Question

A three-year old 10-year 8% semi-annual coupon bond is selling at $1,200 today. If the yield increases by 25 basis points, how much of the price change is due to

convexity of the bond? (Face Value = $1,000)

Answer 1

K = Nx2

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

k=1

K =10x2

1200 =∑ [(8*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^10x2

k=1

YTM% = 5.39

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc	Convexity Calc
0	($1,200.00)	=(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	40.00	1.03	38.95	38.95	73.87
2	40.00	1.05	37.93	75.86	215.78
3	40.00	1.08	36.93	110.80	420.24
4	40.00	1.11	35.96	143.85	682.02
5	40.00	1.14	35.02	175.10	996.18
6	40.00	1.17	34.10	204.60	1,358.05
7	40.00	1.20	33.21	232.44	1,763.21
8	40.00	1.24	32.33	258.68	2,207.49
9	40.00	1.27	31.49	283.37	2,686.95
10	40.00	1.30	30.66	306.60	3,197.87
11	40.00	1.34	29.86	328.41	3,736.74
12	40.00	1.38	29.07	348.86	4,300.26
13	40.00	1.41	28.31	368.01	4,885.31
14	40.00	1.45	27.57	385.92	5,488.97
15	40.00	1.49	26.84	402.64	6,108.48
16	40.00	1.53	26.14	418.21	6,741.27
17	40.00	1.57	25.45	432.68	7,384.90
18	40.00	1.61	24.78	446.11	8,037.11
19	40.00	1.66	24.13	458.54	8,695.78
20	1,040.00	1.70	611.01	12,220.17	243,331.34
			Total	17,639.80	312,311.80

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

=312311.8/(1200*2^2)

=65.06

Using convexity adjustment

Convexity adjustment = 0.5*convexity*Yield_Change^2*Bond_Price

0.5*65.06*0.0025^2*1200

=0.24