Question

Bond Duration: What is the duration of a bond with 7% discount rate, 3-year maturity, and 10% coupon paid annually?

Answer 1

K = N

Bond Price =∑ [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =3

Bond Price =∑ [(10*1000/100)/(1 + 7/100)^k]     +   1000/(1 + 7/100)^3

k=1

Bond Price = 1078.73

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,078.73)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	100.00	1.07	93.46	93.46
2	100.00	1.14	87.34	174.69
3	1,100.00	1.23	897.93	2,693.78
			Total	2,961.93

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=2961.93/(1078.73*1)

=2.745755

Modified duration = Macaulay duration/(1+YTM)

=2.75/(1+0.07)

=2.566127