Question

- Consider two $1,000 par coupon bonds,
*A*and*B*. Bond*A*has a coupon rate of 5% with ten-year maturity and bond*B*has a coupon rate of 8% with five years until maturity.- Define interest rate risk.

b.Proof that Bond *A* has higher interest risk than bond
*B*.

Answer #1

A) A fundamental principle of bond investing is that market
interest rates and bond prices generally move in opposite
directions. When market interest rates rise, prices of fixed-rate
bonds fall. this phenomenon is known as **interest rate
risk.**

If two bonds offer different coupon rates while all of their other characteristics (e.g., maturity and credit quality) are the same, the bond with the lower coupon rate generally will experience a greater decrease in value as market interest rates rise. Bonds offering lower coupon rates generally will have higher interest rate risk than similar bonds that offer higher coupon rates.

**Lower fixed-rate bond coupon rates -->higher interest
rate risk**

**Higher fixed-rate bond coupon rates --> lower
interest rate risk**

For example, imagine one bond that has a coupon rate of 2% while another bond has a coupon rate of 4%. All other features of the two bonds—when they mature, their level of credit risk, and so on—are the same. If market interest rates rise, then the price of the bond with the 2% coupon rate will fall more than that of the bond with the 4% coupon rate. remember:

Lower market interest rates-->higher fixed-rate bond prices-->lower fixed-rate bond yields--> higher interest rate risk to rising market interest rate.

B) A bond’s maturity is the specific date in the future at which the face value of the bond will be repaid to the investor. A bond may mature in a few months or in a few years. Maturity can also affect interest rate risk. The longer the bond’s maturity, the greater the risk that the bond’s value could be impacted by changing interest rates prior to maturity, which may have a negative effect on the price of the bond. Therefore, bonds with longer maturities generally have higher interest rate risk than similar bonds with shorter maturities.

**Longer maturity-->higher interest rate
risk**

**Shorter maturity ---> lower interest rate
risk**

To compensate investors for this interest rate risk, long-term bonds generally offer higher coupon rates than short-term bonds of the same credit quality.

**Longer maturity --> higher interest rate risk -->
higher coupon rate**

**Shorter maturity --> lower interest rate risk -->
lower coupon rate**

**From this it is clear that Bond A is more riskier than
Bond B**

4. Consider two $1,000 par coupon bonds, A
and B. Bond A has a coupon rate of 5% with ten-year maturity and
bond B has a coupon rate of 8% with five years until
maturity.
a. Define interest rate risk.
b. Proof that Bond A has higher interest risk than bond
B.

Consider these two bonds which are both newly issued and trading
at par.
Coupon Rate
Time Until Maturity
Bond A
7.5%
5 years
Bond B
7.5%
8 years
If the market interest rate unexpectedly changes from 9% to 11%,
then both bonds will ________________ in value, but bond ____ will
decrease more than bond _____.
decrease; A; B
decrease; B; A
increase; A; B
increase; B; A

Consider two bonds: bond XY and bond ZW . Bond XY has a face
value of $1,000 and 10 years to maturity and has just been issued
at par. It bears the current market interest rate of 7% (i.e. this
is the yield to maturity for this bond). Bond ZW was issued 5 years
ago when interest rates were much higher. Bond ZW has face value of
$1,000 and pays a 13% coupon rate. When issued, this bond had a...

Three 10-year, $1,000 par value, noncallable bonds have the same
level of risk. Bond EIGHT has an eight percent annual coupon, Bond
TEN has a ten percent annual coupon, and Bond TWELVE has a twelve
percent annual coupon. Bond TEN sells for $1,000. Assuming that
interest rates remain constant for the next ten years, which of the
following statements is CORRECT?
- Bond EIGHT sells at a discount (its price is less than par),
and its price is expected to...

Consider two bonds: bond XY and bond ZW . Bond XY has a face
value of $1,000 and 10 years to maturity and has just been issued
at par. It bears the current market interest rate of 7% (i.e. this
is the yield to maturity for this bond). Bond ZW was issued 5 years
ago when interest rates were much higher. Bond ZW has face value of
$1,000 and pays a 13% coupon rate. When issued, this bond had a...

Two bonds have the following
terms:
Bond A
Principal
$1,000
Coupon
8%
Maturity
10
years
Bond B
Principal
$1,000
Coupon
7.6%
Maturity
10
years
Bond B has an additional feature: It
may be redeemed at par after five years (i.e., it has a put
feature). Both bonds were initially sold for their face amounts
(i.e., $1,000).
If interest rates fall to 7 percent, what will be the price of
each bond?
If interest rates rise to 9 percent,
what will...

Consider two bonds, both pay annual interest. Bond C
has a coupon rate of 7% annually, with 5 years to maturity. Bond D
has a coupon rate of 8% annually with 5 years to maturity. The
yield to maturity today for these bonds is 6%.
What is the Modified duration for Bond C

a
20 year, 8% coupon rate, $1,000 par bond that pays interest
semi-annually bought five years ago for $850. this bond is
currently sold for 950. what is the yield on this bond?
a.12.23%
b.11.75%
c.12.13%
d.11.23%
an increase in interest rates will lead to an increase in the
value of outstanding bonds.
a. true
b. false
a bond will sell ____ when coupon rate is less than yield to
maturity, ______ when coupon rate exceeds yield to maturity, and...

A coupon bond has an 8% coupon rate and has a par value of
$1,000, matures in 5 years, and has a yield to maturity of 10%.
What will be the intrinsic value of the bond today if the coupon
rate is 8%?

a. Consider a coupon bond that pays interest of $60 annually,
has a par value of $1,000, matures in 2 years, and is selling today
at a price of $1000. What is the yield to maturity on this
bond?
b. Consider a zero-coupon bond with a par value of $1,000 that
costs $500 and matures in ten years. What is the yield to maturity
on this bond? Give the formula, and solve.
c. For the bond in part (b) above,...

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