Question

Find the convexity of a 10-year maturity, 5% coupon bond selling at a yield to maturity of 6%. the bond pays its coupons annually.

Answer 1

K = N

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

k=1

K =10

Bond Price =∑ [(5*1000/100)/(1 + 6/100)^k]     +   1000/(1 + 6/100)^10

k=1

Bond Price = 926.4

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc	Convexity Calc
0	($926.40)	=(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	50.00	1.06	47.17	47.17	83.96
2	50.00	1.12	44.50	89.00	237.63
3	50.00	1.19	41.98	125.94	448.35
4	50.00	1.26	39.60	158.42	704.96
5	50.00	1.34	37.36	186.81	997.59
6	50.00	1.42	35.25	211.49	1,317.57
7	50.00	1.50	33.25	232.77	1,657.32
8	50.00	1.59	31.37	250.96	2,010.22
9	50.00	1.69	29.59	266.35	2,370.54
10	1,050.00	1.79	586.31	5,863.15	57,399.96
			Total	7,432.07	67,228.10

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

=67228.1/(926.4*1^2)

=72.57