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Test bank For

Fixed Income Securities: Valuation, Risk, and Risk

Management by Pietro Veronesi Preliminary Version

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Chapter 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’).

• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

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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.

• 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.

• 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.

• 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.

• 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 timet:

• Buy bond atP

tand deliver the bond to the repo dealer.ii. The repo dealer will payP t−haircut to the trader, which is made whole (minus the haircut) for the cost of the bond.

At timeT:

iii. The trader gets the bond from the repo dealer and sells it forP T.iv. With the proceedsP Tthe trader pays back (Pt−haircut)×(1+Repo) to the repo dealer.

• 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 timet:

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• Borrows the bond from the repo dealer and sells it atPt.

ii. ReceivesP twhich he posts as collateral with the repo dealer.

At timeT:

iii. The trader buys the bond forP Tand gives it back to the repo dealer.iv. The repo dealer paysP t×(1+Repo). The dealer makes a profit if this is larger thanP T.

• What’s the return on capital for a trader who entered into a one-month

repo whereP t=98.5,P T=99.01, Repo= 5% and haircut= 0.8?Ans.The return on capital is 0.13.

• What’s the profit for a trader who entered into a one-week reverse repo

whereP t=99.40,P T=99.48 and Repo= 6%?Ans.The profit is 0.0347.

• 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.

• 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.

• What are the gains from trade of entering into a swap for these two firms?

Firm A Firm B Fixed Rate 13% 16% Floating RateLIBOR + 3% LIBOR + 6% Ans.Gains from trade are zero.

• 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 RateLIBOR + 2% LIBOR + 4% Ans.Gains from trade are 3.5%.

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