Question
Consider a bond with the following features and a hypothetical settlement date of 10 October 2019. Annual Coupon5% Coupon Payment FrequencySemiannual Interest Payment Dates: 30
Consider a bond with the following features and a hypothetical settlement date of 10 October 2019.
Annual Coupon5%
Coupon Payment FrequencySemiannual
Interest Payment Dates: 30 December and 30 June
Maturity Date: 30 December 2020
Day-Count Convention30/360
Annual Yield-to-Maturity: 6%
A. Without considering the convexity effect, what is the approximate percentage price change if the bond's yield to maturitydecreasesby 50 basis points. Use the formula that relies on modified duration. Round your answer tothree decimal placesand express your answer in percentage terms (e.g., 3.500% not 0.035).
B. What is the bond's approximate modified duration assuming a 10 bp change in its annual yield-to-maturity? Remember to annualize your answer and roundyour answer tothree decimal places.
C. What is the bond's approximate convexity assuming a 10 bp change in its annual yield-to-maturity? Round tothree decimal places.
D. Now, considering the convexity effect, what is the approximate percentage price change if the bond's yield to maturitydecreasesby 50 basis points. Use the formula that relies on approximate modified duration and approximate convexity. Round your answer tothree decimal placesand express your answer in percentage terms (e.g., 3.500%not 0.035)
E. You are saving so that you can take your dream trip around the world in 5 years. To do so, you buy a newly issued, 12-year, 8% annual coupon bond. The bond is purchased at par value, so its yield to maturity is 8% stated as an effective annual rate. You plan to liquidate the bond in 5 years so that you can pay for your trip.What is theduration gapin this scenario? Round your answer tothree decimal places.
F. Same scenario as in Questions 9with one additionalpiece of information. You wantto immunize yourself from interest rate to ensure that you can take your trip. You see that there is a 2-year zero coupon bond available in the market. If you want to fully hedge against interest rate risk, what percentage of your portfolio should you invest in thezero coupon bond? Express your answer in percentage terms rounded tothree decimal places(e.g., 50.000 not 0.500).
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