3. The continuously compounded yield curve is given as follows: Maturity (years) Yield 0.5 5% 1 5.5% 1.5 6% 2 6.5% Calculate the duration and convexity of the following securities: (a) A 2 year coupon bond paying 4% semi-annually. (b) A 1 year floating rate bond with a 60 basis point spread, with coupons paid semi- annually. Compute its duration and convexity immediately after issuance (i.e., the first coupon is fixed). Note that: floating coupon with spread s =floating coupon with zero spread + fixed coupon s. (c) Construct a duration hedge for the 2 year coupon bond using 6 month ZCBs. (d) Construct a duration and convexity hedge for the 2 year coupon bond using 6 month and 1 year ZCBs. (e) You are additionally given the following information: year 1.5 year 2 6 month 1 year B (level) 1 1 1 1 B (slope) -0.5 -0.25 0.25 0.5 Construct a hedge for the 2 year coupon bond using 6 month and 1 year ZCBs. The portfolio must hedge against movements in both level and slope