Bond Prices and Yields
Chapter 2.2
Chapter 10
Learning Objectives




Understand the pricing characteristics of fixed
income securities (bonds, debt)
Calculate yields and prices of various types of
bonds
Understand how bond prices change across time
Evaluate the impact of default and credit risk on
bond pricing (CDSs, CDOs)
2
What is a Bond?

A bond is a legally binding agreement between
an issuer (borrower) and a bondholder (lender,
creditor)
3
Bond Terminology

Face value (F): The principal repaid at
maturity
 For

a corporate bond this is generally $1,000
Coupon rate: Determines the interest (Coupon)
payment
 This
is a Stated Annual Rate
 Corporate bonds generally pay semi-annually
Zero- coupon bond
 Yield to Maturity
 Rating

4
U.S. Treasury Bonds

Bonds and notes may be purchased directly
from the Treasury
 Note
maturity is 1-10 years; Bond maturity is 1030 years
Denomination can be as small as $100, but
$1,000 is more common
 Bid quote as 100:08

 Is
really 100 & 8/32
 So the price of the bond is price of 1,002.50

1,000 * 0.10025 = 1,002.50
5
Other Domestic Issuers
State, local governments (municipal bonds)
 Federal Home Loan Bank Board
 Farm Credit agencies
 Ginnie Mae, Fannie Mae, Freddie Mac

6
International Bonds

Foreign bonds
 Issued
by a foreign company, but are denominated
in the currency of the domestic market


EX: French firm issuing dollar denominated debt in the
US
Eurobonds
 Issued
by a foreign company and denominated in
the currency of the foreign firm

EX: French firm issuing Euro denominated debt in the
US
7
Corporate Bonds

Callable bonds
 The

Convertible bonds
 Can


issuer can repurchased the bond before maturity
be exchanged for firm’s shares
Pre-specified conversion
Puttable Bonds
A
bond with an embedded put option
 Holder has the right to demand early repayment of the
principal

Floating-rate bonds
 Coupon
rate periodically resets
8
Bond Pricing
What is a bond worth?
 What cash flows do bondholders receive?

9
Bond Pricing
ParValue
C
PB  

T
t
(1 r )
t 1 (1 r )
T
PB = Price of the bond
Ct = interest or coupon payments
T = number of periods to maturity
r = discount rate appropriate to coupon payment
frequency
10
Coupon Bond Pricing: BA II plus
N = The number of coupon payments
 I/Y= The discount rate corresponding to the
coupon frequency
 PV = The price of the bond today
 PMT= The amount of the coupon payment
 FV = The principal that will be repaid

11
Bond Pricing Example
Price of a 30 year, 8% coupon bond,
semiannual. Market rate of interest is 10%.
60
$40
$1000
Price  

t
60
1.05
t 1 1.05
12
Valuing a Corporate Bond

DuPont issued a 30 year bonds with a coupon rate of
7.95%.
 Interest is




paid semi-annually
These bonds currently have 28 years remaining to
maturity and are rated AA.
The bonds have a par value of $1,000
Newly issued AA bonds with maturities greater than
10 years are currently yielding 7.73%
What is the value of DuPont bond today?
 What
are the coupon payments?
 What is the appropriate discount rate?
 How many periods?
13
Bond Prices and Yields

Yield-to-Maturity is the return that the bond is
offering if you bought it today and held it till
maturity
 Also

know as the Bond Equivalent Yield
YTM is determined by the riskiness of the bond,
which is a function of:
1.
Time to maturity

2.
Longer term bonds are riskier
Risk of default

Generally measured by bond ratings
14
Bond Prices & Yields Continued

Bond Prices and Yields have an Inverse
Relationship
15
Coupon Rate, Yields & Prices
 If
the Coupon rate = YTM, Price will be
Bond
 If
the Coupon rate > YTM, Price will be
Bond
 If
is selling
is selling
the Coupon rate < YTM, Price will be
Bond
is selling
16
Bond Prices and Yields
8% coupon, 30 year, S.A.
17
Bond Prices at Different Interest Rates

8% Coupon Bond (semi-annual)
18
Example

A bond has a coupon rate of 10% paid semiannually,
with three years till maturity. The six month market
rate is 4%.
 Find
the bond’s price today and after its next payment
 What
is the total 6-month return on the bond?
 What
is the total 6-month return if the market rate increases
(unexpectedly) to 5% per half year immediately after the
next payment?
19
Computing Yield to Maturity
Finding the YTM requires trial and error if you
do not have a financial calculator
 If you have a financial calculator, enter N, PV,
PMT, and FV,

 Remembering

the sign convention
PMT and FV need to have the same sign, PV the
opposite sign
20
Yield to Maturity Example

Suppose an 8% coupon, 30 year bond is selling for
$1276.76. What is its YTM?
N
 I/Y
 PV
 PMT
 FV
=
=
=
=
=
What is the 6 month rate? SAR? EAR?
 Again Remembering the sign convention

21
YTM Example
What is the YTM of a 20-year bond with an
8% coupon if the price is:
A. $950

B. $1,000
C. $1,050
22
Bond Yields: YTM vs. Current Yield

Yield to Maturity
 Bond’s

Current Yield
 Bond’s

annual coupon payment divided by the bond price
When bonds sell at a premium


internal rate of return
Coupon rate > Current yield > YTM
When bonds sell at a discount

Coupon rate < Current yield < YTM
23
Yield to Call

The return an investor would earn if they held
the bond until the call date
 Like
Yield to Maturity, but assumes that the bond
is called
Calculated like yield to maturity
 Time until call replaces time until maturity;
call price replaces par value

24
Yield to Call Example

You buy a bond with 20 years till maturity, a
$1,000 face value and 8% coupon paid semiannually, for $900. What is the YTM?

If the bond is callable in 5 years for 103% of
face, what is the Yield to Call?
25
Yield to Call Example

A 30-year bond with an 8% coupon is callable
in 5 years with a call price of $1,100. The bond
currently sells at a yield to maturity of 7%.
 What
is the yield to call?
 What is the yield to call if the call price is $1,050?
 What is the yield to call if the call price is $1,100,
but the bond can be called in 2 years?
26
Interest Rates and Bond Prices
 If
interest rates fall:
The
price of a normal bond will ________
The price of a callable bond will ________
 Hint:
what will the issuing firm do?
27
Yield to Call
If interest rates fall, price of straight bond can
rise considerably.
 The price of the callable bond is flat over a
range of low interest rates because the risk of
repurchase (being called) is high.
 When interest rates are high, the risk of a call
is negligible and the values of the straight and
the callable bond converge.
 Bonds selling at a Premium are more likely to
be called than bonds selling at a Discount.

28
Bond Prices: Callable and Straight Debt
8% coupon, 30 years
29
YTM versus Return
YTM assumes that coupons are reinvested at
the YTM, but what if they aren’t?
 Realized Compound Return

 This
is the return earned when coupon payments
are reinvested at a rate other than YTM


Grow coupons till maturity then calculate return
Horizon analysis
 Analysis
of bond returns over multiyear, based on
forecasts of bond’s YTM and investment options

Reinvestment rate risk
 What
will coupons earn
30
FV of Invested Funds: 2 year 10% bond
31
Realized Compound Return
You buy a bond for $900, with 3 years till
maturity. The face value is $1,000 and the
coupon rate is 10% paid annually. What is the
YTM?
 If you are able to earn 9% on your reinvestments what is your Realized Compound
Return?

32
Realized Compound Return
Example 2
Which bond offers the highest expected rate of return
over the next 5-years?

Bond 1: 7% (annual) 30-year bond priced at $867.42.

Bond 2: 6.5% (annual) 20-year bond price at $879.50.

In 5 years E(YTM) are: 25yr = 8%, 15yr = 7.5%

Analyst expects that coupons will be invested in
short-term securities at 6%
33
Bond Price Over Time: Market rate is constant
34
YTM vs. HPR
YTM



YTM is the average
return if the bond is held
to maturity.
YTM depends on
coupon rate, maturity,
and par value.
All of these are readily
observable.
HPR



HPR is the rate of return over
a particular investment
period.
HPR depends on the bond’s
price at the end of the holding
period, which is unknown
HPR can only be forecasted.
35
Zero Coupon Bond
Zero-coupon bond: Carries no coupons,
provides all return in form of price appreciation
 STRIPS: Separate Trading of Registered
Interest and Principal of Securities

 Broker
ask Treasury to treat each coupon payment
as an individual Zero-coupon bond
36
Zero Example

A newly issued zero-coupon bond with a 20year maturity, a yield to maturity of 8%, and a
face value of $1,000.
 What
is the price in year 1?
 What
is the price in year 10?
 What
is the price in year 19?
37
Price of a 30-Year Zero-Coupon Bond over Time
38
Default Risk and Bond Pricing

Rating Agencies:
 Moody’s
Investor Service, Standard & Poor’s,
Fitch

Rating Categories
 Highest
rating is AAA or Aaa
 Investment
grade bonds are rated BBB or Baa
and above
 Speculative
grade/junk bonds have ratings
below BBB or Baa.
39
Default Risk Determinants



Coverage ratios: Company earnings to fixed costs
Leverage ratio: Debt to equity
Liquidity ratios
 Current:
Current assets to current liabilities
 Quick: Assets excluding inventories to current liabilities


Profitability ratios: Measures of RoR on assets or
equity
Cash flow-to-debt ratio: Total cash flow to
outstanding debt
40
Financial Ratios and Default Risk by Rating
Class
41
Bondholders Beware:
names changed to protect the guilty

Marriot Inc
 Owes

$1 billion and has $500 million in assets
Management creates a new firm Marriot Co
 Every

Inc shareholder receives shares in Co
The same shareholders own both firms
Inc sells its $500m in assets to Co for $1.00
 Co has $499,999,999 in assets and no debt
 Inc has $1 in assets and $1b in debt

 How
happy are debt holders?
42
Bond Indentures

Sinking funds:
 Issuer
is required to periodically repurchase a portion of the
outstanding bonds before maturity

Subordination of future debt:
 Any

subsequently issued debt will have a lower priority
Dividend restrictions:
 Force

firm to retain assets rather than pay dividends
Collateral:
A
particular asset bondholders receive if the firm defaults
 Debt that is issued without collateral is known as
Debenture
43
Default Risk and YTM

YTM is based on promised payments

However, corporate bonds are subject to risk of
default, the promised yield to maturity may not
be equal to the expected yield to maturity.

We can measure the default premium
(return investors demand to hold bonds that
could default) as the difference between
stated YTM and the yield on similar treasury
bonds
44
Promised vs Expected Example


Consider a one-year bond that promises a coupon rate
of 8% (annual) and has a principal (par value) of
$1,000. Further assume the bond is currently trading
for $850. What is the promised yield to maturity?
Assume there is a 40% probability of default on this
bond and if the bond defaults, the bondholders will
receive only 60% of the principal and interest owed.
What is the expected YTM on this bond?
45
Yield Spreads:10 Yr Corporate and Treasury Bonds
20
Aaa -rated
18
Baa-rated
B-rated
14
12
10
8
6
4
2
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
0
1997
Yield spread (%)
16
46
Credit Default Swaps

CDS act like an insurance policy for debt
buyers
 Intended
to allow lenders to buy protection against
losses on large loans
CDS buyer pays annual premiums.
 CDS issuer agrees to buy the bond in default
or pay the difference between par and market
values to the CDS buyer.

47
Credit Default Swaps Other Uses

Institutional bondholders, e.g. banks, used
CDS to enhance creditworthiness of their loan
portfolios, to manufacture AAA debt.

CDS can also be used to speculate that bond
prices will fall.
 Speculating
on financial health of companies is an
increasingly popular use for CDS
 This
means there can be more CDS outstanding
than there are bonds to insure!
48
Prices of CDSs, U.S. Banks
49
Collateralized Debt Obligations (CDOs)

Major mechanism to reallocate credit risk in the
fixed-income markets


Mortgage-backed CDOs were a disaster in 2007-2009
Structured Investment Vehicle (SIV) often used to
create CDOs, less regulated and off balance sheet
 Allowed
commercial banks to remove risk from B.S.
lowering their capital requirements
 Use

short term borrowing to buy longer term
asset-backed securities,
Pools loans and creates tranches with different
default risk
50
CDO Example
Wells Fargo creates “SIV1” which buys 5,000
mortgages from Wells
 SIV1 issues $100 million in bonds with an
expected return of 15%, in 3 tranches A,B,C

A


($25m) is senior to B ($50m) which is senior to C
($25m)
No Default: A $2.5m(10%) B $7.5m(15%) C $5m(20%)
If there is default and interest collected drops to $11m
A
$2.5m(10%) B $7.5m(15%) C $1m(4%)
51
The Yield Curve

Graph of YTM as function of time to maturity
 Also
know as: Term Structure of Interest Rates
Yield
Corporate
Default Premium
Treasuries
Maturity
52
The Yield Curve
2 possible explanations for why YTM and
Maturity are related
1) Expectations Hypothesis

 Yields
to Maturity determined solely by
expectations of future short-term interest rates
 Idea: Buying and holding a long term bond has to
offer the same return as rolling over short term
bonds
53
Expectation Hypothesis
Current 1 year rate is 8%
 Expect next year’s 1 year rate to be 10%
 If I invest for 1 year (@8%) and roll it over for
another year (@10%) 1 make 18.8% HPR
 What must a 2 year investment offer me now to
make me indifferent between the two options?

54
Expectation Example
Year 1
1 Year Rate
Year 2
1 Year Rate
Year 3
1 Year Rate
Year 4
1 Year Rate
10%
12%
15%
9%
What must a 2 year investment offer today?
 What must a 3 year investment offer today?
 What must a 4 year investment offer today?

55
Forward Rates

If we reverse our analysis we can infer what the
market thinks the 1 year rate will be next year
 Forward
Rate: the inferred short term rate
(1+yn)n = (1+yn-1)n-1 * (1+fn)
 If the current 1 year rate is 9%, and the yield on
a two year bond is 12% what is the forward rate
for year 2?
 1.122 = 1.09 * (1 + Forward Rate)
56
Forward Rate Example
The current 1 year rate is 8%
 The current 2 year rate is 8.995%
 The current 3 year rate is 10.314%
 What does the market expect the 1 year rate to
be in two years?
 What does the market expect the 2 year rate to
be in one year?

 What
is the price of a two year $1,000 bond?
57
2) Liquidity Preference Theory
Investors demand a risk premium for longer
term investments
 Implies that the forward rate is not just the
expected future rate
 fn = E(rn) + Liquidity Premium

58
Innovation in the Bond Market

Indexed Bonds
 Treasury

Inverse Floaters
 Coupon

from specified assets used to service debt
Pay-in-kind bonds
 Issuers

rate falls when interest rates rise
Asset-Backed Bonds
 Income

Inflation Protected Securities (TIPS).
can pay interest in cash or additional bonds
Catastrophe Bonds
59
Principal and Interest Payments for a Treasury
Inflation Protected Security
3-year maturity
 Par=$1,000,
 4% coupon paid annually

60