Options Futures And Other Derivatives 9th Edition By John C. Hull – Test Bank
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Hull: Options, Futures and Other Derivatives, Ninth Edition
Chapter 4: Interest Rates
Multiple Choice Test Bank: Questions with Answers
1. The compounding
frequency for an interest rate defines
a. The
frequency with which interest is paid
b. A
unit of measurement for the interest rate
c. The
relationship between the annual interest rate and the monthly interest rate
d. None
of the above
Answer: B
The compounding frequency is a unit of measurement. The
frequency with which interest is paid may be different from the compounding
frequency used for quoting the rate.
2. An
interest rate is 6% per annum with annual compounding. What is the equivalent
rate with continuous compounding?
e. 79%
f. 21%
g. 83%
h. 18%
Answer: C
The equivalent rate with continuous compounding is ln(1.06) =
0.0583 or 5.83%.
3. An
interest rate is 5% per annum with continuous compounding. What is the
equivalent rate with semiannual compounding?
e. 06%
f. 03%
g. 97%
h. 94%
Answer: A
The equivalent rate with semiannual compounding is 2×(e0.05/2−1) =
0.0506 or 5.06%.
4. An
interest rate is 12% per annum with semiannual compounding. What is the
equivalent rate with quarterly compounding?
k. 83%
l. 66%
m. 77%
n. 92%
Answer: A
The equivalent rate per quarter is . The annualized rate with
quarterly compounding is four times this or 11.83%.
5. The
two-year zero rate is 6% and the three year zero rate is 6.5%. What is the
forward rate for the third year? All rates are continuously compounded.
f. 75%
g. 0%
h. 25%
i. 5%
Answer: D
The forward rate for the third year is (3×0.065−2×0.06)/(3−2) =
0.075 or 7.5%.
6. The
six-month zero rate is 8% per annum with semiannual compounding. The price of a
one-year bond that provides a coupon of 6% per annum semiannually is 97. What
is the one-year continuously compounded zero rate?
h. 02%
i. 52%
j. 02%
k. 52%
Answer: C
If the rate is R we
must have
or
so that R =
ln(1/0.9137) = 0.0902 or 9.02%.
7. The
yield curve is flat at 6% per annum. What is the value of an FRA where the
holder receives interest at the rate of 8% per annum for a six-month period on
a principal of $1,000 starting in two years? All rates are compounded
semiannually.
i. $9.12
j. $9.02
k. $8.88
l. $8.63
Answer: D
The value of the FRA is the value of receiving an extra
0.5×(0.08−0.06)×1000 = $10 in 2.5 years. This is 10/(1.035) =
$8.63.
8. Under
liquidity preference theory, which of the following is always true?
a. The
forward rate is higher than the spot rate when both have the same maturity.
b. Forward
rates are unbiased predictors of expected future spot rates.
c. The
spot rate for a certain maturity is higher than the par yield for that
maturity.
d. Forward
rates are higher than expected future spot rates.
Answer: D
Liquidity preference theory argues that individuals like their
borrowings to have a long maturity and their deposits to have a short maturity.
To induce people to lend for long periods forward rates are raised relative to
what expected future short rates would predict.
9. The
zero curve is upward sloping. Define X as the 1-year par yield, Y as the 1-year
zero rate and Z as the forward rate for the period between 1 and 1.5 year.
Which of the following is true?
a. X is
less than Y which is less than Z
b. Y is
less than X which is less than Z
c. X is
less than Z which is less than Y
d. Z is
less than Y which is less than X
Answer: A
When the zero curve is upward sloping, the one-year zero rate is
higher than the one-year par yield and the forward rate corresponding to the
period between 1.0 and 1.5 years is higher than the one-year zero rate. The
correct answer is therefore A.
10. Which
of the following is true of the fed funds rate
a. It is
the same as the Treasury rate
b. It is
an overnight interbank rate
c. It is
a rate for which collateral is posted
d. It is
a type of repo rate
Answer: B
At the end of each day some banks have surplus reserves on
deposit with the Federal Reserve others have deficits. They use overnight
borrowing and lending at what is termed the fed funds rate to rectify this.
11. The
modified duration of a bond portfolio worth $1 million is 5 years. By
approximately how much does the value of the portfolio change if all yields
increase by 5 basis points?
a. Increase
of $2,500
b. Decrease
of $2,500
c. Increase
of $25,000
d. Decrease
of $25,000
Answer: B
When yields increase bond prices decrease. The proportional
decrease is the modified duration times the yield increase. In this case, it is
5×0.0005=0.0025. The decrease is therefore 0.0025×1,000,000 or $2,500.
12. A
company invests $1,000 in a five-year zero-coupon bond and $4,000 in a ten-year
zero-coupon bond. What is the duration of the portfolio?
13. 6
years
14. 7
years
15. 8
years
16. 9
years
Answer: D
The duration of the first bond is 5 years and the duration of
the second bond is 10 years. The duration of the portfolio is a weighted
average with weights corresponding to the amounts invested in the bonds. It is
0.2×5+0.8×10=9 years.
13. Which
of the following is true of LIBOR
a. The
LIBOR rate is free of credit risk
b. A
LIBOR rate is lower than the Treasury rate when the two have the same maturity
c. It is
a rate used when borrowing and lending takes place between banks
d. It is
subject to favorable tax treatment in the U.S.
Answer: C
LIBOR is a rate used for interbank transactions.
14. Which
of following describes forward rates?
1.
a. Interest
rates implied by current zero rates for future periods of time
b. Interest
rate earned on an investment that starts today and last for n-years in the
future without coupons
c. The
coupon rate that causes a bond price to equal its par (or principal) value
d. A
single discount rate that gives the value of a bond equal to its market price
when applied to all cash flows
Answer: A
The forward rate is the interest rate implied by the current
term structure for future periods of time. For example, earning the zero rate
for one year and the forward rate for the period between one and two years
gives the same result as earning the zero rate for two years.
15. Which
of the following is NOT a theory of the term structure
1.
a. Expectations
theory
b. Market
segmentation theory
c. Liquidity
preference theory
d. Maturity
preference theory
Answer: C
Maturity preference theory is not a theory of the term
structure. The other three are.
16. A
repo rate is
a. An uncollateralized
rate
b. A
rate where the credit risk is relative high
c. The
rate implicit in a transaction where securities are sold and bought back later
at a higher price
d. None
of the above
Answer: C
A repo transaction is one where a company agrees to sell
securities today and buy them back at a future time. It is a form of
collateralized borrowing. The credit risk is very low.
17. Bootstrapping
involves
a. Calculating
the yield on a bond
b. Working
from short maturity instruments to longer maturity instruments determining zero
rates at each step
c. Working
from long maturity instruments to shorter maturity instruments determining zero
rates at each step
d. The
calculation of par yields
Answer: B
Bootstrapping is a way of constructing the zero coupon yield curve
from coupon-bearing bonds. It involves working from the shortest maturity bond
to progressively longer maturity bonds making sure that the calculated zero
coupon yield curve is consistent with the market prices of the instruments.
18. The
zero curve is downward sloping. Define X as the 1-year par yield, Y as the
1-year zero rate and Z as the forward rate for the period between 1 and 1.5
year. Which of the following is true?
a. X is
less than Y which is less than Z
b. Y is
less than X which is less than Z
c. X is less
than Z which is less than Y
d. Z is
less than Y which is less than X
Answer: D
The forward rate accentuates trends in the zero curve. The par
yield shows the same trends but in a less pronounced way.
19. Which
of the following is true?
a. When
interest rates in the economy increase, all bond prices increase
b. As
its coupon increases, a bond’s price decreases
c. Longer
maturity bonds are always worth more that shorter maturity bonds when the
coupon rates are the same
d. None
of the above
Answer: D
When interest rates increase the impact of discounting is to
make future cash flows worth less. Bond prices therefore decline. A is
therefore wrong. As coupons increase a bond becomes more valuable because
higher cash flows will be received. B is therefore wrong. When the coupon is
higher than prevailing interest rates, longer maturity bonds are worth more
than shorter maturity bonds. When it is less than prevailing interest rates,
longer maturity bonds are worth less than shorter maturity bonds. C is
therefore not true. The correct answer is therefore D.
20. The
six month and one-year rates are 3% and 4% per annum with semiannual
compounding. Which of the following is closest to the one-year par yield
expressed with semiannual compounding?
c. 99%
d. 98%
e. 97%
f. 96%
Answer: A
The six month rate is 1.5% per six months. The one year rate is
2% per six months. The one year par yield is the coupon that leads to a bond
being worth par. A is the correct answer because
(3.99/2)/1.015+(100+3.99/2)/1.022 =
100. The formula in the text can also be used to give the par yield as
[(100-100/1.022)×2]/(1/1.015+1.022)=3.99.
Hull: Options, Futures, and Other Derivatives, Ninth Edition
Chapter 7: Swaps
Multiple Choice Test Bank: Questions with Answers
1. A
company can invest funds for five years at LIBOR minus 30 basis points. The
five-year swap rate is 3%. What fixed rate of interest can the company earn by
using the swap?
b. 4%
c. 7%
d. 0%
e. 3%
Answer: B
When the company invests at LIBOR minus 0.3% and then enters
into a swap where it pays LIBOR and receives 3% it earns 2.7% per annum. Note
that it is the bid rate that will apply to the swap.
2. Which
of the following is true?
a. Principals
are not usually exchanged in a currency swap
b. The
principal amounts usually flow in the opposite direction to interest payments
at the beginning of a currency swap and in the same direction as interest
payments at the end of the swap.
c. The
principal amounts usually flow in the same direction as interest payments at
the beginning of a currency swap and in the opposite direction to interest
payments at the end of the swap.
d. Principals
are not usually specified in a currency swap
Answer: B
The correct answer is B. There are two principals in a currency
swap, one for each currency. They flow in the opposite direction to the
corresponding interest payments at the beginning of the life of the swap and in
the same direction as the corresponding interest payments at the end of the
life of the swap.
3. Company
X and Company Y have been offered the following rates
|
|
Fixed Rate |
Floating Rate |
|
Company X |
3.5% |
3-month LIBOR plus 10bp |
|
Company Y |
4.5% |
3-month LIBOR plus 30 bp |
Suppose that Company X borrows fixed and company Y borrows
floating. If they enter into a swap with each other where the apparent benefits
are shared equally, what is company X’s effective borrowing rate?
1. 3-month
LIBOR−30bp
2. 1%
3. 3-month
LIBOR−10bp
4. 3%
Answer: A
The interest rate differential between the fixed rates is 100
basis points. The interest rate differential between the floating rates is 20 basis
points. The difference between the interest rates differentials is 100 – 20 =
80 basis points. This is the total apparent gain from the swap to the two
sides. Since the benefits are shared equally company X should be able to borrow
at 40 bp less than it is currently offered in the floating rate market, i.e.,
at LIBOR minus 30 bp.
4. Which
of the following describes the five-year swap rate?
a. The
fixed rate of interest which a swap market maker is prepared to pay in exchange
for LIBOR on a 5-year swap
b. The
fixed rate of interest which a swap market maker is prepared to receive in
exchange for LIBOR on a 5-year swap
c. The
average of A and B
d. The
higher of A and B
Answer: C
The swap rate is the average of the bid swap rate (i.e. A) and
the offer swap rate (i.e. B)
5. Which
of the following is a use of a currency swap?
a. To
exchange an investment in one currency for an investment in another currency
b. To
exchange borrowing in one currency for borrowings in another currency
c. To
take advantage situations where the tax rates in two countries are different
d. All
of the above
Answer: D
A currency swap can be used for any of A, B, and C.
6. The
reference entity in a credit default swap is
a. The
buyer of protection
b. The
seller of protection
c. The
company or country whose default is being insured against
d. None
of the above
Answer: C
In a credit default swap the buyer of protection pays a CDS
spread to the seller of protection and the protection seller has to make a
payoff if there is a default by the reference entity.
7. Which
of the following describes an interest rate swap?
a. The
exchange of a fixed rate bond for a floating rate bond
b. A
portfolio of forward rate agreements
c. An
agreement to exchange interest at a fixed rate for interest at a floating rate
d. All
of the above
Answer: D
The answer is D because all of A, B, and C are true for an
interest rate swap.
8. Which
of the following is true for an interest rate swap?
a. A
swap is usually worth close to zero when it is first negotiated
b. Each
forward rate agreement underlying a swap is worth close to zero when the swap
is first entered into
c. Comparative
advantage is a valid reason for entering into the swap
d. None
of the above
Answer: A
A swap is worth close to zero at the beginning of its life. (It
may not be worth exactly zero because of the impact of the market maker’s
bid-offer spread.) It is not true that each of the forward contracts underlying
the swap are worth zero. (The sum of the value of the forward contracts is
zero, but this does not mean that each one is worth zero.) The remaining
floating payments on a swap are worth the notional principal immediately after
a swap payment date, but this is not necessarily true for the remaining fixed
payments.
9. Which
of the following is true for the party paying fixed in a newly negotiated
interest rate swap when the yield curve is upward sloping?
a. The
early forward contracts underlying the swap have a positive value and the later
ones have a negative value
b. The
early forward contracts underlying the swap have a negative value and the later
ones have a positive value
c. The
swap is designed so that all forward rates have zero value
d. Sometimes
A is true and sometimes B is true
Answer: B
The forward contracts are contracts where fixed is paid and
floating is received. They can be valued assuming that forward rates are
realized. Forward rates increase with maturity. This means that the value of
the forward contracts increase with maturity. The total value of the
forward contracts is zero. This means that the value of the early contracts is
negative and the value of the later contracts is positive.
10. A
bank enters into a 3-year swap with company X where it pays LIBOR and receives
3.00%. It enters into an offsetting swap with company Y where is receives LIBOR
and pays 2.95%. Which of the following is true:
a. If
company X defaults, the swap with company Y is null and void
b. If
company X defaults, the bank will be able to replace company X at no cost
c. If
company X defaults, the swap with company Y continues
d. The
bank’s bid-offer spread is 0.5 basis points
Answer: C
The bank`s bid-offer spread is 5 basis points not 0.5 basis
points. The bank has quite separate transactions with X and Y. If one defaults,
it still has to honor the swap with the other.
11. When
LIBOR is used as the discount rate:
a. The
value of a swap is worth zero immediately after a payment date
b. The
value of a swap is worth zero immediately before a payment date
c. The
value of the floating rate bond underlying a swap is worth par immediately
after a payment date
d. The
value of the floating rate bond underlying a swap is worth par immediately
before a payment date
Answer: C
The value of the floating rate bond underlying an interest rate
swap is worth par immediately after a swap payment date. This result is used
when the swap is valued as the difference between two bonds.
12. A
company enters into an interest rate swap where it is paying fixed and
receiving LIBOR. When interest rates increase, which of the following is true?
a. The
value of the swap to the company increases
b. The
value of the swap to the company decreases
c. The
value of the swap can either increase or decrease
d. The
value of the swap does not change providing the swap rate remains the same
Answer: A
It is receiving the floating rate. When interest rates increase
the floating rate can be expected to be higher and so the swap becomes more
valuable. The answer is therefore A.
13. A
floating for floating currency swap is equivalent to
a. Two
interest rate swaps, one in each currency
b. A
fixed-for-fixed currency swap and one interest rate swap
c. A
fixed-for-fixed currency swap and two interest rate swaps, one in each currency
d. None
of the above
Answer: C
A floating-for-floating currency swap where the currency paid is
X and the currency received is Y is equivalent to (a) a fixed-for-fixed
currency swap where, say, 5% in currency X is paid and say, say, 4% in currency
Y is received, (b) a regular interest rate swap where 5% in currency X is
received and floating in currency X is paid and (c) a regular interest rate
swap where 4% in currency Y is paid and floating in currency Y is received.
14. A
floating-for-fixed currency swap is equivalent to
a. Two
interest rate swaps, one in each currency
b. A
fixed-for-fixed currency swap and one interest rate swap
c. A
fixed-for-fixed currency swap and two interest rate swaps, one in each currency
d. None
of the above
Answer: B
A floating-for-fixed currency swap where the floating rate is
paid in currency X and the fixed rate is received in currency Y is equivalent
to (a) a fixed-for-fixed currency swap where, say, 5% in currency X is paid and
the fixed rate in currency Y is received, (b) a regular interest rate swap
where 5% in currency X is received and floating in currency X is paid.
15. An
interest rate swap has three years of remaining life. Payments are exchanged
annually. Interest at 3% is paid and 12-month LIBOR is received. A exchange of
payments has just taken place. The one-year, two-year and three-year LIBOR/swap
zero rates are 2%, 3% and 4%. All rates an annually compounded. What is the
value of the swap as a percentage of the principal when LIBOR discounting is
used.
a. 00
b. 66
c. 06
d. 06
Answer: B
Suppose the principal 100. The value of the floating rate bond
underlying the swap is 100. The value of the fixed rate bond is 3/1.02+3/(1.03)2+103/(1.04)3=97.34.
The value of the swap is therefore 100−97.34 = 2.66 or 2.66% of the principal
16. A
semi-annual pay interest rate swap where the fixed rate is 5.00% (with
semi-annual compounding) has a remaining life of nine months. The six-month
LIBOR rate observed three months ago was 4.85% with semi-annual compounding.
Today’s three and nine month LIBOR rates are 5.3% and 5.8% (continuously
compounded) respectively. From this it can be calculated that the forward LIBOR
rate for the period between three- and nine-months is 6.14% with semi-annual
compounding. If the swap has a principal value of $15,000,000, what is
the value of the swap to the party receiving a fixed rate of interest?
a. $74,250
b. −$70,760
c. −$11,250
d. $103,790
Answer: B
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