Explanation:
For a zero-coupon bond with continuous compounding, the first-order duration approximation is
where and . That gives the stated 10.50% price decline.
The convexity adjustment for a bond priced with continuous compounding is
For a zero-coupon bond, convexity is . Thus,
or 0.55125% of price.
Initial price:
So the convexity benefit is
This reduces the estimated loss by about $0.1230, making the total estimated drop about $2.2199. Therefore the correct answer is A.
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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