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Answer: To reduce the estimated bond price drop by $0.1230 so that the total estimated drop is only $2.2199
For a zero-coupon bond with continuous compounding, the first-order duration approximation is \[ \frac{\Delta P}{P} \approx -D\Delta y \] where \(D=30\) and \(\Delta y = 0.0035\). That gives the stated 10.50% price decline. The convexity adjustment for a bond priced with continuous compounding is \[ \frac{\Delta P}{P} \approx -D\Delta y + \frac{1}{2}C(\Delta y)^2 \] For a zero-coupon bond, convexity is \(C = T^2 = 30^2 = 900\). Thus, \[ \text{Convexity term} = \frac{1}{2}(900)(0.0035)^2 = 0.0055125 \] or **0.55125% of price**. Initial price: \[ P_0 = 100e^{-0.05\cdot 30} = 100e^{-1.5} \approx 22.3130 \] So the convexity benefit is \[ 22.3130 \times 0.0055125 \approx 0.1230 \] This reduces the estimated loss by about **$0.1230**, making the total estimated drop about **$2.2199**. Therefore the correct answer is **A**.
Author: Manit Arora
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Q-2. 715.2. A 30-year zero-coupon bond with a face value of $100.00 has a yield of 5.0% per annum with continuous compounding. Peter the analyst wants to estimate the impact of a 35 basis point increase ("shock up") in the yield without fully re-pricing the bond. Using duration, he estimates the bond price will drop by 10.50% or $2.34287. This was easy to compute as the bond has a duration of 30.0 years and 30.0 * 0.00350 = 10.50%. However, this calculation forgets to include a convexity term. Which is nearest to the additional impact of the convexity term only?
A
To reduce the estimated bond price drop by $0.1230 so that the total estimated drop is only $2.2199
B
To reduce the estimated bond price decrease by $0.2460 so that the total estimated drop is only $2.0969
C
To increase the estimated bond price decrease by $0.1674 so that the total estimated drop is $2.5102
D
To increase the estimated bond price decrease by $0.5690 so that the total estimated drop is $2.9118
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