Test bank
to accompany the textbook
Fixed Income Securities: Valuation, Risk, and Risk
Management by Pietro Veronesi
Preliminary Version
Author: Javier Francisco Madrid
1
,Chapter 1
1. Is the following an arbitrage opportunity? A gift that makes me feel good
just by having it.
Ans. This is an arbitrage opportunity because it doesn’t cost anything at initi-
ation and it generates a positive profit by a certain date in the future (i.e.
’you feel good’).
2. Is the following an arbitrage opportunity? A bond that cost nothing but
will payoff zero with certainty in the future.
Ans. This is not an arbitrage opportunity, since it doesn’t give a positive payoff
in the future.
3. Is the following an arbitrage opportunity? A free car that if I repair well, I
won’t have to spend money on gasoline or maintenance costs (i.e. repairs)
ever.
Ans. This is not an arbitrage opportunity, since I have to pay money (to repair
the car) in order to be free of future costs.
4. Is the following an arbitrage opportunity? Suppose you are in the desert
and are given a bag of ice with a penny inside. Assume that the ice will
melt instantly and the cost of disposing of the bag is zero.
Ans. This is an arbitrage opportunity because even though I can’t take advan-
tage of the ice, I gain the penny for free.
5. Is the following an arbitrage opportunity? A security that cost zero and
might pay a dollar in the future, but pays zero otherwise.
Ans. This is an arbitrage opportunity because I get for free the chance of getting
a dollar in the future.
6. What steps would you follow in order to take advantage of the following
arbitrage opportunity (if there is one)? Security A costs $3 and pays $5
in 2 years, while security B costs $3 and pays $4 in 2 years.
Ans. You borrow security B and sell it, which means you receive $3, with these
proceeds you buy security A. In 2 years you receive $5 and have to pay
$4. You make a $1 profit.
7. What steps would you follow in order to take advantage of the following
arbitrage opportunity (if there is one)? Security A costs $100 and pays
$120 in 3 years. Security B costs $100 and pays $110 in one year. Your
friend tells you that he would like you to lend him $110 in a year and that
he would give $130 the following year. Finally you know that in two years,
with $130, you can invest in a security that will pay you either $140 or
$121 (with equal probability) after a year.
2
,Ans. You borrow security A and sell it, with the proceeds you buy security B.
After a year you lend the money to your friend. The next year when he
pays back, you invest in the risky security. After the third year, this will
give you either $140 or $121, while you have to pay $120. So you either
have a profit of $20 or $1.
8. What steps would you follow in order to take advantage of the following
arbitrage opportunity (if there is one)? Security A costs $100 and pays
$110 in 2 years. Security B costs $100 and pays $109 in one year. You
know that in a year with $109 you can invest in a security that pays $120
or $109 (with equal probability) the following year.
Ans. This is not an arbitrage opportunity.
9. Intuitively, is the Federal Funds rate generally higher, lower or the same
as LIBOR? Why?
Ans. The LIBOR rate should be higher than the Federal Funds rate, since it
should include a higher probability of default by the banks trading LIBOR.
10. Intuitively, is LIBOR generally higher, lower or the same as the repo rate?
Why?
Ans. LIBOR should be higher than the repo rate since it is not collateralized
with another security, as it occurs with the repo rate.
11. What are the steps to take a long position on a given U.S. security via the
repo market?
Ans. The trader must take the following steps (repo):
At time t:
i. Buy bond at Pt and deliver the bond to the repo dealer.
ii. The repo dealer will pay Pt − haircut to the trader, which is made
whole (minus the haircut) for the cost of the bond.
At time T :
iii. The trader gets the bond from the repo dealer and sells it for PT .
iv. With the proceeds PT the trader pays back (Pt −haircut)×(1+Repo)
to the repo dealer.
12. What are the steps to take a short position on a given U.S. security via
the repo market?
Ans. The trader must take the following steps (reverse repo):
At time t:
3
, i. Borrows the bond from the repo dealer and sells it at Pt .
ii. Receives Pt which he posts as collateral with the repo dealer.
At time T :
iii. The trader buys the bond for PT and gives it back to the repo dealer.
iv. The repo dealer pays Pt × (1+Repo). The dealer makes a profit if
this is larger than PT .
13. What’s the return on capital for a trader who entered into a one-month
repo where Pt = 98.5, PT = 99.01, Repo= 5% and haircut= 0.8?
Ans. The return on capital is 0.13.
14. What’s the profit for a trader who entered into a one-week reverse repo
where Pt = 99.40, PT = 99.48 and Repo= 6%?
Ans. The profit is 0.0347.
15. You find a bond that has a repo rate substantially lower than the GCR.
Is this, for certain, an arbitrage opportunity?
Ans. No, it might be that the bond is short on supply (hard to find), which
means that the trader might be thinking that the bond is overpriced and
is speculating that the price will fall. By entering in a reverse repo, the
trader might make a substantial profit, even willing to forgo part of the
rate to be in the transaction.
16. You are told that there is an ample supply for the bond mentioned in
question 13. Does this affect your previous answer?
Ans. Yes, since it shows that the lower rate is not due to scarcity of a specific
type of bond.
17. What are the gains from trade of entering into a swap for these two firms?
Firm A Firm B
Fixed Rate 13% 16%
Floating Rate LIBOR + 3% LIBOR + 6%
Ans. Gains from trade are zero.
18. What are the gains from trade of entering into a swap for these two firms?
Firm A Firm B
Fixed Rate 10% 15.5%
Floating Rate LIBOR + 2% LIBOR + 4%
Ans. Gains from trade are 3.5%.
4
to accompany the textbook
Fixed Income Securities: Valuation, Risk, and Risk
Management by Pietro Veronesi
Preliminary Version
Author: Javier Francisco Madrid
1
,Chapter 1
1. Is the following an arbitrage opportunity? A gift that makes me feel good
just by having it.
Ans. This is an arbitrage opportunity because it doesn’t cost anything at initi-
ation and it generates a positive profit by a certain date in the future (i.e.
’you feel good’).
2. Is the following an arbitrage opportunity? A bond that cost nothing but
will payoff zero with certainty in the future.
Ans. This is not an arbitrage opportunity, since it doesn’t give a positive payoff
in the future.
3. Is the following an arbitrage opportunity? A free car that if I repair well, I
won’t have to spend money on gasoline or maintenance costs (i.e. repairs)
ever.
Ans. This is not an arbitrage opportunity, since I have to pay money (to repair
the car) in order to be free of future costs.
4. Is the following an arbitrage opportunity? Suppose you are in the desert
and are given a bag of ice with a penny inside. Assume that the ice will
melt instantly and the cost of disposing of the bag is zero.
Ans. This is an arbitrage opportunity because even though I can’t take advan-
tage of the ice, I gain the penny for free.
5. Is the following an arbitrage opportunity? A security that cost zero and
might pay a dollar in the future, but pays zero otherwise.
Ans. This is an arbitrage opportunity because I get for free the chance of getting
a dollar in the future.
6. What steps would you follow in order to take advantage of the following
arbitrage opportunity (if there is one)? Security A costs $3 and pays $5
in 2 years, while security B costs $3 and pays $4 in 2 years.
Ans. You borrow security B and sell it, which means you receive $3, with these
proceeds you buy security A. In 2 years you receive $5 and have to pay
$4. You make a $1 profit.
7. What steps would you follow in order to take advantage of the following
arbitrage opportunity (if there is one)? Security A costs $100 and pays
$120 in 3 years. Security B costs $100 and pays $110 in one year. Your
friend tells you that he would like you to lend him $110 in a year and that
he would give $130 the following year. Finally you know that in two years,
with $130, you can invest in a security that will pay you either $140 or
$121 (with equal probability) after a year.
2
,Ans. You borrow security A and sell it, with the proceeds you buy security B.
After a year you lend the money to your friend. The next year when he
pays back, you invest in the risky security. After the third year, this will
give you either $140 or $121, while you have to pay $120. So you either
have a profit of $20 or $1.
8. What steps would you follow in order to take advantage of the following
arbitrage opportunity (if there is one)? Security A costs $100 and pays
$110 in 2 years. Security B costs $100 and pays $109 in one year. You
know that in a year with $109 you can invest in a security that pays $120
or $109 (with equal probability) the following year.
Ans. This is not an arbitrage opportunity.
9. Intuitively, is the Federal Funds rate generally higher, lower or the same
as LIBOR? Why?
Ans. The LIBOR rate should be higher than the Federal Funds rate, since it
should include a higher probability of default by the banks trading LIBOR.
10. Intuitively, is LIBOR generally higher, lower or the same as the repo rate?
Why?
Ans. LIBOR should be higher than the repo rate since it is not collateralized
with another security, as it occurs with the repo rate.
11. What are the steps to take a long position on a given U.S. security via the
repo market?
Ans. The trader must take the following steps (repo):
At time t:
i. Buy bond at Pt and deliver the bond to the repo dealer.
ii. The repo dealer will pay Pt − haircut to the trader, which is made
whole (minus the haircut) for the cost of the bond.
At time T :
iii. The trader gets the bond from the repo dealer and sells it for PT .
iv. With the proceeds PT the trader pays back (Pt −haircut)×(1+Repo)
to the repo dealer.
12. What are the steps to take a short position on a given U.S. security via
the repo market?
Ans. The trader must take the following steps (reverse repo):
At time t:
3
, i. Borrows the bond from the repo dealer and sells it at Pt .
ii. Receives Pt which he posts as collateral with the repo dealer.
At time T :
iii. The trader buys the bond for PT and gives it back to the repo dealer.
iv. The repo dealer pays Pt × (1+Repo). The dealer makes a profit if
this is larger than PT .
13. What’s the return on capital for a trader who entered into a one-month
repo where Pt = 98.5, PT = 99.01, Repo= 5% and haircut= 0.8?
Ans. The return on capital is 0.13.
14. What’s the profit for a trader who entered into a one-week reverse repo
where Pt = 99.40, PT = 99.48 and Repo= 6%?
Ans. The profit is 0.0347.
15. You find a bond that has a repo rate substantially lower than the GCR.
Is this, for certain, an arbitrage opportunity?
Ans. No, it might be that the bond is short on supply (hard to find), which
means that the trader might be thinking that the bond is overpriced and
is speculating that the price will fall. By entering in a reverse repo, the
trader might make a substantial profit, even willing to forgo part of the
rate to be in the transaction.
16. You are told that there is an ample supply for the bond mentioned in
question 13. Does this affect your previous answer?
Ans. Yes, since it shows that the lower rate is not due to scarcity of a specific
type of bond.
17. What are the gains from trade of entering into a swap for these two firms?
Firm A Firm B
Fixed Rate 13% 16%
Floating Rate LIBOR + 3% LIBOR + 6%
Ans. Gains from trade are zero.
18. What are the gains from trade of entering into a swap for these two firms?
Firm A Firm B
Fixed Rate 10% 15.5%
Floating Rate LIBOR + 2% LIBOR + 4%
Ans. Gains from trade are 3.5%.
4
