ECOM074 Bond Market Strategies Tutorial Class 1
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ECOM074 Bond Market Strategies
Tutorial Class 1
Question topics
1. Calculating bond prices for annual coupon bonds using given yields.
2. Calculating bond prices for semi-annual coupon bonds using given yields.
3. Calculating bond prices for zero coupon bonds using given yields.
4. Calculating implied interest rates using given bond prices for zero coupon bonds.
5. Financial engineering and arbitrage using zero coupon bonds.
Reference material
1. Lecture 2 Bond prices and interest rates: part 5.
2. Lecture 2 Bond prices and interest rates: part 6.
Question 1
Consider a 10-year German government bond (Bund) with a 5.00% coupon rate and a par value of €100. This bond makes annual coupon payments. What is the price for this bond if its yield is 0.50%? Explain your answer and comment on the result.
Question 2
Consider another 10-year German government bond (Bund) with an 0.50% coupon rate and a par value of €100. This bond also makes annual coupon payments. What is the price for this bond if its yield is 2.20%? Explain your answer and comment on the result.
Question 3
Consider a 10-year Italian government bond (BTP) with a 1.00% coupon rate, an annual coupon payment frequency and a par value of €100. What is the price for this bond if its yield is 4.00%? Explain your answer and comment on the result.
Question 4
Consider a 10-year UK government bond (Gilt) with an 0.50% coupon rate, a semi-annual coupon payment frequency and a par value of £100. What is the price for this bond if its yield is 3.00%? Explain your answer and comment on the result.
Question 5
Consider a 10-year US Treasury bond with a 1.00% coupon rate and a par value of $100. This bond makes semi-annual coupon payments. What is the price of this bond if its yield is 3.50%? Explain your answer and comment on the result .
Question 6
Consider a 5-year Euro area zero-coupon bond that has a par value of €100 and is priced at €87.1033.
a) Calculate the implied yield for this bond.
b) What is the relationship between the implied yield and the implied interest rate for this bond?
Question 7
Consider a 5-year Euro area government bond with an 0.50% coupon rate and a par value of €100. This bond makes annual coupon payments. The yield is 2.80%. The price information is provided in the following table:
Time period |
Cash flow |
Discount factor |
Present value |
1 2 3 4 5 |
€ 0.50 € 0.50 € 0.50 € 0.50 € 100.50 |
0.9728 0.9463 0.9205 0.8954 0.8710 |
€ 0.4864 € 0.4731 € 0.4602 € 0.4477 € 87.5388 |
Sum |
€ 89.4063 |
Look at the following portfolio of zero-coupon bonds that produces matching future cash flows for this coupon bond. Is there an arbitrage opportunity?
Zero- Coupon Bonds |
Time period |
Cash flow |
Discount factor |
Present value |
|
1 € 0.50 € 0.4864 2 € 0.50 € 0.4731 3 € 0.50 € 0.4602 4 € 0.50 € 0.4477 5 € 100.50 € 87.5388 |
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1 |
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2 |
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3 |
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4 |
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5 |
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Sum |
€ 89.4063 |
Question 8
Consider the same coupon bond in question 7 and look at the following new portfolio of zero- coupon bonds that produces matching future cash flows for this bond. Is there an arbitrage opportunity? Explain how you would exploit this opportunity.
Zero- Coupon Bonds |
Time Discount period Cash flow factor Present value |
|
1 € 0.50 € 0.4888 2 € 0.50 € 0.4778 3 € 0.50 € 0.4670 4 € 0.50 € 0.4565 5 € 100.50 € 89.6991 |
1 |
|
2 |
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3 |
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4 |
|
5 |
|
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|
Sum |
€ 91.5891 |
Question 9
Consider the same coupon bond in question 7 and look at the following new portfolio of zero- coupon bonds that produces matching future cash flows for this bond. Is there an arbitrage opportunity? Explain how you would exploit this opportunity.
Zero- Coupon Bonds |
Time Discount period Cash flow factor Present value |
|
1 € 0.50 € 0.4840 2 € 0.50 € 0.4686 3 € 0.50 € 0.4536 4 € 0.50 € 0.4391 5 € 100.50 € 85.4406 |
1 |
|
2 |
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3 |
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4 |
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5 |
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|
Sum |
€ 87.2859 |
2023-02-28