Fixed Income Quiz 1
Question #1: Use the table of US 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 ½ s of 11/15/2010 102.1581
0s of 5/15/2011 99.6012
1 ¾ s of 11/15/2011 101.6435
Discount Factors (Use four decimal points and not in 32nd):
D(0.5) = _________________0.9991
D (1.0) = _________________0.9960
D (1.5) = _________________0.9903
Show your work or formula.
(100+4.5 /2) d(0.5) = 102.1581 => d(0.5) = 102.1581 / 102.25 = 0.9991
0 d(0.5) + 100 d (1.0) = 99.6012 => d(1.0) = 99.6012 / 100 = 0.9960
1 ¾ /2 d(0.5) + 1 ¾ /2 d(1.0) + (100 + 1 ¾ /2) d(1.5) = 101.6435
= > d(1.5) = [101.6435 – 0.875 (0.9991) – 0.875 (0.9960)] / (100 + 0.875) = 0.9903
Question #2: Suppose there is a Treasury issue with a coupon of 2% maturing on 11/15/2011. Using the discount factors derived from Question #1 above to answer the following questions. (please use four decimals and not 32nd)
(a) What would be the fair price today for the 2s of 11/15/2011? _____________102.0154
(b) If the bond was traded at a price of 101 instead of the price derived from (a) above, was the bond rich or cheap? ___________Cheap
(c) How could an arbitrageur profit from this price difference using the bonds in the above table? _______________________Buy this 2s and short the replicate portfolio
Show your work.
(a)
2/2 d(0.5) + 2/2 d(1.0) + (100+2/2) d(1.5)
= 1 (0.9991) + 1 (0.9960) + 101 (0.9903)
= 102.0154
(b)
Since the fair value (102.0154) is higher than traded price (101), the bond is
Bond Price
4 ½ s of 11/15/2010 102.1581
0s of 5/15/2011 99.6012
1 ¾ s of 11/15/2011 101.6435
Discount Factors (Use four decimal points and not in 32nd):
D(0.5) = _________________0.9991
D (1.0) = _________________0.9960
D (1.5) = _________________0.9903
Show your work or formula.
(100+4.5 /2) d(0.5) = 102.1581 => d(0.5) = 102.1581 / 102.25 = 0.9991
0 d(0.5) + 100 d (1.0) = 99.6012 => d(1.0) = 99.6012 / 100 = 0.9960
1 ¾ /2 d(0.5) + 1 ¾ /2 d(1.0) + (100 + 1 ¾ /2) d(1.5) = 101.6435
= > d(1.5) = [101.6435 – 0.875 (0.9991) – 0.875 (0.9960)] / (100 + 0.875) = 0.9903
Question #2: Suppose there is a Treasury issue with a coupon of 2% maturing on 11/15/2011. Using the discount factors derived from Question #1 above to answer the following questions. (please use four decimals and not 32nd)
(a) What would be the fair price today for the 2s of 11/15/2011? _____________102.0154
(b) If the bond was traded at a price of 101 instead of the price derived from (a) above, was the bond rich or cheap? ___________Cheap
(c) How could an arbitrageur profit from this price difference using the bonds in the above table? _______________________Buy this 2s and short the replicate portfolio
Show your work.
(a)
2/2 d(0.5) + 2/2 d(1.0) + (100+2/2) d(1.5)
= 1 (0.9991) + 1 (0.9960) + 101 (0.9903)
= 102.0154
(b)
Since the fair value (102.0154) is higher than traded price (101), the bond is