Question 2[8+8=16 marks] Clefable is interested in buying an index-linked bond that has a \$1 million nominal value. At the end of December 2020 , she spent $1 million purchasing this bond. The bond pays semi-annual coupons at an effective coupon rate of 1.08% per half-year, and the payments occur at the end of June and December each year. Clefable aims to sell this bond at $1.02 million at the end of December 2022 right after receiving the coupon on the same date. The coupons are linked to the Consumer Prices Index (CPI) with a three-month lag. For example, the coupon paid (in nominal dollar) at the end of June 2021 is calculated based on the CPI at the end of March 2021. The inflation is 2% per annum effective starting from three months before the bond was issued, and such inflation will continue until three months before the bond is going to be re-sold. Assume there are 30 days in each month. a) Calculate the effective rate of retum per annum (to the nearest 0.1% ) of this bond over Clefable's holding period. (Hint: calculate the rate of return in the nominal term, without any inflation adjustments). b) Assume the real rate of retum of this bond is 1% per annum convertible semi-annually over Clefable's holding period. Calculate the annual effective inflation (to the nearest 0.1% ) from the end of September 2022 to the end of December 2022. Question 2[8+8=16 marks] Clefable is interested in buying an index-linked bond that has a \$1 million nominal value. At the end of December 2020 , she spent $1 million purchasing this bond. The bond pays semi-annual coupons at an effective coupon rate of 1.08% per half-year, and the payments occur at the end of June and December each year. Clefable aims to sell this bond at $1.02 million at the end of December 2022 right after receiving the coupon on the same date. The coupons are linked to the Consumer Prices Index (CPI) with a three-month lag. For example, the coupon paid (in nominal dollar) at the end of June 2021 is calculated based on the CPI at the end of March 2021. The inflation is 2% per annum effective starting from three months before the bond was issued, and such inflation will continue until three months before the bond is going to be re-sold. Assume there are 30 days in each month. a) Calculate the effective rate of retum per annum (to the nearest 0.1% ) of this bond over Clefable's holding period. (Hint: calculate the rate of return in the nominal term, without any inflation adjustments). b) Assume the real rate of retum of this bond is 1% per annum convertible semi-annually over Clefable's holding period. Calculate the annual effective inflation (to the nearest 0.1% ) from the end of September 2022 to the end of December 2022
