Question
In: Finance
A bond portfolio named DEX, comprises four bonds (face value=$1000): 1)50 semi-annual bond, 5-year maturity, a...
A bond portfolio named DEX, comprises four bonds (face value=$1000):
1)50 semi-annual bond, 5-year maturity, a coupon rate of 4%.
2)100 annual bonds, 30-year maturity, 8% coupon bond.
3)150 zero coupon bonds, 10-year maturity.
4) 200 zero coupon bonds, 20-year maturity.
YTM/discount rate: 6%
Considering DEX’s convexity, if each bond’s convexity is given as follow:
Bond 1 (semi-annual coupon bond): 23.19
Bond 2 (annual coupon bond): 212.40
Bond 3 (zero coupon bond): 98.97
Bond 4 (zero coupon bond): 107.00
Given DEX’ convexity, when the interest rate increases from 6% to 7%, the DEX’s market value should fall by?
Solutions
Expert Solution
| Bond A | Bond B | Bond C | Bond D | ||
| Number of Bonds | 50 | 100 | 150 | 200 | |
| Weight | 0.1 | 0.2 | 0.3 | 0.4 | |
| Settlement Date | Settlement | 13/12/2019 | 13/12/2019 | 13/12/2019 | 13/12/2019 |
| Maturity | Maturity | 13/12/2024 | 13/12/2049 | 13/12/2029 | 13/12/2039 |
| Coupon | Coupon | 4.00% | 8.00% | 0.00% | 0.00% |
| Yield | yld | 6.00% | 6.00% | 6.00% | 6.00% |
| Coupon Payment/year | Frequency | 2 | 1 | 0 | 0 |
| Note | Duration of Zero Coupon bond is Maturity | ||||
| Modified Duration | Use MDuration in Excel | 4.424888359 | 13.10327299 | 10 | 20 |
| Convexity Given | 23.19 | 212.4 | 98.97 | 107 | |
| Convexity Annual | Convexity Given x Frequency^2 | 92.76 | 212.4 | 98.97 | 98.97 |
| Change in price = [–Modified Duration *Change in yield] +[1/2 * Convexity*(change in yield)^2] | |||||
| Change in Yield | Up from 6% to 7% | 1.00% | 1.00% | 1.00% | 1.00% |
| Ch Price | Using above Formula | -0.0396 | -0.1204 | -0.0951 | -0.1951 |
| Weighted Change in Price | w X Ch Price | -0.0040 | -0.0241 | -0.0285 | -0.0780 |
| Change in Price | Sum of weighted change in Price | -0.1346 | |||
jeff jeffy answered 4 months agoRelated Solutions
A bond portfolio named VEX, comprises four bonds (face value=$1000): 100 semi-annual bond, 5-year maturity, a...
A bond portfolio named VEX, comprises four bonds (face
value=$1000):
100 semi-annual bond, 5-year maturity, a coupon rate of 4%
200 annual bonds, 30-year maturity, 8% coupon bond.
300 zero coupon bonds, 10-year maturity.
400 zero coupon bonds, 20-year maturity.
a) If required yield (discount rate) is 6% for all bonds per
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weight in the portfolio?
b) Given the 6% initial yield, what is the VEX’s duration...
A bond portfolio named VEX comprises four bonds (face value=$1000): 1) 100 semi-annual bond, 5-year maturity,...
A bond portfolio named VEX comprises four bonds (face
value=$1000):
1) 100 semi-annual bond, 5-year maturity, a coupon rate of
4%
2) 200 annual bonds, 30-year maturity, 8% coupon bond.
3) 300 zero-coupon bonds, 10-year maturity.
4) 400 zero-coupon bonds, 20-year maturity.
1. If the required yield (discount rate) is 6% for all bonds per
year, what is the market fair value of VEX? What is each bond’s
weight in the portfolio?
A bond portfolio named VEX comprises four bonds (face value=$1000): 1) 100 semi-annual bond, 5-year maturity,...
A bond portfolio named VEX comprises four bonds (face
value=$1000):
1) 100 semi-annual bond, 5-year maturity, a coupon rate of
4%
2) 200 annual bonds, 30-year maturity, 8% coupon bond.
3) 300 zero-coupon bonds, 10-year maturity.
4) 400 zero-coupon bonds, 20-year maturity.
2. Given the 6% initial yield, what is the VEX’s duration (use
Macaulay’s duration)?
A bond portfolio named VEX comprises four bonds (face value=$1000): 1) 100 semi-annual bond, 5-year maturity,...
A bond portfolio named VEX comprises four bonds (face
value=$1000):
1) 100 semi-annual bond, 5-year maturity, a coupon rate of
4%
2) 200 annual bonds, 30-year maturity, 8% coupon bond.
3) 300 zero-coupon bonds, 10-year maturity.
4) 400 zero-coupon bonds, 20-year maturity.
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shorter or longer than its time to maturity? What is the meaning of
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A bond portfolio named VEX comprises four bonds (face value=$1000): 1) 100 semi-annual bond, 5-year maturity,...
A bond portfolio named VEX comprises four bonds (face
value=$1000):
1) 100 semi-annual bond, 5-year maturity, a coupon rate of
4%
2) 200 annual bonds, 30-year maturity, 8% coupon bond.
3) 300 zero-coupon bonds, 10-year maturity.
4) 400 zero-coupon bonds, 20-year maturity.
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