Question

Your portfolio contains 60% of Bond I and 40% of Bond II. Details of the two bonds are given below:

10-year zero coupon government bond, par value $1000, current price = $613.91

10-year zero coupon corporate bond, par value $1000, default premium= 2%

What is the convexity of Bond II?

Answer 1

YTM of the zero coupon government bond = [(par value/bond price)^(1/n)] -1

= [(1,000/613.91)^(1/10)] -1 = 5.00%

YTM of the zero coupon corporate bond = YTM of the zero coupon government bond + default premium

= 5.00% + 2.00% = 7.00%

Price of the zero coupon corporate bond = par value/(1+YTM)^10 = 1,000/(1+7%)^10 = 508.35

Since the only cash flow which a zero coupon bond will have is the par value payment at maturity,

convexity of the corporate bond is

= 1,000*(10^2 + 10)/(508.35*(1+7%^2)*(1+7%)^10) = 96.08