A 10-year US government bond issued on July 1, 2004 had an annual coupon of 4.39% paid semi-annually, a face value of $1000, and the first coupon payable in 6 months on January 3, 2005. Suppose the yield curve when the bond was issued was as given in the middle column Table 1.
Table 1: Yield curves
|
Term to maturity
|
Effective annual spot rate 7/1/2004
(% per annum)
|
Effective annual spot rate 7/2/2012
(% per annum)
|
|
6 months
|
1.64
|
0.15
|
|
12 months
|
2.07
|
0.21
|
|
18 months
|
2.35
|
0.25
|
|
24 months
|
2.64
|
0.30
|
|
30 months
|
2.86
|
0.34
|
|
36 months
|
3.08
|
0.39
|
|
42 months
|
3.24
|
0.46
|
|
48 months
|
3.41
|
0.53
|
|
54 months
|
3.57
|
0.60
|
|
60 months
|
3.74
|
0.67
|
|
66 months
|
3.85
|
0.76
|
|
72 months
|
3.96
|
0.85
|
|
78 months
|
4.07
|
0.95
|
|
84 months
|
4.18
|
1.04
|
|
90 months
|
4.24
|
1.13
|
|
96 months
|
4.31
|
1.23
|
|
102 months
|
4.39
|
1.32
|
|
108 months
|
4.55
|
1.42
|
|
114 months
|
4.56
|
1.51
|
|
120 months
|
4.57
|
1.61
|
(a) What would have been the market price for the bond on July 1, 2004?
(b) What would have been the market price for the bond on July 2, 2012 (immediately after the July 2012 coupon was paid)?
(c) Can you explain why the bond is selling at a premium in 2012?
Now suppose you purchased the bond on July 2, 2012 (immediately after the July 2012 coupon was paid) and you held it to maturity.
(d) Calculate the ex-post effective annual rate of return you would have earned on your investment. [Hint: If you do not have a financial calculator that calculates the IRR, you might have to graph the NPV function to obtain this.]
Suppose you also purchased on July 2, 2012 (immediately after the July 2012 coupon was paid) a 5-year US government note issued on July 1, 2009 with an annual coupon of 2.16% paid semi-annually.
(e) Calculate the price of the note at the interest rates in the third column of Table 1.
Once again, suppose that you hold the note to maturity.
(f) Calculate the ex-post effective annual rate of return you would have earned on this investment.
(g) Does the bond or the note yield a higher ex-post effective annual rate of return?
(h) Calculate the durations of the bond and the note at the set of interest rates in the third column of Table 2.
(i) How does the answer to (h) relate to your answer to (g)?