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Chapter 9

# Chapter 9 - End-of Chapter 9 Questions 1 What are the two...

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1 End-of Chapter 9 Questions 1. What are the two different general interpretations of the concept of duration , and what is the technical definition of this term? How does duration differ from maturity? Duration measures the average life of an asset or liability in economic terms. As such, duration has economic meaning as the interest sensitivity (or interest elasticity) of an asset’s value to changes in the interest rate. Duration differs from maturity as a measure of interest rate sensitivity because duration takes into account the time of arrival and the rate of reinvestment of all cash flows during the assets life. Technically, duration is the weighted-average time to maturity using the relative present values of the cash flows as the weights. 2. Two bonds are available for purchase in the financial markets. The first bond is a 2-year, \$1,000 bond that pays an annual coupon of 10 percent. The second bond is a 2-year, \$1,000, zero-coupon bond. a. What is the duration of the coupon bond if the current yield-to-maturity (YTM) is 8 percent? 10 percent? 12 percent? (Hint: You may wish to create a spreadsheet program to assist in the calculations.) Coupon Bond Par value = \$1,000 Coupon = 0.10 Annual payments YTM = 0.08 Maturity = 2 Time Cash Flow PVIF PV of CF PV*CF*T 1 \$100.00 0.92593 \$92.59 \$92.59 2 \$1,100.00 0.85734 \$943.07 \$1,886.15 Price = \$1,035.67 Numerator = \$1,978.74 Duration = 1.9106 = Numerator/Price YTM = 0.10 Time Cash Flow PVIF PV of CF PV*CF*T 1 \$100.00 0.90909 \$90.91 \$90.91 2 \$1,100.00 0.82645 \$909.09 \$1,818.18 Price = \$1,000.00 Numerator = \$1,909.09 Duration = 1.9091 = Numerator/Price YTM = 0.12 Time Cash Flow PVIF PV of CF PV*CF*T 1 \$100.00 0.89286 \$89.29 \$89.29 2 \$1,100.00 0.79719 \$876.91 \$1,753.83 Price = \$966.20 Numerator = \$1,843.11 Duration = 1.9076 = Numerator/Price

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2 b. How does the change in the current YTM affect the duration of this coupon bond? Increasing the yield-to-maturity decrease the duration of the bond. c. Calculate the duration of the zero-coupon bond with a YTM of 8 percent, 10 percent, and 12 percent. Zero Coupon Bond Par value = \$1,000 Coupon = 0.00 YTM = 0.08 Maturity = 2 Time Cash Flow PVIF PV of CF PV*CF*T 1 \$0.00 0.92593 \$0.00 \$0.00 2 \$1,000.00 0.85734 \$857.34 \$1,714.68 Price = \$857.34 Numerator = \$1,714.68 Duration = 2.0000 = Numerator/Price YTM = 0.10 Time Cash Flow PVIF PV of CF PV*CF*T 1 \$0.00 0.90909 \$0.00 \$0.00 2 \$1,000.00 0.82645 \$826.45 \$1,652.89 Price = \$826.45 Numerator = \$1,652.89 Duration = 2.0000 = Numerator/Price YTM = 0.12 Time Cash Flow PVIF PV of CF PV*CF*T 1 \$0.00 0.89286 \$0.00 \$0.00 2 \$1,000.00 0.79719 \$797.19 \$1,594.39 Price = \$797.19 Numerator = \$1,594.39 Duration = 2.0000 = Numerator/Price d. How does the change in the current YTM affect the duration of the zero-coupon bond? Changing the yield-to-maturity does not affect the duration of the zero coupon
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Chapter 9 - End-of Chapter 9 Questions 1 What are the two...

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