Question

5.Calculate the effective duration of a bond to a 100 basis point change in interest rates with a 6-1/4 coupon, 10-years remaining to maturity, and an asking quote of 110.7811 (decimal, not 32nds).

6.Calculate the effective convexity to a 100 basis point change of the bond in Question 5

7.Calculate the total percentage price change (duration and convexity) to a 65 basis point decrease in interest rates for the bond in Questions 5 and 6.

Answer 1

FV	100
coupon rate	6.25%
PMT=FV* COUPON %	6.25
time	10
YTM	4.86%	100 point	5.86%	100 point	3.86%
CPT           PV	110.81		102.89		119.52
	p0		p1		p2
?   YTM	0.01
Effective Duration =   (P2 – P1) / (2 *P0 *?YTM)
(119.52-102.89)/2*110.81*.01	7.50
Effective Convexity =   ( P2 – P1 – 2P0) / (2*P0* ?   YTM)^2)
(119.52-102.89-2*110.81)/(2*110.81*.01^2)		-9249.62
Effective duration (ED)	7.50
Effective Convexity (EC)	-9249.62
% ?price for ED =-ED* ?YTM*100
-7.5*0.065*100	-48.75
% ?price for EC =-EC* ?YTM*100
--9249.62*0.065*100	60122.53