Question

Using bond prices to calculate duration and convexity: A 20-year bond with a 6.5% coupon paid semiannually has a yield of 6.24%. Using a 1 bp change in yield, compute the approximate modified duration and approximate convexity of the bond. Using these, compute the approximate change in bond price when the bond yield increases by 150 bps. Calculate the exact change in bond price when the bond yield increases by 150 bps, and compare the two.

Answer 1

Set following parameters in financial calculator
Original
Coupon(PMT)	3.25	(100 x 6.5%/2)	Adjsutments for semiannual compounding
rate(i/y)	3.12%	(6.24%/2)
Period(N)	40	(20 x 2)
FV	100
PV	?
Press CPT + PV, PV will be
PV	$102.947473
PV for 1% change in yield + or -
For +				For -
Coupon(PMT)	3.25	(100 x 6.5%/2)		Coupon(PMT)	3.25	(100 x 6.5%/2)
rate(i/y)	3.1250%	(6.25%/2)		rate(i/y)	3.1150%	(6.23%/2)
Period(N)	40	(20 x 2)		Period(N)	40	(20 x 2)
FV	100			FV	100
PV	?			PV	?
Press CPT + PV, PV will be				Press CPT + PV, PV will be
PV	$102.831842			PV	$103.063289
Approx modified duration =		(PV for decrease in yield - PV for increase in Yeld)/(2 x % change in yield x original PV)
		(103.063289-102.831842)/(2 x .0001 x 102.947473)
		11.2410
Approximate convexity =		(PV for decresae in yield + PV for increase in yield - (2 x Original PV)) /( (% change)^2 x Original PV)
		(103.063289+102.831842 - (2 x 102.947473))/((.0001)^2 x 102.947473)
		179.703
Convexity adjusted price for 150BPS change
		(-11.2410 x 0.0150) + (1/2 x 179.703 x (0.0150)^2)
		(0.148398)	Change in drop of price
Actual price change on change of yield by 150 Bps
Coupon(PMT)	3.25	(100 x 6.5%/2)
rate(i/y)	3.87%	(7.74%/2)
Period(N)	40	(20 x 2)
FV	100
PV	?
Press CPT + PV, PV will be
PV	$87.487456
as % change from original pv =				(87.487456-102.947473)/102.947473
				-0.150173837
Actual % change				-15.0174
Convexity adjusted % change				-14.8398
Whild modified duration based % change				-16.8615