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LOS g, (Part 2): Estimate a bond's percentage price change, given the bond's duration and convexity and a specified change in interest rates.ffice ffice" />
Q1. For a given bond, the duration is 8 and the convexity is 50. For a 60 basis point decrease in yield, what is the approximate percentage price change of the bond?
A) 4.98%.
B) 4.62%.
C) 2.52%.
Correct answer is A)
The estimated price change is -(duration)(?y) + (convexity) × (?y)2 = -8 × (-0.006) + 50 × (-0.0062) = +0.0498 or 4.98%.
Q2. A bond has a duration of 10.62 and a convexity of 91.46. For a 200 basis point increase in yield, what is the approximate percentage price change of the bond?
A) -24.90%.
B) -1.62%.
C) -17.58%.
Correct answer is C)
The estimated price change is:
-(duration)(?y) + (convexity) × (?y)2 = -10.62 × 0.02 + 91.46 × (0.022) = -0.2124 + 0.0366 = -0.1758 or –17.58%.
Q3. If a Treasury bond has a duration of 10.27 and a convexity of 71.51. Which of the following is closest to the estimated percentage price change in the bond for a 125 basis point increase in interest rates?
A) -11.718%.
B) -13.956%.
C) -9.325%.
Correct answer is A)
The estimated percentage price change = the duration effect plus the convexity effect. The formula is: [–duration × (Δy)] + [convexity × (Δy)2]. Therefore, the estimated percentage price change is: [–(10.27)(1.25%)] + [(71.51)(0.0125)2] = –12.8375 + 1.120% = –11.7175%.
Q4. Consider a bond with a duration of 5.61 and a convexity of 21.92. Which of the following is closest to the estimated percentage price change in the bond for a 75 basis point decrease in interest rates?
A) 4.33%.
B) 4.21%.
C) 4.12%.
Correct answer is A)
The estimated percentage price change is equal to the duration effect plus the convexity effect. The formula is: [–duration × (Δy)] + [convexity × (Δy)2]. Therefore, the estimated percentage price change is: [–(5.61)(–0.0075)] + [(21.92)(-0.0075)2] = 0.042075 + 0.001233 = 0.043308 = 4.33%.
Q5. A bond has a convexity of 25.72. What is the approximate percentage price change of the bond due to convexity if rates rise by 150 basis points?
A) 0.71%.
B) 0.58%.
C) 0.26%.
Correct answer is B)
The convexity effect, or the percentage price change due to convexity, formula is: convexity × (Δy)2. The percentage price change due to convexity is then: (25.72)(0.015)2 = 0.0058.
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发表于 2009-3-5 11:33
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