Question

# Consider the following step up security (\$1,000 par) with semi-annual coupons (all CFs are at the...

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.

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

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