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Bond Yields and Interest
Rates
(chapter 17)
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KEY TERMS

Maturity: time when bond principal and all interest will be
paid in full

Term-to-Maturity: years remaining until maturity
Par Value: face amount, or principle of bond
-
Discount and Premium to par

Coupon Rate: rate promised based on par value of bond
principal—determines interest paid

Current Yield: rate based on interest paid divided by current
bond price
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Interest Rates
Rates and basis points
- 100 basis points are equal to one percentage point
 Short-term riskless rate
- Provides foundation for other rates
- Approximated by rate on Treasury bills
- Other rates differ because of

Maturity differentials
Security risk premiums
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Determinants of Interest Rates

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Real rate of interest
- Rate that must be offered to persuade individuals to save
rather than consume
- Rate at which real capital physically reproduces itself
Nominal interest rate
- Function of the real rate of interest and expected inflation
premium
Bonds benefits from a weak economy
- Interest rates decline and bond prices increase
Important relationship is between bond yields and inflation rates
- Investors react to expectations of future inflation rather than
current actual inflation
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Determinants of Interest Rates
Market interest rates on riskless debt  real
rate +expected inflation
- Fisher Hypothesis
 Real rate estimates obtained by subtracting the
expected inflation rate from the observed
nominal rate
 Real interest rate is an ex ante concept

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The Term Structure of Interest Rates

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Term structure of interest rates
- Relationship between time to maturity and yields
Yield curves
- Graphical depiction of the relationship between yields and time
for bonds that are identical except for maturity
Upward-sloping yield curve
- typical, interest rates rise with maturity
Downward-sloping yield curves
- Unusual, predictor of recession?
Term structure theories
- Explanations of the shape of the yield curve and why it changes
shape over time
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Yield curve and the term structure of
interest rates



Yield
(%)
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Term structure –
relationship between
interest rates (or yields)
and maturities.
The yield curve is a
graph of the term
structure.
The November 2005
Treasury yield curve is
shown at the right.
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4
3
2
1
0
0.25
0.5
2
5
10
Maturity (years)
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What is the relationship between the
Treasury yield curve and the yield curves for
corporate issues?
Corporate yield curves are higher than that
of Treasury securities, though not
necessarily parallel to the Treasury curve.
 The spread between corporate and Treasury
yield curves widens as the corporate bond
rating decreases.

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What determines the yield curve?:
Pure (unbiased) Expectations Hypothesis


The PEH contends that the shape of the yield curve depends on investor’s
expectations about future interest rates.
If interest rates are expected to increase, L-T rates will be higher than S-T rates,
and vice-versa. Thus, the yield curve can slope up, down, or even bow.

Assumes that the maturity risk premium for Treasury securities is zero.

Long-term rates are an average of current and future short-term rates.

Most evidence supports the general view that lenders prefer S-T securities, and
view L-T securities as riskier.
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An example:
Observed Treasury rates and the PEH
Maturity
1 year
2 years
Yield
6.0%
6.2%
If expectations hypothesis holds, what does the
market expect will be the interest rate on one-year
securities, one year from now?
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Forward rates

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Forward rates are rates that are expected to prevail in the future
For example a two year bond would carry an interest that is an
average of the current rate for one year and the forward one year
rate one year from now
(1+R2)^2= (1+R1)*(1+r1)
r1=(1+R2)^2/(1+R1) -1
r1 = (1+0.062)^2/(1+0.06) -1 = 6.4%
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Measuring Bond Yields

Yield to maturity
- Most commonly used
- Promised compound rate of return received from a
-
bond purchased at the current market price and
held to maturity
Equates the present value of the expected future
cash flows to the initial investment
Investors earn the YTM if the bond is held to
maturity and all coupons are reinvested at YTM
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Yields

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Yield spread = Yield – Treasury yield
Yield spreads are a function of bond
characteristics(see previous slide)
Yield spread varies inversely to the business cycles
Premium bond: if the bond yield is lower than the
coupon rate
Discount bond: if the bond yield is greater than the
coupon rate
Current yield: bond’s annual coupon divided by bond
price
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Factors affecting the Yield spreads
Differences in quality
 Differences in time to maturity
 Differences in call features
 Differences in coupon interests
 Differences in marketability
 Differences in tax treatments
 Cross country differences

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What is the YTM on a 10-year, 9% annual
coupon, $1,000 par value bond, selling for
$887?

Must find the ytm that solves this model.
C
C
FV
VB 
 ... 

1
N
(1  ytm)
(1  ytm)
(1  ytm)N
90
90
1,000
$887 
 ... 

1
10
(1  ytm)
(1  ytm)
(1  ytm)10
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Realized Compound Yield

Rate of return actually earned on a bond given the
reinvestment of the coupons at varying rates
 Total endingwealth 
RCY  

 Purchase price of bond 
1/ 2 n
 1.0
Ex: Total ending wealth = $1,340.1
Purchase price (par) = $1,000
Three years holding, coupon paid semi annual
RCY = 0.05 simiannual and 10% bond equivalent annual

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What is interest rate (or price) risk?
(no calculations for the exam)

Interest rate risk is the concern that rising kd will
cause the value of a bond to fall.
% change
+4.8%
-4.4%
1 yr
$1,048
$1,000
$956
rd
5%
10%
15%
10yr
$1,386
$1,000
$749
% change
+38.6%
-25.1%
The 10-year bond is more sensitive to interest rate
changes, and hence has more interest rate risk.
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What is reinvestment rate risk?
(no calculations for the exam)

Reinvestment rate risk is the concern that kd will fall, and future CFs will have
to be reinvested at lower rates, hence reducing income.
EXAMPLE: Suppose you just won $1,000,000 playing the lottery. You
intend to invest the money and live off the interest.

If you choose to invest in series of 1-year bonds, that pay a 8% coupon you
receive $80,000 in income and have $1,000,000 to reinvest.
But, if 1-year rates fall to 3%, your annual income would fall to $30,000.
If you choose a 30-year bond that pay a 10 % coupon you receive $100,000 in
income; you can lock in a 10% interest rate, and $100,000 annual income for
30 years
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Conclusions about interest rate and
reinvestment rate risk
Interest
rate risk
Reinvestment
rate risk

Short-term AND/OR
High coupon bonds
Long-term AND/OR
Low coupon bonds
Low
High
High
Low
CONCLUSION: Nothing is riskless!
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Interest Rate Risk : Malkiel’s Theorems
 Malkiel’s theorems are a set of relationships
among bond prices, time to maturity, and interest
rates.
 Theorem One : Bond prices move inversely with
yields.
 Theorem Two : Long-term bonds have more risk.
 Theorem Three : Higher coupon bonds have less
risk.
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Learning objectives
Know the key characteristics of a bond
Everything except:
Sections NOT on the exam: No calculations using the 5 TVM keys to
value a bond; Yield to call p. 456; Realized Compound Yield p 457
End of chapter questions 17.1 to 20, 24
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