Deck 5: Interest Rate Risk

Question 1

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There are three zero coupon bonds with a face value of $10 million.One matures one year from now and is selling at $9,433,962.30.The second matures two years from now and is selling for $8,573,388.20.The third matures three years from now and is selling at
$7,117,802.50.
What is the implied forward rate between time 2 and time 3?

A)12%
B)15%
C)18%
D)21%
E)24%

Answer 1

D

Question 2

Duration is different from maturity because duration reflects

A)intermediate cash flows instead of principal value
B)the current yield rather than the yield to maturity
C)the timing of all cash flows that accrue to the asset holder
D)investors' expectations about future interest rates
E)all of the above

Answer 2

C

Question 3

Use the following information for questions
There are three zero coupon bonds with a face value of $10 million.One matures one year from now and is selling at $9,433,962.30.The second matures two years from now and is selling for $8,573,388.20.The third matures three years from now and is selling at
$7,117,802.50.
What is the yield to maturity of the second bond?

A)6%
B)8%
C)10%
D)12%
E)14%

Answer 3

B

Question 4

Use the following information for questions
There are three zero coupon bonds with a face value of $10 million.One matures one year from now and is selling at $9,433,962.30.The second matures two years from now and is selling for $8,573,388.20.The third matures three years from now and is selling at
$7,117,802.50.
What is the yield to maturity of the third bond?

A)6%
B)8%
C)10%
D)12%
E)14%

Question 5

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There are two riskless bonds which mature at t = 2.The first is a zero coupon bond that pays a balloon of $ 1,200.The other is a coupon bond with an annual coupon of $100 and a balloon payment of $990.The current yield on a riskless bond that mature in one year is 10%, the annualized yield on a two-year bond is also 10%.
If the interest rate at t = 1 can be 8% or 12%, what is the percentage price change for the coupon bond

Question 6

Financial institutions are interested in duration because

A)duration allows them to improve the management of assets while holding the liabilities constant
B)duration allows them to improve the management of liabilities while holding the assets constant
C)duration allows them to maximize their profits without changing their asset structure
D)duration can protect them against adverse movement in interest rates
E)duration can protect them against borrower's default

Question 7

What is the duration of a three-year bond with a 5% coupon rate, a face value of $1,000, and a yield to maturity of 6%? Interest payments are made annually.

A)2 years
B)2.58 years
C)2.86 years
D)3 years
E)Insufficient information

Question 8

Use the following information for questions
There are two riskless bonds which mature at t = 2.The first is a zero coupon bond that pays a balloon of $ 1,200.The other is a coupon bond with an annual coupon of $100 and a balloon payment of $990.The current yield on a riskless bond that mature in one year is 10%, the annualized yield on a two-year bond is also 10%.
If the interest rate at t = 1 can be 8% or 12%, what is the percentage price change for the zero coupon bond

Question 9

The moral hazard problem created by the institution of the lender-of-last resort facility is

A)there is an incentive to take less deposits
B)there is an incentive to maintain less liquid assets
C)there is an incentive to mismatch the duration of assets and liabilities
D)only b and c
E)all of the above

Question 10

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There is a two-period zero coupon bond that will pay $10 million at t = 2.At t = 0, a call option on this bond is selling at $225,000.The holder can exercise the option at t = 1 at a price of $9,250,000.The current yield on a riskless zero coupon bond that matures at t = 1 is 8%.It is known that the yield on one-period bonds at t = 1 will be 6% or 10%.All bonds are identical except in maturity.
What is the payoff to the option holder?

A)$125,875.50
B)$143,676.30
C)$175,876.20
D)$183,962.30
E)$250,000.00

Question 11

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A bank has an obligation of $750 at the end of the first period and $550 at the end of the second period.It also has $1,528.93 to invest and can choose between zero-coupon bond or the coupon bond.The coupon bond matures in two years, pays an annual coupon of $100, and has a balloon payment of $1,400.The zero-coupon bond has a balloon payment of $1,610 at the end of the second year.The default-free yield on a one-year bond is 10%, and the annualized yield on a two-year bond is also 10%.
What is the present value of the bank's equity?

A)$1,528.93
B)$1,500.00
C)$1,300.00
D)$1,136.36
E)$392.57

Question 12

Use the following information for questions
There are two riskless bonds which mature at t = 2.The first is a zero coupon bond that pays a balloon of $ 1,200.The other is a coupon bond with an annual coupon of $100 and a balloon payment of $990.The current yield on a riskless bond that mature in one year is 10%, the annualized yield on a two-year bond is also 10%.
What is the duration of each bond

Question 13

Use the following information for questions
There are three zero coupon bonds with a face value of $10 million.One matures one year from now and is selling at $9,433,962.30.The second matures two years from now and is selling for $8,573,388.20.The third matures three years from now and is selling at
$7,117,802.50.
What is the implied forward rate between time 1 and time 2?

A)6%
B)8%
C)10%
D)12%
E)14%

Question 14

The term structure of interest rates:

A)describes the relationship between the holding period yield of debt instruments with similar interest rate risk characteristics
B)describes the relationship between the yield to maturity of debt instruments with similar default risk characteristics
C)describes the relationship between the holding period yield of debt instruments with similar default risk characteristics
D)describes the relationship between the yield to maturity of debt instruments with similar interest rate risk characteristics

Question 15

Use the following information for questions
There is a two-period zero coupon bond that will pay $10 million at t = 2.At t = 0, a call option on this bond is selling at $225,000.The holder can exercise the option at t = 1 at a price of $9,250,000.The current yield on a riskless zero coupon bond that matures at t = 1 is 8%.It is known that the yield on one-period bonds at t = 1 will be 6% or 10%.All bonds are identical except in maturity.
Suppose that the payoff to the option holder is $250,000.What is the risk-neutral probability that the interest rate will be 6% round up to the nearest figure)?

A)1%
B)2%
C)3%
D)5%
E)8%

Question 16

By exactly matching the duration of assets and liabilities, an institution

A)can eliminate its credit risk
B)can eliminate its interest rate risk
C)forgoes profitable asset transformation service
D)only b and c
E)all of the above

Question 17

Use the following information for questions
There is a two-period zero coupon bond that will pay $10 million at t = 2.At t = 0, a call option on this bond is selling at $225,000.The holder can exercise the option at t = 1 at a price of $9,250,000.The current yield on a riskless zero coupon bond that matures at t = 1 is 8%.It is known that the yield on one-period bonds at t = 1 will be 6% or 10%.All bonds are identical except in maturity.
Suppose that the risk-neutral probability that the interest rate will be 6% is 10%.What is the annualized yield on the two-year bond round up to the nearest figure)?

A)5%
B)7%
C)9%
D)12%
E)15%

Question 18

An inverted yield curve indicates that:

A)the short-term yields are higher than the long-term yields
B)the short-term yields are lower than the long-term yield
C)the yield to maturity increases with maturity
D)the yield to maturity decreases with maturity
E)both a and d

Question 19

Duration and maturity are usually_____related, while duration and yield are usually _______ related.

A)positively, positively
B)positively, negatively
C)negatively, positively
D)negatively, negatively
E)none of the above

Question 20

Which of the following statement/s is/are true?

A)The shorter the duration of a bond, the lower is its price volatility.
B)Other things equal, an increase in coupon payments increases duration
C)A zero-coupon bond has a zero duration
D)The duration of a coupon bond is always greater than its maturity
E)Other things equal, an increase in the yield to maturity increases duration

Question 21

Use the following information for questions
A bank has an obligation of $750 at the end of the first period and $550 at the end of the second period.It also has $1,528.93 to invest and can choose between zero-coupon bond or the coupon bond.The coupon bond matures in two years, pays an annual coupon of $100, and has a balloon payment of $1,400.The zero-coupon bond has a balloon payment of $1,610 at the end of the second year.The default-free yield on a one-year bond is 10%, and the annualized yield on a two-year bond is also 10%.
Suppose the interest rate at t = 1 can be 8% or 12%.What will be the bank's equity if it invests in the coupon bond

Question 22

What is the usefulness of convexity when duration is available as a measure of interest rate risk?
Suggested

Question 23

Use the following information for questions
A bank has an obligation of $750 at the end of the first period and $550 at the end of the second period.It also has $1,528.93 to invest and can choose between zero-coupon bond or the coupon bond.The coupon bond matures in two years, pays an annual coupon of $100, and has a balloon payment of $1,400.The zero-coupon bond has a balloon payment of $1,610 at the end of the second year.The default-free yield on a one-year bond is 10%, and the annualized yield on a two-year bond is also 10%.
Suppose the interest rate at t = 1 can be 8% or 12%.What will be the bank's equity if it invests in the zero-coupon bond

Question 24

Use the following information for questions
A bank has an obligation of $750 at the end of the first period and $550 at the end of the second period.It also has $1,528.93 to invest and can choose between zero-coupon bond or the coupon bond.The coupon bond matures in two years, pays an annual coupon of $100, and has a balloon payment of $1,400.The zero-coupon bond has a balloon payment of $1,610 at the end of the second year.The default-free yield on a one-year bond is 10%, and the annualized yield on a two-year bond is also 10%.
What is the duration of the bank's liability?

A)2.5 years
B)2 years
C)1.85 years
D)1.4 year
E)0.77 year