%

P = [(0.5)2(25) 2+(0.5) 2(12) 2+2(0.5)(0.5)(25)(12)(0.2)]1/2

= (156.25+36+30)1/2

= (222.25) 1/2

= 14.91%


Portfolio Risk/Return Two Securities: Correlation Effects

Relationship depends on correlation coefficient

-1.0 < < +1.0 The smaller the correlation, the greater

the risk reduction potential If= +1.0, no risk reduction is possible


Case Study: A Portfolio

Weight E(R) Std DevGPU 0 0.1267 0.1715Teledyne 0.25 0.1396 0.2893Kodak 0.25 0.1402 0.3082Thai Fund 0 0.2075 0.3278Merck 0 0.1781 0.341ATT 0.5 0.1126 0.1606TOTAL 1


Portfolio Return Computation

ASSET RETURN WEIGHT PRODUCT1 GPU 12.67% 0.00% 0.00002 Teledyne 13.96% 25.00% 0.03493 Kodak 14.02% 25.00% 0.03514 Thai Fund 20.75% 0.00% 0.00005 Merck 17.81% 0.00% 0.00006 ATT 11.26% 50.00% 0.0563

TOTAL 100%Portfolio return 12.63%


Portfolio Risk Computation

CORRELATION MATRIXPRODUCT STD DEV GPU TeledyneKodakThai FundMerck ATT

GPU 0.1715 1Teledyne 0.2893 0.44 1Kodak 0.3082 0.17 0.65 1Thai Fund 0.3278 0.22 0.44 0.24 1Merck 0.341 0.35 0.15 0.13 0.03 1ATT 0.1606 0.68 0.4 0.43 0.23 0.6327 1

Portfolio Variance 3.48%Portfolio Std Deviation 18.66%


To Find the Risk-Return Possibilities, Vary the Proportions

A

E(r)

B


The Minimum-Variance Frontier of Risky Assets

“Efficient frontier”

Individual assets

Global minimum-variance portfolio

E(r)


Risk

Bond RiskBond Risk

Market RiskMarket Risk Credit RiskCredit Risk


Bond Credit Ratings

Moody’sStandard &Poor’s Interpretation

AaaAa

AAAAA

High-quality debt instruments

ABaa

ABBB

Strong to adequate ability topay principal and interest

BaBCaaCaC

BBBCCCCCC

Ability to pay interest andprincipal speculative

D In default


Credit Risk versus Market Risk


CreditMetrics Methodology

Establishes the exposure profile of each obligor in a portfolio.

Computes the volatility in value of each instrument caused by possible upgrades, downgrades, and defaults.

Taking into account correlations between each of these events, it combines the volatility of the individual instruments to give an aggregate portfolio volatility.


CreditMetrics Roadmap

Compute exposure profile of

each asset

Compute exposure profile of

each asset

Compute the volatility of value caused by

upgrades/downgrades and defaults

Compute the volatility of value caused by

upgrades/downgrades and defaults

Compute correlations

Compute correlations

Portfolio value-at-risk due to creditPortfolio value-at-risk due to credit

Exposures Value-at-risk due to credit Correlations


Volatilities from “Transition Matrix”


Construction of Volatility Across Credit Horizons


Defaults and Recovery Rates


A Picture of a BBB Bond’s Value Distribution


Calculating Mean and Standard Deviation


CreditMetrics

www.jpmorgan.com


The Bond Markets

Treasuries Corporates International Bonds Market Risk Credit risk



www.giddy.org



www.giddy.org

Ian Giddy

NYU Stern School of Business

Tel 212-998-0332; Fax 212-995-4233

[email protected]

http://www.giddy.org

Documents

The Capital Markets: Bonds Prof. Ian Giddy New York University New York University/ING Barings