Question

1. Present the formula for the convexity of a bond. Build a spreadsheet to calculate the convexity of an 8% (3 year duration) coupon bond at the initial yield to maturity of 10% and a zero coupon bond (3 year duration) at a 10% interest rate for both

Spreadsheet format

Time until payment	Payment	Payment Discounted at 10%	Weight	Column 1 * Column 4
1
2
3

Answer 1

Assuming Face Value (Par Value) 100

8% Coupon Bond
Time until payment	Payment	Payment Discounted at 10%	Weight of Discounted Values	Column 1 * Column 4	Convexity= PV*t*(t+1)/Price
1	8	7.27	0.08	0.08	14.55
2	8	6.61	0.07	0.14	39.67
3	108	81.14	0.85	2.56	973.70
		95.03	1.00	2.78	1,027.92
Zero Coupon Bond
Time until payment	Payment	Payment Discounted at 10%	Weight	Column 1 * Column 4
1	0	0.00	0.00	0	0.00
2	0	0.00	0.00	0	0.00
3	100	75.13	1.00	3	901.58
		75.13	1.00	3.00	901.58

Price of 8% Bond = 95.03

Price of Zero Coupon Bond = 75.13

Duration of 8% Bond = 2.78

Duration of zero coupon Bond = 3

Convexity of 8% Bond = 1027.92/95.03 =10.82

Convexity of zero coupon Bond = 901.58/75.13 = 12