Three investors invest in the same 10-year 8% annual coupon bond. They bought the bond at the same price ($85.503075 for a par value of $100) and at the same time. A is a buy-and-hold investor (hold till maturity), B will sell the bond after four years, and C will sell the bond after seven years. 1. What is the yield to maturity of this bond at the time of purchase? 2. After the bond is purchased by the three investors and before the first coupon is received, interest rate go up to 11.4%. Calculate: i. What is the change in IOI for each investor? (Hint: Find the difference between the IOI under the original YTM and the IOI under the changed yield. For how to find IOI, refer to problem 18 of the last midterm). ii. What is the capital gain/loss for each investor? (Hint: capital gain/loss= price at sale or maturity - carrying value. For how to find capital gain/loss, refer to problem 18 of the last midterm) What is the difference between change in IOI and capital gain/loss for each investor? 3. What is the Macaulay duration of this bond? 4. For each of these three investors, find their respective duration gap. (Hint: The difference between the Macaulay duration of a bond and an investor's investment horizon is called the duration gap). 5. Use the answers from 1-4 to describe the relations between duration gap, interest rate risk, and reinvestment risk (Hint: Refer to the discussions in Lecture 5-Section 1 to answer the question). iii. Three investors invest in the same 10-year 8% annual coupon bond. They bought the bond at the same price ($85.503075 for a par value of $100) and at the same time. A is a buy-and-hold investor (hold till maturity), B will sell the bond after four years, and C will sell the bond after seven years. 1. What is the yield to maturity of this bond at the time of purchase? 2. After the bond is purchased by the three investors and before the first coupon is received, interest rate go up to 11.4%. Calculate: i. What is the change in IOI for each investor? (Hint: Find the difference between the IOI under the original YTM and the IOI under the changed yield. For how to find IOI, refer to problem 18 of the last midterm). ii. What is the capital gain/loss for each investor? (Hint: capital gain/loss= price at sale or maturity - carrying value. For how to find capital gain/loss, refer to problem 18 of the last midterm) What is the difference between change in IOI and capital gain/loss for each investor? 3. What is the Macaulay duration of this bond? 4. For each of these three investors, find their respective duration gap. (Hint: The difference between the Macaulay duration of a bond and an investor's investment horizon is called the duration gap). 5. Use the answers from 1-4 to describe the relations between duration gap, interest rate risk, and reinvestment risk (Hint: Refer to the discussions in Lecture 5-Section 1 to answer the question)
