Question

Consider a bond whose annual coupon rate is 10% and coupons are paid twice a year evenly. Its face-value is $100,000 and maturity is 2 years. Yield-to-maturity is 10% (annual) (fixed). What are the duration (in years) and convexity of the bond?

Answer 1

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =2x2

Bond Price =∑ [(10*100000/200)/(1 + 10/200)^k]     +   100000/(1 + 10/200)^2x2

k=1

Bond Price = 100000

.

C =

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc	Convexity Calc
0	($100,000.00)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period	=duration calc*(1+period)/(1+YTM/N)^2
1	5,000.00	1.05	4,761.90	4,761.90	8,638.38
2	5,000.00	1.10	4,535.15	9,070.29	24,681.07
3	5,000.00	1.16	4,319.19	12,957.56	47,011.57
4	105,000.00	1.22	86,383.76	345,535.04	1,567,052.33
			Total	372,324.80	1,647,383.35

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

=372324.8/(100000*2)

=1.861624

Modified duration = Macaulay duration/(1+YTM)

=1.86/(1+0.1)

=1.772975

Convexity =(∑ convexity calc)/(bond price*number of coupon per year^2)

=1647383.35/(100000*2^2)

=4.12