Question

Please solve and show work!

Use the quick formula to find the approximated duration from a 10 basis point change in yield, note you will need to find the change in the price up and down using the bond pricing formula. (4 digits after the decimal). Bond ABC Coupon 3.0096 Yield to maturity 2.5096 Maturity (years) Par $100.00 Price per par $101.8920 Face value 1000

Answer 1

Solution) Coupon = 3%

YTM = 2.5%

Maturity (years) = 4

Par value = $100

Bond quoted at Price per par (V0) = $101.8920

Face Value = $1000

Change in Yield, $\Delta y$ = 10 basis point = 10/10000 = 0.001 = 0.1%

First, increase the yield on the bond (YTM) by 10 basis points from 2.5% to 2.6%. The new price (V+), quoted on par, is computed as:

Year	Cash Flows
t=1	$                    3
t=2	$                    3
t=3	$                    3
t=4	$               103
YTM	2.60%
Bond Current Price	=NPV(YTM, Cash flows)
	$         101.5012

Thus, V+ = $101.50

Second, decrease the yield on the bond (YTM) by 10 basis points, from 2.5% to 2.4%. The new price (V-), quoted on par, is computed as:

Year	Cash Flows
t=1	$                    3
t=2	$                    3
t=3	$                    3
t=4	$               103
YTM	2.40%
Bond Current Price	=NPV(YTM, Cash flows)
	$         102.2626

Thus, V- = $102.26

Approximate modified duration is calculated using the below formula:

Modified Duration = (V_-V) 2(V)(Ay)

where, $\Delta y$ = change in yield = 0.1% = 0.001

Thus, Approximate modified duration = (102.2626 - 101.5012)/2*101.8920*0.001 = 0.7614/0.203784 = 3.7363