Question

Portfolio A consists of a l-year zero-coupon bond with a face value of $$\$ 2,000$$ and a 10-year zero-coupon bond with a face value of $$\$ 6,000$$. Portfolio B consists of a 5.95 -year zero-coupon bond with a face value of $$\$ 5,000$$. The current yield on all bonds is $10 \%$ per annum. (a) Show that both portfolios have the same duration. (b) Show that the percentage changes in the values of the two portfolios for a $0.1 \%$ per annum increase in yields are the same. (c) What are the percentage changes in the values of the two portfolios for a $5 \%$ per annum increase in yields?

   Portfolio A consists of a l-year zero-coupon bond with a face value of $$\$ 2,000$$ and a 10-year zero-coupon bond with a face value of $$\$ 6,000$$. Portfolio B consists of a 5.95 -year zero-coupon bond with a face value of $$\$ 5,000$$. The current yield on all bonds is $10 \%$ per annum.
(a) Show that both portfolios have the same duration.
(b) Show that the percentage changes in the values of the two portfolios for a $0.1 \%$ per annum increase in yields are the same.
(c) What are the percentage changes in the values of the two portfolios for a $5 \%$ per annum increase in yields?

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 4, Problem 33

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Step 1

- For Portfolio A: - The 1-year zero-coupon bond with a face value of \$2,000 has a PV of $ PV = \frac{2000}{(1 + 0.10)^1} = \frac{2000}{1.10} = \$1818.18 $. - The 10-year zero-coupon bond with a face value of \$6,000 has a PV of \( PV = \frac{6000}{(1 + Show more…

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Portfolio A consists of a l-year zero-coupon bond with a face value of $$\$ 2,000$$ and a 10-year zero-coupon bond with a face value of $$\$ 6,000$$. Portfolio B consists of a 5.95 -year zero-coupon bond with a face value of $$\$ 5,000$$. The current yield on all bonds is $10 \%$ per annum. (a) Show that both portfolios have the same duration. (b) Show that the percentage changes in the values of the two portfolios for a $0.1 \%$ per annum increase in yields are the same. (c) What are the percentage changes in the values of the two portfolios for a $5 \%$ per annum increase in yields?

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