Question

 

Calculate the duration for a $1,000, 4‐year bond with a 4.5 percent annual coupon, currently selling at par.

Use the bond’s duration to estimate the percentage change in the bond’s price for a decrease in the market interest rate to 3.5 percent.

Answer 1

If the bond is selling at par means Coupon rate and Yield are same.

Duration:
Duaration = Sum [ Weight * Year ]

Year	CF	PVF @4.5%	Disc CF	Weight	Wt * Year
1	$      45.00	0.9569	$   43.06	0.0431	0.0431
2	$      45.00	0.9157	$   41.21	0.0412	0.0824
3	$      45.00	0.8763	$   39.43	0.0394	0.1183
4	$      45.00	0.8386	$   37.74	0.0377	0.1509
4	$ 1,000.00	0.8386	$ 838.56	0.8386	3.3542
Duration	3.7490

Modified duaration :
Modified duration = Duration / [ 1 + YTM ]
It specifies% change in Price in opposite direction due to 1% change in YTM.

= 3.7490 / 1+ 0.045

= 3.7490 / 1.045

= 3.5875

i.e 1% change in Disc rate affects the price by 3.5875%

If the Int rate has become 3.5% [ 4.5% - 1% ] . price will change by 3.5875%