Question

Consider the following step up security ($1,000 par) with semi-annual coupons (all CFs are at the end of the semi-annual):

Year	1	2	3
Coupon rate	3%	4%	5%

17. Manager C plans to buy the security at beginning of year 2 (after 2 coupon payments) and hold it to maturity with YTM of 3.9%. What is the security’s convexity (in years squared) at the beginning of year 2? Round the final answer to nearest 3 decimals i.e. 1.234.

Answer 1

You have to find the convexity after 2 years or one years before maturity

Periodic coupon payment = 1000*0.05/2 = 25

Periodic YTM = 3.9/2 = 1.95%

Year	Period (t)	Coupon	Face Value	CF	DCF = CF/1.0195^t	w = DCF/PV	Macaulay Duration = t * w	Convexity w*t*(t+1)/(1+y)^2
0.5	1	25		25	24.522	0.024	0.024	0.047
1	2	25	1000	1025	986.165	0.976	1.951	5.633
				PV =	1010.686	1.000	1.976	5.679

Semi-annual convexity = 5.679

Annual convexity = 5.679 / (2^2) = 1.420