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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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14. On February 8, 2007 KC Kincaid paid \$1000 for a U.S. Government bond having a yield to maturity of 6 percent, a par value of \$1000, and exactly 10 years to maturity. Assume that on February 9, 2007 (?the day after?) the required yield to maturity for KC?s bond increases to 6.5 percent and remains constant, so that all future coupon payments for the bond will be reinvested at 6.5 percent compounded semiannually. Determine
a. the price of KC?s bond on February 8, 2008,
b. the future amount to which KC?s \$1000 will have grown by February 8, 2017 (the maturity date for the bond), assuming that each of the coupon payments that KC receives are reinvested at 6.5 percent compounded semiannually.

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