Homework 3
Finance Capstone Advanced Topics
Homework Three
AIJIA ZHOU
The general information of the two bonds are shown below: Coupon | 10.625% | 4.25% | Coupon frequency | Semi-annual | Semi-annual | Coupon type | Fixed | Fixed | Day count | Act/Act | Act/Act | Issue date | August 15, 1985 | August 15, 2005 | Maturity date | August 15, 2015 | August 15, 2015 | Amount issued | 7.15 billion | 32.47 billion | Amount outstanding | 4.02 billion | 32.47 billion |
Modified Duration Method
In order to create a long-short portfolio that had no exposure to changes in interest rates, we can use modified duration hedge ratio.
The following formula is the function to calculate modified duration hedge ratio. The term K is a measure of the responsiveness of the yield spread to changes in the two bonds. We assume K is 1. Meanwhile DL is the duration of the 10.625% bond and DS is the duration of the 4.25% bond. L and S are the price of the 10.625% bond and 4.25% bond, respectively.
N=DLLDSSK
According to the case, the modified duration of the 10.625% bond was 5.14, and the modified duration of the 4.25% bond was 5.84. The price of the 10.625% bond is $1,441.96 (= 1,418.28+23.68). The price of the 4.25% bond is $1,069.16 (= 1,059.69 + 9.47). Therefore, the modified duration ratio is:
N=5.14×1,441.965.84×1,069.16×1=1.1870
In order to hedge the risk, when Franey invest 1,000 10.625% bond, he should also short 1,187 4.25% bond.
Val01 Method
The 10.625% bond was priced at 141.8281 (per $100 face amount) and had a Val01 of 0.0741. The 4.25% bond was priced at 105.9688 and had a Val01 of 0.0625. To create a long-short portfolio that had no exposure to changes in interest rates, for each $1,000 face amount of the 10.625% bond, he would sell $1,1185.60 face amount of the 4.25% bond for $1,256.37+$11.23 accrual. The result from this method is very similar to the result from modified duration method.
1,185.60=1,000×0.07410.0625
1,2537 +
Homework Three
AIJIA ZHOU
The general information of the two bonds are shown below: Coupon | 10.625% | 4.25% | Coupon frequency | Semi-annual | Semi-annual | Coupon type | Fixed | Fixed | Day count | Act/Act | Act/Act | Issue date | August 15, 1985 | August 15, 2005 | Maturity date | August 15, 2015 | August 15, 2015 | Amount issued | 7.15 billion | 32.47 billion | Amount outstanding | 4.02 billion | 32.47 billion |
Modified Duration Method
In order to create a long-short portfolio that had no exposure to changes in interest rates, we can use modified duration hedge ratio.
The following formula is the function to calculate modified duration hedge ratio. The term K is a measure of the responsiveness of the yield spread to changes in the two bonds. We assume K is 1. Meanwhile DL is the duration of the 10.625% bond and DS is the duration of the 4.25% bond. L and S are the price of the 10.625% bond and 4.25% bond, respectively.
N=DLLDSSK
According to the case, the modified duration of the 10.625% bond was 5.14, and the modified duration of the 4.25% bond was 5.84. The price of the 10.625% bond is $1,441.96 (= 1,418.28+23.68). The price of the 4.25% bond is $1,069.16 (= 1,059.69 + 9.47). Therefore, the modified duration ratio is:
N=5.14×1,441.965.84×1,069.16×1=1.1870
In order to hedge the risk, when Franey invest 1,000 10.625% bond, he should also short 1,187 4.25% bond.
Val01 Method
The 10.625% bond was priced at 141.8281 (per $100 face amount) and had a Val01 of 0.0741. The 4.25% bond was priced at 105.9688 and had a Val01 of 0.0625. To create a long-short portfolio that had no exposure to changes in interest rates, for each $1,000 face amount of the 10.625% bond, he would sell $1,1185.60 face amount of the 4.25% bond for $1,256.37+$11.23 accrual. The result from this method is very similar to the result from modified duration method.
1,185.60=1,000×0.07410.0625
1,2537 +