Question: Please help to answer the following questions: 2. a) (7 points) The discount factors for different maturities (t) are as follows: t (years) Z(0,t) 0.5

Please help to answer the following questions:

2. a) (7 points) The discount factors for different maturities (t) are as follows: t (years) Z(0,t) 0.5 0.9480 1 0.9260 1.5 0.8840 2 0.8530 Calculate the duration and the convexity of a portfolio which consists of all of the following securities: 2 units of 1-year fixed-rate coupon bonds with a coupon rate of 6%, which pay coupons semi-annually, and which have a face value of $100 each; . 6 units of 2-year zero-coupon bonds, with a face value of $100 each; 1 unit of a 1.5-year floating-rate bond paying the 6-month semi-annually- compounded spot rate (and no spread) semi-annually, with a face value of $100, which has just been issued. b) (3 points) If the continuously-compounded spot yield curve shifts downwards by 3%-points parallelly, by how many dollars will the value of the portfolio in question a) change approximately? Use the second-order Taylor-approximation (i.e., duration and convexity)

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