T7.1 Chapter Outline
Chapter 7
Interest Rates and Bond Valuation
Chapter Organization
 7.1 Bonds and Bond Valuation
 7.2 More on Bond Features
 7.3 Bond Ratings
 7.4 Some Different Types of Bonds
 7.5 Bond Markets
 7.6 Inflation and Interest Rates
 7.7 Determinants of Bond Yields
 7.8 Summary and Conclusions
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Bond Valuations
In the bond market there are 2 basic situations:
 For a given bond and a given interest rate – what is the
bond worth – what should I pay for this bond?
 For a given bond and a price for that bond – what is the
yield to maturity (YTM) I will earn?
Basic premise – bonds are tradeable financial instruments
that change in value driven by a range of factors but in
large part by changing interest rates.
Irwin/McGraw-Hill
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T7.2 Bond Features
 Bond - evidence of debt issued by a corporation or a
governmental body. A bond represents a loan made by
investors to the issuer. In return for his/her money, the
investor receives a legaI claim on future cash flows of the
borrower. The issuer promises to:
Make regular coupon payments every period until the bond
matures, and
Pay the face/par/maturity value of the bond when it matures.
 Default - since the above mentioned promises are contractual
obligations, an issuer who fails to keep them is subject to
legal action on behalf of the lenders (bondholders).
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T7.2 Bond Features (concluded)
 If a bond has five years to maturity, an $80 annual coupon,
and a $1000 face value, its cash flows would look like this:
Time
0
Coupons
1
2
3
4
5
$80
$80
$80
$80
$80
Face Value
$ 1000
Market Price $____
 How much is this bond worth? It depends on the level of
current market interest rates. If the going rate on bonds
like this one is 10%, then this bond has a market value of
$924.18.
Irwin/McGraw-Hill
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T7.2 Bond Features (concluded)
 A bond has five years to maturity, an $80 annual coupon,
and a $1000 face value, its cash flows would look like this:
Time
Coupons
0
1
2
3
4
5
$80
$80
$80
$80
$80
Face Value
$ 1000
 Coupons - the stated interest payments made on the bond
 Face Value - (Par Value) - the principal amount of a bond
that is repaid at the end of the term
 Coupon rate - annual coupon divided by the face value
 Maturity - specified date at which the principal amount is
paid
Irwin/McGraw-Hill
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T7.2 Bond Value
 A bond has five years to maturity, an $80 annual coupon,
and a $1000 face value, its cash flows would look like this:
Time
0
Coupons
1
2
3
4
5
$80
$80
$80
$80
$80
Face Value
$ 1000
Market Value = ‘s
PV of the coupon payments (annuity)
+
PV of the principal (PV of a single cash flow)
Irwin/McGraw-Hill
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T7.2 Bond Value
 If a bond has five years to maturity, an $80 annual coupon,
and a $1000 face value, its cash flows would look like this:
Time
0
Coupons
1
2
3
4
5
$80
$80
$80
$80
$80
Face Value
$ 1000
Market Value with r @ 10% = ?
PV of the coupon payments (annuity) - $303.26
PV of the principal (PV of a single cash flow) - $620.92
=‘s $924.18
Irwin/McGraw-Hill
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T7.3 Bond Rates and Yields
 Consider again our example bond. It sells for $924.18, pays
an annual coupon of $80, and it matures in 5 years. It has a
face value of $1000. What are its coupon rate, current yield,
and yield to maturity (YTM)?

1. The coupon rate (or just “coupon”) is the annual
dollar coupon as a percentage of the face value:
Coupon rate = $80 /$1000 = 8%

2. The current yield is the annual coupon divided by
the current market price of the bond:
Current yield = $80 / 924.18 = 8.66%
Irwin/McGraw-Hill
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T7.2 Bond Yield to Maturity - YTM
 A bond has five years to maturity, an $80 annual coupon,
and a $1000 face value, its cash flows would look like this:
Time
Coupons
0
1
2
3
4
5
$80
$80
$80
$80
$80
Face Value
$ 1000
YTM - the market interest rate that equates a bond’s
present value of interest payments and principal
repayment with its price
If you paid $924.18 for this bond and received the above
cash flows - what is the YTM?
Irwin/McGraw-Hill
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T7.3 Bond Rates and Yields (concluded)
 3.
The yield to maturity (or “YTM”) is the rate that makes the
market price of the bond equal to the present value of its
future cash flows. It is the unknown r in the equation below:
$924.18 = $80  [1 - 1/(1 + r)5]/r + $1000/(1 + r)5
The only way to find the YTM (long hand) is by trial and
error:
a. Try 8%: $80  [1 - 1/(1.08)5]/.08 + $1000/(1.08)5 = $1000
b. Try 9%: $80  [1 - 1/(1.09)5]/.09 + $1000/(1.09)5 = $961.10
c. Try 10%: $80  [(1 - 1/(1.10)5]/.10 + $1000/(1.10)5 = $924.18
So, the yield to maturity is 10%.
Irwin/McGraw-Hill
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Bond Values and YTM
Let’s understand what has happened before going much
further........
• We have a 5 year bond that with a coupon of $80
• Face Value is $1000 - principal repayment in 5 years time
will be $1000
• Interest rates for 5 year bonds were about 8% when the
bond was issued - let’s assume this - so the bond would
have been issued at $1000
• interest rates change - 5 year interest rates move up to
the 10% level
The value of this bond has declined - because there are
competing products in the market place paying 10%
interest when this bond only pays 8% - to buy this bond
and still earn a 10% YTM I should only pay $924.18
What should we conclude? - bond values move up and
down in response to financial events - in this case a
change in interest rates
Irwin/McGraw-Hill
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Bond Values and Yields - what is the relationship?
 there is a relationship between the value of the bond and
rates of return (YTM) in market equilibrium

when interest rates change - we suddenly do not have market
equilibrium - to achieve equilibrium the values of existing
bonds in the marketplace need to shift to reflect the new
financial reality!

If interest rates move up - bond values decline
If interest rates move down - bond values increase

.....as the bond market strives for equilibrium in the face of
changes in the financial/business marketplace
Irwin/McGraw-Hill
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T7.4 Valuing a Bond
 Let’s do another one. Assume you have the following information.
ABC company bonds have a $1000 face value.
The promised annual coupon is $100.
The bonds mature in 20 years.
The market’s required return on similar bonds is 10%
What is the bond’s value?

1. Calculate the present value of the face value
= $1000  [1/1.1020 ] = $1000  .14864 = $148.64

2. Calculate the present value of the coupon payments
= $100  [1 - (1/1.1020)]/.10 = $100  8.5136 = $851.36

3. The value of each bond = $148.64 + 851.36 = $1000
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T7.5 Example: A Discount Bond
 Assume you have the following information.
ABC Company bonds have a $1000 face value
The promised annual coupon is $100
The bonds mature in 20 years
The market’s required return on similar bonds is 12%

1. Calculate the present value of the face value
= $1000  [1/1.1220 ] = $1000  .10366 = $103.66

2. Calculate the present value of the coupon payments
= $100  [1 - (1/1.1220)]/.12 = $100  7.4694 = $746.94

3. The value of each bond = $103.66 + 746.94 = $850.60
Why is this bond selling at a discount to its face value?
Irwin/McGraw-Hill
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T7.6 Example: A Premium Bond

Now you have the following information.
ABC Company bonds have a $1000 face value
The promised annual coupon is $100
The bonds mature in 20 years
The market’s required return on similar bonds is 8%

1. Calculate the present value of the face value
= $1000  [1/1.0820 ] = $1000  .21455 = $214.55

2. Calculate the present value of the coupon payments
= $100  [1 - (1/1.0820)]/.08 = $100  9.8181 = $981.81

3. The value of each bond = $214.55 + 981.81 = $1,196.36
Why is this bond selling at a premium to par?
Irwin/McGraw-Hill
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T7.7 Bond Price Sensitivity to YTM
Bond price
$1,800
Coupon = $100
20 years to maturity
$1,000 face value
$1,600
Key Insight: Bond prices and
YTM’s are inversely related.
$1,400
$1,200
$1,000
$ 800
$ 600
Yield to maturity, YTM
4%
6%
Irwin/McGraw-Hill
8%
10%
12%
Slide 16
14%
16%
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T7.8 The Bond Pricing Equation
 Bond Value = Present Value of the Coupons
+ Present Value of the Face Value
= C  [1 - 1/(1 + r )t]/r + F  1/(1 + r )t
where: C = Coupon paid each period
r = Rate per period
t = Number of periods
F = Bond’s face value
Irwin/McGraw-Hill
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T7.9 Interest Rate Risk and Time to Maturity (Figure 7.2)
Irwin/McGraw-Hill
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Interest Rate Risk
 the ‘risk that arises for bond owners from fluctuating
interest rates (market yields)’

the risk or sensitivity to interest rate changes is a function of
• time to maturity - the longer the time to maturity the
greater the interest rate risk
• coupon rate - the lower the coupon rate the greater the
interest rate risk

time to maturity - longer term bonds have greater interest rate
risk due to the timing of the the principal repayment - if it
occurs in 30 years a small interest rate change can have a
major impact on the PV of that cash flow vs if the principal is
due in one year
coupon rate - for a given YTM a higher coupon bond has
larger cash flows earlier than another bond with the same
YTM but lower coupon payments (more of the YTM is made up
of the face amount to be received at maturity)

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Reinvestment Risk
 Uncertainty concerning the interest rates at which cash
flows e.g. coupon payments can be reinvested
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T7.10 Summary of Bond Valuation (Table 7.1)
I. Finding the value of a bond
Bond value = C

[1 - 1/(1 + r )t]/r + F/(1 + r)t
where: C = Coupon paid each period
r = Rate per period
t = Number of periods
F = Bond’s face value
II. Finding the yield on a bond
Given a bond value, coupon, time to maturity, and face value, it is
possible to find the implicit discount rate, or yield to maturity, by trial
and error only. To do this, try different discount rates until the
calculated bond value equals the given bond value. Remember that
increasing the rate decreases the bond value.
Irwin/McGraw-Hill
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T7.11 Bond Pricing Theorems
 The following statements about bond pricing are always true.

1. Bond prices and market interest rates move in opposite
directions.

2. When a bond’s coupon rate is (greater than / equal to /
less than) the market’s required return, the bond’s
market value will be (greater than / equal to / less than)
its par value.

3. Given two bonds identical but for maturity, the price of
the longer-term bond will change more (in percentage
terms) than that of the shorter-term bond, for a given
change in market interest rates.

4. Given two bonds identical but for coupon, the price of
the lower-coupon bond will change more (in percentage
terms) than that of the higher-coupon bond, for a given
change in market interest rates.
Irwin/McGraw-Hill
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Differences Between Debt and Equity 7.2


Debt





Not an ownership interest
Bondholders do not have
voting rights
Interest is considered a
cost of doing business and
is tax deductible
Bondholders have legal
recourse if interest or
principal payments are
missed
Excess debt can lead to
financial distress and
bankruptcy
Irwin/McGraw-Hill
Slide 23
Equity





Ownership interest
Common shareholders
vote for the board of
directors and other
issues
Dividends are not
considered a cost of
doing business and are
not tax deductible
Dividends are not a
liability of the firm and
shareholders have no
legal recourse if
dividends are not paid
An all equity firm can not
go bankrupt
2005
Bond Characteristics cont’d
 Bonds vs Debentures
 a bond is a form of secured debt - certain assets are pledged
as security
 a debenture is a form of unsecured debt - specific assets are
not pledged as security
However, typically the term ‘bond’ is used for all forms of
debt
 Public vs Private Debt
 Public debt is offered to the public while private debt is where
the debt is placed with a single lender - often a pension fund,
insurance firm, etc.
Irwin/McGraw-Hill
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T7.12 Features of a May Department Stores Bond
Term
Explanation
Amount of issue
$200 million
The company issued $200 million worth
of bonds.
Date of issue
8/4/94
The bonds were sold on 8/4/94.
Maturity
8/1/24
The principal will be paid 30 years after
the issue date.
Face Value
$1,000
The denomination of the bonds is $1,000.
Annual coupon
8.375
Each bondholder will receive $83.75 per
bond per year (8.375% of the face value).
Offer price
100
The offer price will be 100% of the $1,000
face value per bond.
Irwin/McGraw-Hill
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T7.12 Features of a May Department Stores Bond (concluded)
Term
Explanation
Coupon payment dates
2/1, 8/1
Coupons of $83.75/2 = $41.875 will be
paid on these dates.
Security
None
The bonds are debentures.
Sinking fund
Annual
beginning 8/1/05
The firm will make annual payments
toward the sinking fund.
Call provision
Not callable
before 8/1/04
The bonds have a deferred call feature.
(See Appendix 7C on Canada plus calls.)
Call price
104.188 initially,
declining to 100
After 8/1/04, the company can buy back
the bonds for $1,041.88 per bond,
declining to $1,000 on 8/1/14.
Rating
Moody’s A2
This is one of Moody’s higher ratings.
The bonds have a low probability of
default.
Irwin/McGraw-Hill
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7.13 The Bond Indenture
The Bond Indenture
 The bond indenture is a three-party contract between the
bond issuer, the bondholders, and the trustee. The trustee
is hired by the issuer to protect the bondholders’ interests.
The indenture includes






The basic terms of the bond issue
The total amount of bonds issued
A description of the security
The repayment arrangements
The call provisions
Details of the protective covenants
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Additional Bond Features
 registered vs bearer
 security
 bond
 debenture
 collateral
 mortgage securities
 seniority
 senior
 junior
 subordinated debt
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Additional Bond Features
 Repayment
 repaid at maturity
 early repayment
• sinking fund - an account managed by a bond trustee for
the purpose of repaying the bonds - the trustee uses the
funds and purchases the required amounts in the open
market or calling in a fraction of the outstanding bonds.
• value of a sinking fund to investors - reduces the risk that
the company will be unable to repay the principal at
maturity thus improving the marketability of the bonds
 call provisions
 protective covenants
• part of the loan agreement that limits actions of the
borrowing firm - e.g. restrictions on dividends and sales
of major assets
Irwin/McGraw-Hill
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T7.14 Bond Ratings
Investment-Quality Bond Ratings
Moody’s
DBRS (S&P)
Low Quality, speculative,
and/or “Junk”
High Grade
Medium Grade
Low Grade
Very Low Grade
Aaa
AAA
A
A
Ba
BB
Caa
CCC
Aa
AA
Baa
BBB
B
B
Ca C
CC C
D
D
Moody’s DBRS
Aaa
AAA
Debt rated Aaa and AAA has the highest rating. Capacity to pay
interest and principal is extremely strong.
Aa
AA
Debt rated Aa and AA has a very strong capacity to pay interest and
repay principal. Together with the highest rating, this group
comprises the high-grade bond class.
A
A
Debt rated A has a strong capacity to pay interest and repay
principal, although it is somewhat more susceptible to the adverse
effects of changes in circumstances and economic conditions than
debt in high rated categories.
Irwin/McGraw-Hill
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T7.14 Bond Ratings (concluded)
Baa
BBB
Debt rated Baa and BBB is regarded as having an
adequate capacity to pay interest and repay principal.
Whereas it normally exhibits adequate protection
parameters, adverse economic conditions or changing
circumstances are more likely to lead to a weakened
capacity to pay interest and repay principal for debt in
this category than in higher rated categories. These
bonds are medium-grade obligations.
Ba, B
BB, B
CC, C
Debt rated in these categories is regarded, on balance, as Ca, C
predominantly speculative with respect to capacity to pay
interest and repay principal in accordance with the terms of
the obligation. BB and Ba indicate the lowest degree of
speculation, and CC and Ca the highest degree of
speculation. Although such debt will likely have some quality
and protective characteristics, these are out-weighed by large
uncertainties or major risk exposures to adverse conditions.
Some issues may be in default.
D
D
Debt rated D is in default, and payment of interest and/or
repayment of principal is in arrears
Irwin/McGraw-Hill
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Different Types of Bonds
 Stripped bonds - a bond that makes not coupon payments
and is initially priced at a deep discount


because all of the YTM is in the form of the principal
repayment
interest is both deductible by the issuer and must be claimed
by the investor - even though there is no interest coupon
payments per se....it is imputed from discount
 Floating Rate Bonds (floaters) - the coupon payments are
adjustable (not fixed like a traditional bond)

were introduced by issuers to control the risk of price
fluctuations due to interest rate shifts.
 Income bond - coupon payments are dependent on
company income - only if that income is sufficient
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Different Types of Bonds Cont’d
 Real Return Bonds - coupons and principal are indexed to
inflation to provide a stated real return
 Convertible Bonds - can be ‘converted’ for a fixed number
of shares of the issuer’s stock - anytime before maturity
and at the holder’s option - are considered a ‘hybrid’ of
debt and equity. The convertible aspect provides the
investor with additional incentive to purchase the bond
 Retractable Bonds or ‘put’ bonds - allows the holder to
‘put’ the bonds back to the issuer or force the issuer to
buy the bonds back at a stated price - this effectively
establishes a floor price for the bonds
......issuers will combine various features at any given point in
time to encourage investors to buy a new bond issue!
Irwin/McGraw-Hill
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Bond Markets
 OTC (over the counter) market with dealers connected
electronically
 the bond market in trading volume is many times larger
than the trading volume in stocks

the U.S. Treasury market is the largest securities market in the
world in terms of trading volume
 Bond Price Reporting
 unlike stocks that are traded on an exchange - bonds do not
have that price ‘transparency’ - bonds prices are indications
only and are typically provided by bond dealers (not by the
TSE for example)
 the Monday edition of the Globe & Mail is one of the best
sources for bond information
Irwin/McGraw-Hill
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Inflation and Interest Rates
 Real vs Nominal Rates of Return
 nominal rates - interest rates or rates of return that have not
been adjusted for inflation
 real rates - interest rates or rates of return that have been
adjusted for inflation


nominal rate on an investment is the % change in the number
of dollars you have
real rate on an investment is the % change in how much you
can purchase with your dollars or the % change in buying
power
 Fisher Effect ( or theory)
 R = (r+h) +( r*h) where R is the Nominal rate, r is the real rate
and h is the rate of inflation
Irwin/McGraw-Hill
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T7.16 Inflation and Returns
 Key issues:

What is the difference between a real return and a
nominal return?

How can we convert from one to the other?
 Example:
Suppose we have $1000, and Coke costs $2.00 per six
pack. We can buy 500 six packs. Now suppose the rate of
inflation is 5%, so that the price rises to $2.10 in one year.
We invest the $1000 and it grows to $1100 in one year.
What’s our return in dollars (nominal)? In six packs (real
buying power)?
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T7.16 Inflation and Returns (continued)
 A. Dollars. Our return is
($1,100 - $1,000)/$1,000 = $100/$1,000 = .10.
The percentage increase in our investment is
10%; our return is 10%....this is the nominal return
 B. Six packs. We can buy $1,100/$2.10 = 523.81 six
packs, so our return is
(523.81 - 500)/500 = 23.81/500 = 4.76%
The percentage increase in the amount of coke is
4.76%; our ‘real’ return is 4.76%....this is our buying power
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T7.16 Inflation and Returns (continued)
 Real versus nominal returns:
Your nominal return is the percentage change in
the amount of money you have.
Your real return is the percentage change in the
amount of ‘stuff’ you can actually buy.
Irwin/McGraw-Hill
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T7.16 Inflation and Returns (concluded)
 The relationship between real and nominal returns is described by
the Fisher Effect. Let:
R
=
the nominal return
r
=
the real return
h
=
the inflation rate
 According to the Fisher Effect:
1 + R = (1 + r)  (1 + h)
Or R = (r+h) + (r*h)
 From the example, the real return is 4.76%; the nominal return is
10%, and the inflation rate is 5%:
(1 + R) = 1.10
Irwin/McGraw-Hill
(1 + r)  (1 + h) = 1.0476 x 1.05 = 1.10
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Factors Affecting Bond Yields
What factors affect observed bond yields?
Term Structure of Interest Rates
 The real rate of interest
 Expected future inflation
 Interest rate risk
Other factors
 Default risk premium
 Taxability premium
 Liquidity premium
Irwin/McGraw-Hill
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T7.17 U.S. Interest Rates: 1800-1997
Irwin/McGraw-Hill
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Term Structure of Interest Rates
 Term structure of interest rates is the relationship between
short and long term interest rates or
‘the relationship between nominal interest rates on default- free,
pure discount securities and the time to maturity
 What determines the shape of the term structure?
 Real rate of interest - pure time value of money
 rate of inflation
 interest rate risk
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Term Structure of Interest Rates
 Real rate of interest - basic component underlying every
interest rate - it is the ‘economic rent’ or compensation that
investors demand for forgoing the use of their money.

Tends to influence the overall level of rates more so than the
shape of the structure
 Rate of Inflation - investor demand extra compensation or
an ‘inflation premium’ for the expected erosion of the
value of their investment from inflation 
the key here is the expected inflation - if inflation is expected
to be higher in the future then long term rates will reflect this
and be higher than short term rates
 Interest Rate Risk - risk of interest rates changing and the
resulting impact on the value of the security

risk is greater over the longer term so this risk increases with
the length of maturity
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T7.18 The Term Structure of Interest Rates (Fig. 7.6)
Irwin/McGraw-Hill
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T7.18 The Term Structure of Interest Rates (Fig. 7.6)
Irwin/McGraw-Hill
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Factors Affecting Bond Yields
Other factors in addition to the Term Structure of Interest
Rates
 Credit risk & the default risk premium
• if the risk of default is perceived to be higher - investors
will demand higher compensation - importance of bond
ratings
 Taxation - is the return taxable and how is it taxed
 U.S. Vs Canada
 interest and capital gains
 Liquidity & liquidity premium - investors like ‘liquid’ issues
where there is high levels of trading of that issue provides confidence - low liquidity leads to higher yields liquidity premium demanded by investors increases
Irwin/McGraw-Hill
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Yield Curve
 the ‘yield curve’ is a reflection of the term structure of
interest rates
 the ‘Canada Yield Curve’ reflecting Govt. of Canada bond
yields is essentially the same
 Corporate yield curves - however bring in these other
factors affecting yields - e.g. default risk premium, etc.
....what does the yield curve look like today?
Irwin/McGraw-Hill
Slide 47
2005
Figure 7.5 – Government of Canada Yield Curve
November 29, 2002
Irwin/McGraw-Hill
Slide 48
2005