17
33. Refer to Exhibit 16-3. The value of the swap is ____ basis points in one year
a.
40.4
b.
60.6
c.
80.8
d.
20.5
e.
100.1
18
Exhibit 16-4
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
The following information is given concerning a substitution swap: You currently hold a 25 year, Aa
8% coupon bond priced to yield 10%. As a swap candidate you are considering a 25 year, Aa 8%
coupon bond priced to yield 10.50%. Assume a reinvestment rate of 10%, semiannual compounding,
and a one-year workout period.
Current Bond
Candidate Bond
Dollar Investment
$817.44
?
Coupon
80.00
80.00
i on One Coupon
2.00
2.20
Principal Value at Year End
819.23
782.33
Total Accrued
901.23
864.53
Total Gain
83.79
?
Gain per Invested Dollar
?
?
Realized Compound Yield
?
?
34. Refer to Exhibit 16-4. The dollar investment in the candidate bond is
a.
$780.34
b.
$1483.25
c.
$1361.54
d.
$1413.95
e.
$1000.00
Current Bond
Candidate Bond
Dollar Investment
Coupon
80.00
80.00
i on One Coupon
2.00
2.20
Principal Value at Year End
819.23
782.36
Total Accrued
Total Gain
83.79
84.19
Gain per Invested Dollar
Realized Compound Yield
Current prices: Pcurrent
= 40(PVIFA5%,50) + 1000(PVIF5%,50)
= 40(18.2559) + 1000(0.0872) = $817.44
= 40(PVIFA5.25%,50) + 1000(PVIF5.25%,50)
Year-end prices: Pcurrent
= 40(PVIFA5%,48) + 1000(PVIF5%,48)
= 40(18.0772) + 1000(0.0961) = $819.23
= 40(PVIFA5.25%,48) + 1000(PVIF5.25%,48)
= 40(17.4139) + 1000(0.0858) = $782.36
19
35. Refer to Exhibit 16-4. The realized compound yield on the current bond is
a.
6.00%
b.
7.00%
c.
8.00%
d.
10.00%
e.
12.00%
36. Refer to Exhibit 16-4. The value of the swap is ____ basis points in one year.
a.
26.91
b.
26.25
c.
31.25
d.
41.25
e.
51.25
20
Total Gain
Gain per Invested Dollar
0.102503
0.107889
Realized Compound Yield
Current prices: Pcurrent
= 40(PVIFA5%,50) + 1000(PVIF5%,50)
= 40(18.2559) + 1000(0.0872) = $817.44
Exhibit 16-5
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
The following information is given concerning a pure yield pick-up swap: You currently hold a 20
year, Aa 2% coupon bond priced to yield 9.5%. As a swap candidate you are considering a 20 year, Aa
14% coupon bond priced to yield 10.00. Assume a reinvestment rate of 11%, semiannual
compounding, and a one-year workout period.
Current Bond
Candidate Bond
Dollar Investment
$1222.04
$1343.18
Coupon
110.00
140.00
i on One Coupon
3.3
?
Principal Value at Year End
1218.04
?
Total Accrued
1341.34
?
Realized Compound Yield
9.5351%
?
37. Refer to Exhibit 16-5. The interest on one coupon for the candidate bond is
a.
$70.00
b.
$3.58
c.
$3.85
d.
$8.35
e.
$5.38
Dollar Investment
Coupon
i on One Coupon
Principal Value at Year End
1218.04
Total Accrued
1341.34
Realized Compound Yield
Current prices: Pcurrent
= 60(PVIFA4.75%,40) + 1000(PVIF4.75%,40)
= 60(17.7630) + 1000(0.1563) = $1222.0377
= 70(PVIFA5%,40) + 1000(PVIF5%,40)
= 70(17.1591) + 1000(0.1420) = $1343.18
Year-end prices: Pcurrent
= 60(PVIFA4.75%,38) + 1000(PVIF4.75%,38)
21
38. Refer to Exhibit 16-5. The value of the swap is ____ basis points in one year
a.
0.004921
b.
0.4921
c.
4.921
d.
49.21
e.
492.1
22
Exhibit 16-6
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
The following information is given concerning a substitution swap: You currently hold a 25 year, Aa
10% coupon bond priced to yield 12%. As a swap candidate you are considering a 25 year, Aa 10%
coupon bond priced to yield 13%. Assume a reinvestment rate of 12%, semiannual compounding, and
a one-year workout period.
Current Bond
Candidate Bond
Dollar Investment
$842.38
?
Coupon
100.00
100.00
i on One Coupon
3.0
2.75
Principal Value at Year End
843.50
780.46
Total Accrued
946.50
883.21
Total Gain
104.12
?
Gain per Invested Dollar
?
?
Realized Compound Yield
?
?
39. Refer to Exhibit 16-6. The dollar investment in the candidate bond is
a.
$1515.36
b.
$853.50
c.
$780.46
d.
$779.13
e.
$877.53
Dollar Investment
Coupon
100.00
100.00
i on One Coupon
2.75
Principal Value at Year End
843.50
780.46
Total Accrued
946.50
883.21
Total Gain
104.12
104.08
Gain per Invested Dollar
Realized Compound Yield
Current prices: Pcurrent
= 50(PVIFA6%,50) + 1000(PVIF6%,50)
= 50(15.7619) + 1000(0.0543) = $842.38
= 50(PVIFA6.5%,50) + 1000(PVIF6.5%,50)
Year-end prices: Pcurrent
= 50(PVIFA6%,48) + 1000(PVIF6%,48)
= 50(15.6500) + 1000(0.0610) = $843.50
= 50(14.6359) + 1000(0.0487) = $780.46
23
40. Refer to Exhibit 16-6. The realized compound yield on the current bond is
a.
10.00%
b.
11.9985%
c.
12.9397%
d.
13.9399%
e.
12.3585%
41. Refer to Exhibit 16-6. The value of the swap is ____ basis points in one year.
a.
94.14
b.
0.9414
c.
9.414
d.
941.4
e.
0.09414
24
Exhibit 16-7
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Consider two bonds, both pay semiannual interest. Bond A has a coupon of 8% per year, maturity of
30 years, yield to maturity of 9% per year, and a face value of $1000. Bond B has a coupon of 8% per
year, maturity of 30 years, yield to maturity of 9.5% per year, and a face value of $1000.
42. Refer to Exhibit 16-7. Calculate the percentage gain per invested dollar for Bond A assuming a one
year horizon, and a reinvestment rate of 9% per year.
a.
9.73%
b.
9.93%
c.
9.20%
d.
8.20%
e.
9.50%
25
43. Refer to Exhibit 16-7. Calculate the percentage gain per invested dollar for Bond B assuming a one
year horizon, and a reinvestment rate of 9.5% per year.
a.
9.73%
b.
9.93%
c.
9.20%
d.
8.20%
e.
9.50%
44. Refer to Exhibit 16-7. Calculate the value of swap out of Bond A into Bond B.
a.
0.41%
b.
1.73%
c.
0.23%
d.
0.00%
e.
0.51%
26
Exhibit 16-8
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Consider two bonds, both pay annual interest. Bond C has a coupon of 6% per year, maturity of 5
years, yield to maturity of 6% per year, and a face value of $1000. Bond D has a coupon of 8% per
year, maturity of 15 years, yield to maturity of 6% per year, and a face value of $1000.
45. Refer to Exhibit 16-8. Calculate the modified duration for Bond C.
a.
4.47
b.
4.22
c.
4.34
d.
5
e.
None of the above
46. Refer to Exhibit 16-8. Calculate the modified duration for Bond D.
a.
9.5
b.
9.8
c.
9.2
d.
15
e.
None of the above
27
47. Refer to Exhibit 16-8. Assume that your investment horizon is 6 years and your portfolio consists only
of Bond C and Bond D. Indicate the proportions invested in each bond, so that the portfolio is
immunized.
a.
50% in Bond C and 50% in Bond D
b.
64% in Bond C and 36% in Bond D
c.
36% in Bond C and 64% in Bond D
d.
100% in Bond D
e.
None of the above
Exhibit 16-9
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Consider two bonds, both pay annual interest. Bond Y has a coupon of 6% per year, maturity of 5
years, yield to maturity of 6% per year, and a face value of $1000. Bond X has a coupon of 7% per
year, maturity of 10 years, yield to maturity of 4% per year, and a face value of $1000.
48. Refer to Exhibit 16-9. Calculate the modified duration for Bond Y.
a.
7.8
b.
4.22
c.
4.34
d.
7.5
e.
9.8
28
49. Refer to Exhibit 16-9. Calculate the modified duration for Bond X.
a.
4.22
b.
7.8
c.
7.5
d.
9.2
e.
4.34
50. Refer to Exhibit 16-9. Assume that your investment horizon is 5 years and your portfolio consists only
of Bond Y and Bond X. Indicate the proportions invested in each bond, so that the portfolio is
immunized.
a.
50% in Bond Y and 50% in Bond X
b.
76% in Bond Y and 24% in Bond X
c.
36% in Bond Y and 64% in Bond X
d.
100% in Bond X
e.
100% in Bond Y
29
Exhibit 16-10
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
You are creating a portfolio that consists of the following two bonds. Bond A pays an annual 7%
coupon, matures in two years, has a yield to maturity of 8%, and a face value of $1,000. Bond B pays
an annual 8% coupon, matures in three years, has a yield to maturity of 9%, and a face value of
$1,000.
51. Refer to Exhibit 16-10. Calculate the price of Bond A.
a.
$975.62
b.
$982.17
c.
$990.57
d.
$1,009.50
e.
$1,018.08
52. Refer to Exhibit 16-10. Calculate the price of Bond B.
a.
$974.69
b.
$990.64
c.
$995.22
d.
$1,013.88
e.
$1,025.77
53. Refer to Exhibit 16-10. Calculate the Macaulay Duration for Bond A.
a.
0.98
b.
1.79
c.
1.90
d.
1.93
e.
2.31
30
54. Refer to Exhibit 16-10. Calculate the Macaulay Duration for Bond B.
a.
1.44
b.
2.47
c.
2.55
d.
2.70
e.
2.78
55. Refer to Exhibit 16-10. Calculate the Modified Duration for Bond A.
a.
0.98
b.
1.79
c.
1.90
d.
1.93
e.
2.31
56. Refer to Exhibit 16-10. Calculate the Modified Duration for Bond B.
a.
1.44
b.
2.47
c.
2.55
d.
2.70
e.
2.78
57. Refer to Exhibit 16-10. Assume that your investment horizon is 2 years and your portfolio consists
only of bonds A and B. What proportion should be invested in each bond to immunize the portfolio?
a.
Invest 72.4% in bond A and 27.6% in bond B.
b.
Invest 68.3% in bond A and 31.7% in bond B.
c.
Invest 58.5% in bond A and 41.5% in bond B.
d.
Invest 31.7% in bond A and 68.3% in bond B.
e.
Invest 27.6% in bond A and 72.4% in bond B.
31