Today is 1 January 2018. Sue just purchased a 10-year 4.5% p.a. Treasury bond with a face value of $100 at the yield rate of j2 = 4.3% p.a. The bond is redeemable at par.
The maturity date is 1 January 2028. On receipt of each coupon, Sue deposits the coupon into a bank account earning the reinvestment rate. Sue predicts that there are three potential states for the future economy. (25 marks)
• State 1. Market yield is j2 = 5.05% p.a. from 2018 to 2023 and j2 = 5.2% p.a. from 2024 to 2027. Reinvestment rate is j2 = 5.15% p.a. from 2018 to 2023 and j2 = 5.3% p.a. from 2024 to 2027.
• State 2. Market yield is j2 = 4.55% p.a. from 2018 to 2022 and j2 = 4.7% p.a. from 2023 to 2027. Reinvestment rate is j2 = 4.45% p.a. from 2018 to 2022 and j2 = 4.8% p.a. from 2023 to 2027.
• State 3. Market yield is j2 = 3.8% p.a. from 2018 to 2025 and j2 = 3.7% p.a. from 2026 to 2027. Reinvestment rate is j2 = 3.6% p.a. from 2018 to 2025 and j2 = 3.75% p.a. from 2026 to 2027.
a. Calculate Sue's purchase price on 1 January 2018, ignoring future economic states.
For each economic state, calculate the accumulated value of the reinvested coupons at the end of year 3, 6 and 9 (9 values in total).
b. For each economic state, calculate the Sue's holding period yield rate (express it as a j2 rate) for 3 years, 6 years and 9 years holding periods (9 values in total).
c. Use a bar/column chart to plot your results in part b