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# Fixed Income Securities

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A- A Treasury bond dealer finances a bond purchase by selling \$1,000,000 worth of Treasuries to a bank for \$999,851.39, promising to repurchase the bonds the following day for the face amount. What is the implied repo rate (bank discount basis of 360 days) on this transaction?
a. 5.24%
b. 5.42%
c. 5.50%
d. 5.67%

B- You are a portfolio manager soliciting dealer quotes for averaging a price for marking a position to market. You collect the following bid-ask quotes (in 32nds) from four dealers:
Dealer 1 101.22-23
Dealer 2 101.22-24
Dealer 3 101.21-23
Dealer 4 101.23-25

What is the average price you will use to mark your position to market?
a. 101.22
b. 101.23
c. 101.24
d. 101.25

C- Calculate the percentage price change to a 200 basis point symmetrical change in rates for a bond selling at 93-7/8 with a coupon of 5.56% and a maturity of 20 years.
a. 11.83%
b. 11.93%
c. 23.66%
d. 23.86%

D- A \$5,000 par bond is quoted at a price of 117-3/8. The bond is selling at
a. \$1,173.75 discount.
c. \$5,868.75 discount.

E- The annual effective rate on a step-up note calling for a 4% coupon rate for the first two years, 6.5% for the third and fourth years, and 10% for the fifth year is
a. 6.18%.
b. 6.20%.
c. 6.50%.
d. 8.00%.

F- Long Term Capital (LTC) is a hedge fund that was on the brink of bankruptcy a few years ago. LTC traded on a model that assessed the basis spread between longer-term Treasuries and corporate bonds. The model indicated a narrowing of the spread. LTC placed trades based on the model. What positions did they hold in the Treasury market and the corporate market that resulted in their near-bankruptcy?
a. bought Treasuries/sold corporate
b. bought Treasuries/bought corporate
c. sold Treasuries/sold corporate
d. sold Treasuries/bought corporate

#### Solution Preview

A- A Treasury bond dealer finances a bond purchase by selling \$1,000,000 worth of Treasuries to a bank for \$999,851.39, promising to repurchase the bonds the following day for the face amount. What is the implied repo rate (bank discount basis of 360 days) on this transaction?
a. 5.24%
b. 5.42%
c. 5.50%
d. 5.67%

Answer is not listed, but (B) is correct with slightly different assumptions
Repo Rate= The rate of return that can be earned by simultaneously selling a bond futures or forward contract and then buying an actual bond of equal amount in the cash market using borrowed money.
IRR= [(Invoice Price)/(Purchase Price)- 1][(Day Base)/(Days to Delivery)]
IRR= [1,000,000/999,851.39- 1][360/1]
IRR= 0.05350 (5.35%)
Answer (B) works if you assume a discount basis of 365:
IRR= [1,000,000/999,851.39- 1][365/1]
IRR= 0.0542 (5.42%)

B- You are a portfolio manager soliciting dealer quotes for averaging a price for marking a position to market. You collect the following bid-ask quotes (in 32nds) from four dealers:
Dealer 1 101.22-23
Dealer 2 101.22-24
Dealer 3 101.21-23
Dealer 4 101.23-25

What is the average price you will use to mark your position to market?
a. 101.22
b. 101.23
c. 101.24
d. 101.25 ...

#### Solution Summary

Several word problems regarding the pricing of- and market for- fixed income securities are solved in detail.

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