Question

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A 6.5% coupon bearing bond that pays interest semi-annually has a yield to maturity of 8.2% per year. This bond has a duration of 13.1 years and a convexity of 134. If the market yield decreases 64 basis points, calculate an estimate of the percent price change due to both duration and convexity. (Answer to the nearest hundredth of a percent, i.e. 1.23 but do not use the % sign). Selected Answer: Incorrect 8.93 Correct Answer: Correct 8.33 ± 0.01

Answer #1

In the above formula, duration is Modified Duration and not Macaulay Duration. And in the question we are given Macaulay Duration.

Modified Duration = Macaulay Duration /( 1 + y/n), where y = yield to maturity and n = number of discounting periods in year ( 2 for semi – annual paying bonds )

= 13.1 [1 + (8.20% 2)]

Modified Duration = 12.5841 years

Note: 100 basis points is equal to 1%. In other words, 1 basis point is 1/10000 %.

Yield = - 64/10000 = - 0.0064

Convexity = 134

%Price = ( -
12.5841 x - 0.0064) + 0.5 x 134 x (- 0.0064)^{2}

= 8.05 + 0.28

%Price =
**8.33**

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