Question

Q2. A bond has a coupon rate of 6% The coupon frequency is annual and the bond has 3 years to maturity.

a) If the yield to maturity is 4.85% what is the duration of the bond?

b) What is the modified duration of the bond?

Answer 1

DUration = Sum [Weight * Year ]

Assume $ 1000 as face value

Year	CF	PVF @4.85%	Disc CF	Weight	Wt * year
1	60	0.953743	57.22461	0.055482	0.0555
2	60	0.909627	54.57759	0.052916	0.1058
3	1060	0.86755	919.6034	0.891602	2.6748
Duration					2.8361

Duration of Bond is 2.84 Years

Modified duration is Duration / (1+YTM)

= 2.84 / ( 1 + 0.0485)

= 2.84 / 1.0485

= 2.75

I.e 1% change in YTM leads to 2.75% change in Price of Bond