Question

Find the convexity of a seven-year maturity, 6.2% coupon bond selling at a yield to maturity of 7.7%. The bond pays its coupons annually. (Do not round intermediate calculations. Round your answer to 4 decimal places.) Convexity

Answer 1

N	CF	PVF	PVF x CF	N x (N + 1) x PVF x CF
1	62	0.928505	57.56732	115.1346
2	62	0.862122	53.45155	320.7093
3	62	0.800484	49.63003	595.5604
4	62	0.743254	46.08174	921.6348
5	62	0.690115	42.78713	1283.614
6	62	0.640775	39.72807	1668.579
7	1062	0.594963	631.8509	35383.65
		Sum	921.0967	40288.88
			Convexity	37.70931

Convexity = 1 / (P x (1 + YTM)^2) x Sum of N x (N + 1) x PVF x CF

where, P - Current Bond Price = Sum of PVF x CF = $921.0967

YTM - Yield to Maturity = 7.7%

N - Period

PVF - Present Value Factor = 1 / (1 + YTM)^N

CF - Cash Flow = Coupon + Principal

=> Convexity = 1 / (921.0967 x (1 + 7.7%)^2) x 40,288.88

= 37.7093