PART TWO
ANSWERS
,Chapter 1
1.1 What are the cash flow dates and the cash flows of $1,000 face value of the U.S.
Treasury 2 3/4s of May 31, 2017, issued on May 31, 2010.
A. $13.75 every November 30 and May 31, starting on November 30, 2010,
through May 31, 2010, plus a principal payment of $1,000 on May 31, 2017.
1.2 Use this table of U.S. Treasury bond prices for settle on May 15, 2010, to derive the
discount factors for cash flows to be received in 6 months, 1 year, and 1.5 years.
BOND PRICE
4 1/2s of 11/15/2010 102.15806
0s of 5/15/2011 99.60120
1 3/4s of 11/15/2011 101.64355
A. Solve the following equations
to get ; ;
1.3 Suppose there existed a Treasury issue with a coupon of 2% maturing on
November 15, 2011. Using the discount factors derived from Question 1.2, what would
be the price of the 2s of November 15, 2011?
A. 102.01673:
1.4 Say that the 2s of November 15, 2011, existed and traded at a price of 101 instead
of the price derived from Question 1.3. How could an arbitrageur profit from this price
difference using the bonds in the earlier table? What would that profit be?
, A. First find the replicating portfolio by solving the following equations:
Solving, ; ; . Hence, the
arbitrageur should buy 100 face amount of the 2s for 101 and short the
replicating portfolio for a proceeds of
As the portfolio matures, the cash flows from the 2s will exactly offset the
requirements for covering the short. This leaves the initial profit at the time of the
trade of
per 100 face of the 2s bought.
1.5 Given the prices of the two bonds in the table as of May 15, 2010, find the price of the third
by an arbitrage argument. Since the 3 1/2s of 5/15/2020 is the on-the-run 10-year, why might this
arbitrage price not obtain in the market?
BOND PRICE
0s of 5/15/2020 69.21
3 1/2s of 5/15/2020 ?
8 3/4s of 5/15/2020 145.67
A. Verify that buying 40 face amount of the 8.75s and 60 face amount of the
0s replicates 100 face amount of the 3 1/2s. Therefore, the arbitrage price of the
3.5s is
, The on-the-run 10-year might very well sell for more than this arbitrage
price because of its superior liquidity and financing characteristics relative to the
0s and the 8 3/4s.
Chapter 2
2.1 You invest $100 for two years at 2% compounded semiannually. How much do you
have at the end of the two years?
A. Since two years are 4 semiannual periods,:
2.2 You invested $100 for three years and, at the end of those three years, your
investment was worth $107. What was your semiannually compounded rate of return?
A. Solve for the rate in the equation
2.3 Using the discount factors in the table, derive the corresponding spot and forward rates.
TERM DISCOUNT FACTOR
.5 .998752
1 .996758
1.5 .993529
A. Solve the following equations for the forward rates
ANSWERS
,Chapter 1
1.1 What are the cash flow dates and the cash flows of $1,000 face value of the U.S.
Treasury 2 3/4s of May 31, 2017, issued on May 31, 2010.
A. $13.75 every November 30 and May 31, starting on November 30, 2010,
through May 31, 2010, plus a principal payment of $1,000 on May 31, 2017.
1.2 Use this table of U.S. Treasury bond prices for settle on May 15, 2010, to derive the
discount factors for cash flows to be received in 6 months, 1 year, and 1.5 years.
BOND PRICE
4 1/2s of 11/15/2010 102.15806
0s of 5/15/2011 99.60120
1 3/4s of 11/15/2011 101.64355
A. Solve the following equations
to get ; ;
1.3 Suppose there existed a Treasury issue with a coupon of 2% maturing on
November 15, 2011. Using the discount factors derived from Question 1.2, what would
be the price of the 2s of November 15, 2011?
A. 102.01673:
1.4 Say that the 2s of November 15, 2011, existed and traded at a price of 101 instead
of the price derived from Question 1.3. How could an arbitrageur profit from this price
difference using the bonds in the earlier table? What would that profit be?
, A. First find the replicating portfolio by solving the following equations:
Solving, ; ; . Hence, the
arbitrageur should buy 100 face amount of the 2s for 101 and short the
replicating portfolio for a proceeds of
As the portfolio matures, the cash flows from the 2s will exactly offset the
requirements for covering the short. This leaves the initial profit at the time of the
trade of
per 100 face of the 2s bought.
1.5 Given the prices of the two bonds in the table as of May 15, 2010, find the price of the third
by an arbitrage argument. Since the 3 1/2s of 5/15/2020 is the on-the-run 10-year, why might this
arbitrage price not obtain in the market?
BOND PRICE
0s of 5/15/2020 69.21
3 1/2s of 5/15/2020 ?
8 3/4s of 5/15/2020 145.67
A. Verify that buying 40 face amount of the 8.75s and 60 face amount of the
0s replicates 100 face amount of the 3 1/2s. Therefore, the arbitrage price of the
3.5s is
, The on-the-run 10-year might very well sell for more than this arbitrage
price because of its superior liquidity and financing characteristics relative to the
0s and the 8 3/4s.
Chapter 2
2.1 You invest $100 for two years at 2% compounded semiannually. How much do you
have at the end of the two years?
A. Since two years are 4 semiannual periods,:
2.2 You invested $100 for three years and, at the end of those three years, your
investment was worth $107. What was your semiannually compounded rate of return?
A. Solve for the rate in the equation
2.3 Using the discount factors in the table, derive the corresponding spot and forward rates.
TERM DISCOUNT FACTOR
.5 .998752
1 .996758
1.5 .993529
A. Solve the following equations for the forward rates
