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Q7. A non-callable bond with 18 years remaining maturity has an annual coupon of 7% and a $1,000 par value. The current yield to maturity on the bond is 8%. Which of the following is closest to the effective duration of the bond? ffice ffice" />
A) 8.24.
B) 9.63.
C) 11.89.
Correct answer is B)
First, compute the current price of the bond as:
FV = $1,000; PMT = $70; N = 18; I/Y = 8%; CPT → PV = –$906.28
Then compute the price of the bond if rates rise by 50 basis points to 8.5% as:
FV = $1,000; PMT = $70; N = 18; I/Y = 8.5%; CPT → PV = –$864.17
Then compute the price of the bond if rates fall by 50 basis points to 7.5% as:
FV = $1,000; PMT = $70; N = 18; I/Y = 7.5%; CPT → PV = –$951.47
The formula for effective duration is:
(V- – V+) / (2V0Δy)
Therefore, effective duration is:
($951.47 – $864.17) / (2 × $906.28 × 0.005) = 9.63.
Q8. Calculate the effective duration for a 7-year bond with the following characteristics:
- Current price of $660
- A price of $639 when interest rates rise 50 basis points
- A price of $684 when interest rates fall 50 basis points
A) 6.8.
B) 3.1.
C) 6.5.
Correct answer is A)
The formula for calculating the effective duration of a bond is:
where:
§ V- = bond value if the yield decreases by ?y
§ V+ = bond value if the yield increases by ?y
§ V0 = initial bond price
§ ?y = yield change used to get V- and V+, expressed in decimal form
The duration of this bond is calculated as:
Q9. Consider an annual coupon bond with the following characteristics:
- Face value of $100
- Time to maturity of 12 years
- Coupon rate of 6.50%
- Issued at par
- Call price of 101.75 (assume the bond price will not exceed this price)
For a 75 basis point change in interest rates, the bond's duration is:
A) 5.09 years.
B) 8.79 years.
C) 8.17 years.
Correct answer is A)
Since the bond has an embedded option, we will use the formula for effective duration. (This formula is the same as the formula for modified duration, except that the “upper price bound” is replaced by the call price.) Thus, we only need to calculate the price if the yield increases 75 basis points, or 0.75%.
Price if yield increases 0.75%: FV = 100; I/Y = 6.50 + 0.75 = 7.25; N = 12; PMT = 6.5; CPT → PV = 94.12
The formula for effective duration is
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Where: |
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V- |
= call price/price ceiling |
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V+ |
= estimated price if yield increases by a given amount, Dy |
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V0 |
= initial observed bond price |
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Dy |
= change in required yield, in decimal form |
Here, effective duration = (101.75 – 94.12) / (2 × 100 × 0.0075) = 7.63 / 1.5 = 5.09 years.
Q10. Assume that the current price of a bond is 102.50. If interest rates increase by 0.5% the value of the bond decreases to 100 and if interest rates decrease by 0.5% the price of the bond increases to 105.5. What is the effective duration of the bond?
A) 5.50.
B) 5.48.
C) 5.37.
Correct answer is C)
The duration is computed as follows:
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Duration = |
105.50 ? 100 |
= 5.37 |
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2 × 102.50 × 0.005 |
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发表于 2009-3-5 10:25
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