part iii : debt securities - kocw

Part III : Debt Securities

o Bond Prices and Yields

o Managing Bond Portfolios

Chapter 10

Bond Prices and Yields

Bond Characteristics

A long-term debt instrument in which a

borrower agrees to make payments of

principal and interest, on specific dates, to the

holders of the bond.

Par value – face amount of the bond, which is paid at maturity

Coupon interest rate – stated interest rate (generally fixed)

paid by the issuer. (Floating Rate Bond vs. Zero Coupon Bond)

Maturity date – years until the bond must be repaid.

Yield to maturity - rate of return earned on

a bond held until maturity (also called the “promised yield”).

Different Issuers of Bonds

Treasury Bonds and Notes

Corporations

Municipalities

International Bonds

Eurobonds

Foreign Bonds (Yankee bonds, Samurai bonds, Bulldog bonds, Arirang bonds)

Secured or unsecured

Call provision(수의상환권): bonds that may be repurchased by the issuer at a specified call price during the call period.

Convertible provision: A bond with an option allowing the bondholder to exchange the bond for a specified number of shares of common stock in the firm.

CB, EB, BW

Put provision (putable bonds): A bondholder has an option to extend or retire the bond.

Floating rate bonds: coupon rates periodically reset according to a specified market rate.

Provisions of Bonds

Inverse floaters Coupon interest↓ when market interest rate ↑

Asset-backed bonds Walt Disney, coupon rates tied to the film performance

Pay-in-kind bonds Pay interests either in cash or in additional bonds

Catastrophe bonds Tokyo Disney land, no payment in case of earthquake, transferring “catastrophe risk” from insurance co. to capital mkts

Indexed bonds Payments tied to a price index or the price of a commodity

U.S. Treasury Inflation Protected Securities (TIPS)

Innovation in the bond markets

(EX.)U.S. Treasury Inflation Protected

Securities (TIPS) A newly issued TIPS bond with a three year maturity, par

value of $1000, and a coupon rate of 5%. Assume

annual coupon payments.

Innovation in the bond markets

Bond Pricing

n

n

2

2

1

1

k)(1

CF ...

k)(1

CF

k)(1

CF Value

0 1 2 n k

CF1 CFn CF2 Value

...

ㅇ The value of any financial asset is simply the present

value of the cash flows the asset is expected to produce.

T)PVIF(k,*FVT)PVIFA(k,*INT

)1()1(1

k

FaceValue

kINTP T

T

tt

tB

PB = Price of the bond

INTt = interest or coupon payments

T = number of periods to maturity

K = discount rate or yield to maturity (YTM)

Bond Pricing (cont’d) ㅇ 채권(bond)의 수익구조: 이자 + 액면가

- 일정만기 내에 규칙적으로 발행금리(coupon rate)에 해당하는 이

자를 지급하고 만기 시 액면가(face value)를 지급

What is the opportunity cost of debt capital?

The discount rate (k ) is the

opportunity cost of debt capital, and is

the rate that could be earned on

alternative investments of equal risk.

k = k* + IP + MRP + DRP + LP

Bond Pricing (cont’d)

현금흐름예상되는시점에

만기수익률할인율만기

액면가액표면이자율채권가격

:

)(,:),(:

)(:,:,:

)1()1()1()1(1

0

1t20

tCF

YTMkmaturityn

valuefaceFiB

k

CF

k

F

k

Fi

k

Fi

k

FiB

t

n

tt

nn

n

n

2

2

1

1

k)(1

I ...

k)(1

I

k)(1

I value sBond'

FNTNTNT

intt= i*1,000=80

P = 1000

T = 10 years

r = 6%

Price?: 10-yr, 8% Coupon, FV = $1,000

)03.1(

1000

03.1

40

)06.1(

1000

06.1

80

20

20

1

10

10

1

ttBsa

ttBa

P

P


6-14 Financial Management_Prof. Chung

Using a Financial Calculator to Value a Bond

INPUTS

OUTPUT N I/YR PMT PV FV

10 6 80 1000

-1147.20

i=8% kd=6%

INPUTS

OUTPUT N I/YR PMT PV FV

20 3 40 1000

-1148.77

i=4% kd=3%

PB=80*PVIFA(6%,10)+1000*PVIF(6%,10)=80*7.3601+1000*0.5584

PB=40*PVIFA(3%,20)+1000*PVIF(3%,20)=40*14.8775+1000*0.5537

ㅇ Bonds with Semiannual Coupons

ㅇ Bonds paying interests m times/year

n

tt

nn k

CF

k

F

k

Fi

k

Fi

k

FiB

2

1t2220

)2/1()2/1()2/1(

2/

)2/1(

2/

2/1

2/

)4,(quarterly year per payments interest of number:

)/1()/1()/1(

/

)/1(

/

/1

/

1t20

mm

mk

CF

mk

F

mk

mFi

mk

mFi

mk

mFiB

nm

tt

nmnm


ㅇ Bond pricing between coupon dates (cont’d)

(ex.) issued on Jan.1, 2003, maturity of 3 years (maturing on

Dec. 31, 2005), FV: 1,000,000; coupon rate: 5%, quarterly

interest payment, as of today (May 10, 2003) current interest

rate : 6%

dates payment interest next the and previous the between days of number:

date payment interest next the and date trading the between days of number:

)/1()/1(

/

)1(

1

0t0

q

d

mk

F

mk

mFi

q

d

m

kB

T

Tt

196,981)4/06.01(

000,000,1

)4/06.01(

500,12

)91

51

4

06.01(

110

0t100

tB


Prices and Yields (required rates of

return) have an inverse relationship.

When yields get very high the value of the

bond will be very low.

When yields approach zero, the value of

the bond approaches the sum of the

cash flows.

Bond Prices and Yields

)1()1(1 k

FaceValue

k

INTP T

T

T

t

t

tB

Figure 10.3 The Inverse Relationship

Between Bond Prices and Yields

10-18

Yield to Maturity (YTM)

The rate of return earned on a bond if it is

held to maturity

Interest rate that makes the present value

of the bond’s payments equal to its price.

Solve the bond formula for YTM

)1()1(1 YTM

FaceValue

YTM

INTP T

T

T

t

t

tB

Bond Yields

Bond Yields (cont’d)

10.91%YTM

YTM)(1

1,000

YTM)(1

90 ...

YTM)(1

90 $887

YTM)(1

M

YTM)(1

INT ...

YTM)(1

INT V

10101

NN1B

(YTM example) a 10-year, 9% annual

coupon bond, sells for $887, a face value

of $1,000

6-21 Financial Management_Prof. Chung

INPUTS

OUTPUT

N I/YR PMT PV FV

10

10.91

90 1000 - 887

Using a Financial Calculator to Solve for the YTM


%09.610.03)(1:EAR 6%,:APR year,-halfper 3%YTM

YTM)(1

1,000

YTM)(1

40 ...

YTM)(1

40 $1,276.76

YTM)(1

M

YTM)(1

INT ...

YTM)(1

INT V

2

60601

NN1B

(YTM example) a 30-year, 8% semiannual

coupon bond, sells for $1,276.76, a face

value of $1,000

NN1B)Y(1

Price Call

)Y(1

INT ...

)Y(1

INT V

TCTCTC

YTC (Yield to Call): The rate of return on a

bond if it is called before its maturity


551 )Y(1

1,100

)Y(1

90 ...

)Y(1

90 $887

TCTCTC

(YTC example1) a 10-year, 9% annual

coupon bond, sells for $887, a face value

of $1,000, callable in 5 years at a call price

of $1,100 (YTC=13.79%)

(YTC example2) :

A 20-year maturity 9% coupon bond paying coupons

semiannually is callable in five years at a call price

of $1,050 (face value $1,000). The bond currently

sells at a yield to maturity of 8%. What is the YTC?


%58.710.0372)(1:EAR 7.44%,:APR year,-half per 3.72%YTC

96.098,1)2/08.0(1

1000

)2/08.0(1

45 ...

)2/08.0(1

45 V

YTC)(1

1050

YTC)(1

45 ...

YTC)(1

45 V

2

40401B

10101B

Find the current yield for a 10-year, 9% annual coupon bond that sells for $887, and has a face value of $1,000.

Current yield = $90 / $887 = 0.1015 = 10.15%

CY (Current Yield): The annual interest

payment on a bond divided by the bond’s

current price


The price path of a bond

What would happen to the value of this bond if its coupon rate are different at 10%, at 13%, or at 7%? (FV:$1,000;Kd=10%;N=15)

Years

to Maturity

1,228

1,000

772

15 12 9 6 3 0

i = 13% (premium bond)

i = 7% (discount bond)

i = 10%.

VB

Bond values over time

At maturity, the value of any bond must equal its par value.

If kd remains constant:

The value of a premium bond would decrease over time, until it reached $1,000.

The value of a discount bond would increase over time, until it reached $1,000.

A value of a par bond stays at $1,000.

Rating companies

Moody’s Investor Service

Standard & Poor’s

Duff and Phelps

Fitch

한신평, 한기평, NICE신용평가

Rating Categories Investment grade (AAA/Aaa – BBB/Baa)

Speculative grade: Junk bonds (BB/Ba - )

Default Risk and Ratings

Coverage ratios

Times-interest-earned ratio (=EBIT/interest)

Leverage ratios

Debt-to-equity ratio

Liquidity ratios

Current ratio (CA/CL); Quick ratio

Profitability ratios: firms’ overall financial health

ROA; ROE

Factors Used by Rating Companies

Term structure – relationship between YTM (yield to maturity) and maturities.

The yield curve is a graph of the term structure.

Upward-, downward-sloping, humped shape and flat

YTM(%)

Term Structure of Interest Rates

Expectations Hypothesis

Liquidity Preference

Upward bias over expectations

Market Segmentation

Preferred Habitat

Theories of Term Structure

Expectations Theory

Observed long-term rate is a function of today’s short-term rate and expected future short-term rates.

Forward rates that are calculated from the yield on long-term securities are market consensus expected future short-term rates.

n and 1)-(n periodsbetween rateinterest short future expected:)(

market in the observed periodsn ofmaturity with bond aon YTM:

))](1())(1))((1)(1[()1(

,1

,13,22,11

nn

n

nn

n

n

rE

r

rErErErr

※ Returns to Two 2-year Investment

Strategies

fn = one-year forward rate for period n

yn = YTM for a security with a maturity of n

)1()1()1( 1

1 n

n

n

n

n fyy

※ Forward Rates from Observed Rates

(ex) y4 = 9.993% y3 = 9.660% f4 = ?

(1.0993)4 = (1.0966)3 (1+f4)

(1.46373) / (1.31870) = (1+f4)

f4 = .10998 or 11%

Long-term bonds are riskier.

Investors will demand a premium for the risk

associated with long-term bonds.

The yield curve has an upward bias built into the

long-term rates because of the risk premium.

Forward rates contain a liquidity premium and

are not equal to expected future short-term rates.

Liquidity Preference Theory

PremiumLiquidity :

))(1())(1)(1()1(

121

1,112,11

n

nnn

n

n

LLL

LrELrErr

Liquidity Premiums and Yield Curves

Yields

Maturity

Liquidity

Premium

Expectation

Theory

Liquidity premium

Theory

Short- and long-term bonds are traded in distinct markets.

Trading in the distinct segments determines the various rates.

Observed rates are not directly influenced by expectations.

Market Segmentation

Maturity

YTM

S-T M-T L-T

part iii : debt securities - kocw

Documents