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1)Which ONE of the following bonds would have highest interest rate risk? a
1)Which ONE of the following bonds would have highest interest rate risk?
| a. |
17-year zero coupon bond with $1,000 face value. |
|
| b. |
5-year 10% annual coupon bond with $1,000 face value. |
|
| c. |
12-year 4% annual coupon bond with $1,000 face value. |
|
| d. |
12-year 7% annual coupon bond with $1,000 face value. |
|
| e. |
17-year 5% annual coupon bond with $1,000 face value. |
2)
A $5,000 bond with a coupon rate of 6.4% paid semi-annually has four years to maturity and a yield to maturity of 6.2%. If interest rates fall and the yield to maturity decreases by 0.8%, what will happen to the price of the bond?
| a. |
Fall by $40.49. |
|
| b. |
Rise by $142.78. |
|
| c. |
Rise by $84.46. |
|
| d. |
Fall by $98.64. |
|
| e. |
None of the answers are correct. |
Expert Solution
1)Interest rate risk is defined by duration of bond, and duration is higher for bonds with longer maturity and less coupon rate,
So,
Option A is correct
17 year zero coupon bond with $1,000
2)
Answer)
Given
| Interest Rate |
= 6.2% / 2 = 3.1% |
| Coupon |
= (0.064 X 5000) / 2 =$160 |
| n |
= 4 X 2 = 8 YEARS |
Price = Coupon x [1 - 1 / (1 + r)n] / r + FV / (1 + r)n
Price = 160 x [ 1 - 1 / (1.031)8] / 0.031 + 5000 / (1 + 0.031)8
= 160 x 6.85 + 3937
= $5035
| Interest Rate |
= 6.2% - 0.8% = 5.4% |
| Coupon |
= (0.064 X 5000) / 2 =$160 |
| n |
= 4 X 2 = 8 YEARS |
| Rate |
= 5.4% / 2 = 2.7% |
Price = Coupon x [1 - 1 / (1 + r)n] / r + FV / (1 + r)n
Price = 160 x [ 1 - 1 / (1.027)8] / 0.0327 + 5000 / (1 + 0.027)8
= 160 x 7.09 + 4042
= $ 5177
Change in price = $5177 - $5035
= $142
Price has fallen by $142.
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