Question

QUESTION 28

1. For a 25-year, 5% annual pay bond currently trading at 6%, calculate the approximate convexity based on a change in yield of 100 basis points.

	a.	200.15
	b.	130.05
	c.	259.07

Answer 1

K = N

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

k=1

K =25

Bond Price =∑ [(5*1000/100)/(1 + 6/100)^k]     +   1000/(1 + 6/100)^25

k=1

Bond Price = 872.17

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc	Convexity Calc
0	($872.17)	=(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	50.00	1.79	27.92	279.20	2,733.33
11	50.00	1.90	26.34	289.73	3,094.34
12	50.00	2.01	24.85	298.18	3,449.95
13	50.00	2.13	23.44	304.75	3,797.11
14	50.00	2.26	22.12	309.61	4,133.29
15	50.00	2.40	20.86	312.95	4,456.37
16	50.00	2.54	19.68	314.92	4,764.68
17	50.00	2.69	18.57	315.66	5,056.85
18	50.00	2.85	17.52	315.31	5,331.86
19	50.00	3.03	16.53	313.99	5,588.95
20	50.00	3.21	15.59	311.80	5,827.61
21	50.00	3.40	14.71	308.86	6,047.52
22	50.00	3.60	13.88	305.26	6,248.56
23	50.00	3.82	13.09	301.07	6,430.76
24	50.00	4.05	12.35	296.37	6,594.30
25	1,050.00	4.29	244.65	6,116.21	141,528.63
			Total	12,262.79	224,912.23

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

=224912.23/(872.17*1^2)

=257.88 = 259.07