Your portfolio contains 40% of Bond I, 20% of Bond II, 20% of Bond III, and 20% of Bond IV. Details of the four bonds are given below:
I. 10-year zero coupon government bond, par value $1000, current price = $613.91
II. 10-year zero coupon corporate bond, par value $1000, default premium = 2%
III. 5-year 15% coupon corporate bond, par value $1000, annual coupon payments, default premium = 9%, and YTM for a similar government bond is 6%
IV. 5-year 15% government coupon bond, par value $1000, annual coupon payments, YTM = 6%
a) What is the duration of the portfolio?
b) What is the convexity of Bond I?
c) If Bond I's yield increases by 1.5%, what is the price of Bond I based on duration with-convexity rule?