Suppose you have an obligation to pay € 56 000 in 8 years time. To avoid interest risk you intend to hedge with two bonds. You can use one zero coupon bond that matures 10 years from now and one bond that pays coupons once a year at the rate of 5% and matures in 3 value of 100. Assume a flat yield curve. years with face a (a) What amount do you have to invest in each of the two bonds during the first year to hedge your obligation if the yield is 5%? What is the payoff at maturity (face value) of your investment in the zero coupon bond? How many units of the coupon bond do you have to buy? (Assume that you can buy any fractional amount of the bonds.) (b) What is the value of your portfolio today if immediately after the investment the market rate falls to 4%? What will be the value in 8 years if interest rates will not change again?
Suppose you have an obligation to pay € 56 000 in 8 years time. To avoid interest risk you intend to hedge with two bonds. You can use one zero coupon bond that matures 10 years from now and one bond that pays coupons once a year at the rate of 5% and matures in 3 value of 100. Assume a flat yield curve. years with face a (a) What amount do you have to invest in each of the two bonds during the first year to hedge your obligation if the yield is 5%? What is the payoff at maturity (face value) of your investment in the zero coupon bond? How many units of the coupon bond do you have to buy? (Assume that you can buy any fractional amount of the bonds.) (b) What is the value of your portfolio today if immediately after the investment the market rate falls to 4%? What will be the value in 8 years if interest rates will not change again?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![Suppose you have an obligation to pay € 56 000 in 8 years time. To avoid interest risk you intend
to hedge with two bonds. You can use one zero coupon bond that matures 10 years from now,
and one bond that pays coupons once a year at the rate of 5% and matures in 3 years with a face
value of 100. Assume a flat yield curve.
(a) What amount do you have to invest in each of the two bonds during the first year to hedge
your obligation if the yield is 5%?
What is the payoff at maturity (face value) of your investment in the zero coupon bond?
How many units of the coupon bond do you have to buy?
(Assume that you can buy any fractional amount of the bonds.)
(b) What is the value of your portfolio today if immediately after the investment the market
rate falls to 4%? What will be the value in 8 years if interest rates will not change again?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4bb8fb6e-2e87-488c-90ad-ee89fb9e9aaf%2F4456f8d3-1a26-4885-92b5-b6af099c93d8%2Fluv8kvf_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose you have an obligation to pay € 56 000 in 8 years time. To avoid interest risk you intend
to hedge with two bonds. You can use one zero coupon bond that matures 10 years from now,
and one bond that pays coupons once a year at the rate of 5% and matures in 3 years with a face
value of 100. Assume a flat yield curve.
(a) What amount do you have to invest in each of the two bonds during the first year to hedge
your obligation if the yield is 5%?
What is the payoff at maturity (face value) of your investment in the zero coupon bond?
How many units of the coupon bond do you have to buy?
(Assume that you can buy any fractional amount of the bonds.)
(b) What is the value of your portfolio today if immediately after the investment the market
rate falls to 4%? What will be the value in 8 years if interest rates will not change again?
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