Consider a 2-year coupon bond that pays coupon annually with a coupon rate of 3%, face value $1000, a yield to maturity of 4%.

(a) What is the approximated bond price estimated by both duration and convexity if the yield is increased by 0.5%?

(b) Suppose you purchased 1 unit of the above coupon bond mentioned above and is worried if the interest rate will increase. You are considering taking short position on a zero coupon bond. The zero coupon bond has a maturity of 2 years, face value of 1000 and a yield to maturity of 3.5%. How many zero coupon bonds do you need to short to match the duration?