Subject Do your calculation in Excel Consider the following (outstanding) liability schedule: Year (t) 2014 2015 Liability Lt $12,000 $18,000 2016 $20,000 2017 $20,000 Year (t) Liability L 2018 $16,000 2019 $15,000 2020 $12000 2021 $10,000 L is the liability in year t (paid at the end of the year). One needs to invest in a cash inflow stream today on January 1st 2014 to exactly match the cash outflow that we are liable for in the future (liabilities) at the end of the year 2014 up to at the end of the year 2021. Let N= 10 bonds are considered for this purpose Bond (1) 1 2 3 4 5 6 7 8 9 10 Price (P:) $102 $99 $101 $98 $98 $104 $100 $101 $102 $99 Coupon (C) 5 3.5 5 3.5 4 9 6 8 9 7 Maturity (T) 2015 2016 2016 2017 2018 2019 2029 2020 2021 2022 All bonds have a face value (Fi) of $100.00. Cash available at any time from 2014 to 2020 can be invested at an annual rate (1) of 3%. Question: Assume that all bonds are bought at the same date. (a) Discuss the optimal number of bound i to purchase, the amount of cash reinvested at time zero and at subsequent end of years. (b) To protect against interest rate sensitivity, add an equation for duration. Here, the duration of liability should match duration of the portfolio. Discuss the optimal number of each bound to purchase, cash reinvested at time zero and subsequent time. (c) To protect better against interest rate sensitivity, add another equation for convexity. Here, the convexity of portfolio should be bigger than the convexity of the liability side. Discuss the optimal number of bound i to purchase, cash reinvested at time zero and subsequent time. Subject Do your calculation in Excel Consider the following (outstanding) liability schedule: Year (t) 2014 2015 Liability Lt $12,000 $18,000 2016 $20,000 2017 $20,000 Year (t) Liability L 2018 $16,000 2019 $15,000 2020 $12000 2021 $10,000 L is the liability in year t (paid at the end of the year). One needs to invest in a cash inflow stream today on January 1st 2014 to exactly match the cash outflow that we are liable for in the future (liabilities) at the end of the year 2014 up to at the end of the year 2021. Let N= 10 bonds are considered for this purpose Bond (1) 1 2 3 4 5 6 7 8 9 10 Price (P:) $102 $99 $101 $98 $98 $104 $100 $101 $102 $99 Coupon (C) 5 3.5 5 3.5 4 9 6 8 9 7 Maturity (T) 2015 2016 2016 2017 2018 2019 2029 2020 2021 2022 All bonds have a face value (Fi) of $100.00. Cash available at any time from 2014 to 2020 can be invested at an annual rate (1) of 3%. Question: Assume that all bonds are bought at the same date. (a) Discuss the optimal number of bound i to purchase, the amount of cash reinvested at time zero and at subsequent end of years. (b) To protect against interest rate sensitivity, add an equation for duration. Here, the duration of liability should match duration of the portfolio. Discuss the optimal number of each bound to purchase, cash reinvested at time zero and subsequent time. (c) To protect better against interest rate sensitivity, add another equation for convexity. Here, the convexity of portfolio should be bigger than the convexity of the liability side. Discuss the optimal number of bound i to purchase, cash reinvested at time zero and subsequent time
