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 15^th 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.

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)