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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 3 months ago
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