An Australian Commonwealth Government Security (CGS) has a maturity date of 15 March 2023. The CGS is paying a coupon of 6% and is priced at a yield of 4%. The CGS pays coupons semi-annually on the 15th of the relevant coupon payment month. The settlement date of the trade in this bond is 24 June 2021. There is a zero coupon bond with exactly two years until maturity (i.e. the maturity date is 24 June 2023). The zero coupon bond has a yield to maturity of 4%. The yield curve is flat at 4% per annum. Please use semi-annual compounding, when answer the following questions. a) If you have $1 million invested in the CGS, how many of the 2-year zero-coupon bonds would you need to short-sell to hedge your interest rate risk? (7 marks) b) Without doing any calculations, discuss what actions you would need to take with your short position in the zero coupon to ensure your interest rate risk remained hedged until the maturity of the coupon paying bond. Why do you need to take these actions? (2 marks) c) Explain the concept of bond duration and why this measure is meaningful to investors. (3 marks) d) Explain the concept of bond immunization and the benefits derived from using this technique