ECOM074 Bond Market Strategies Tutorial Class 2
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ECOM074 Bond Market Strategies
Tutorial Class 2
Question topics
1. Calculating duration for a zero-coupon bond using a given yield.
2. Calculating convexity for a zero-coupon bond using a given yield.
3. Calculating duration for a coupon bond using a given yield.
4. Calculating convexity for a coupon bond using a given yield.
5. Calculating expected bond price changes using the Taylor series formula with given duration, convexity, and yield data.
6. Ranking bonds in terms of interest rate risk.
7. Explaining the weakness of using duration on its own to measure interest rate risk.
Reference material
1. Lecture 3 Bond prices and interest rate risk: part 6.
2. Lecture 3 Bond prices and interest rate risk: part 7.
3. Lecture 3 Bond prices and interest rate risk: part 8.
4. Lecture 3 Bond prices and interest rate risk: part 9.
Question 1
Consider a 2-year zero-coupon German government bond (Bund). This bond has a par value of €100 and is priced at €91.6607 with a 4.45% yield.
a) Calculate the duration for this bond using the 4.45% yield.
b) What does your duration result mean for this bond?
c) What is the actual change in price for this bond if the yield increases by 100 basis points?
d) How does your duration estimate (a and b) compare with the actual price change (c)?
Assume an annual coupon payment frequency for your calculations. Explain your answer clearly and add comments where appropriate.
Question 2
Consider a 10-year zero-coupon German government bond (Bund). This bond has a par value of €100 and is priced at €69.9726 with a 3.65% yield.
a) Calculate the duration for this bond using the 3.65% yield.
b) What does your duration result mean for this bond?
c) What is the actual change in price for this bond if the yield increases by 100 basis points?
d) How does your duration estimate (a and b) compare with the actual price change (c)?
Assume an annual coupon payment frequency for your calculations. Explain your answer clearly and add comments where appropriate.
Question 3
Consider a 30-year zero-coupon German government bond (Bund). This bond has a par value of €100 and is priced at €33.6231 with a 3.70% yield.
a) Calculate the duration for this bond using the 3.70% yield.
b) What does your duration result mean for this bond?
c) What is the actual change in price for this bond if the yield increases by 100 basis points?
d) How does your duration estimate (a and b) compare with the actual price change (c)?
Assume an annual coupon payment frequency for your calculations. Explain your answer clearly and add comments where appropriate.
Question 4
The duration estimate works well for the 2-year bond in question 1, and the 10-year bond in question 2, but not so well for the 30-year bond in question 3. Can we improve on the duration estimate for the 30-year bond in question 3?
Question 5
Calculate convexity for all three bonds in questions 1 to 3. A summary of the information for the three bonds is provided in the following table.
|
Bond |
Maturity in years |
Coupon Rate |
Price |
Yield |
|
1 2 3 |
2 10 30 |
0 0 0 |
€ 91.6607 € 69.8726 € 33.6231 |
4.45% 3.65% 3.70% |
Question 6
Consider the 30-year bond in question 3 and the convexity result for the bond in question 5 . Use a Taylor series to show how we can improve on the duration estimate for the percent change in the price of this 30-year bond if the yield is increased by 100 basis points. Explain your answer clearly and add comments where appropriate.
Question 7
A company pension fund has a sequence of future pension liabilities that are hedged with a bond portfolio to remove interest rate risk. The pension fund is using a duration-hedging strategy, but this strategy has not been completely successful in removing interest rate risk, especially when there have been large movements in interest rates. Identify the problem and suggest an appropriate solution.
2023-02-28