Chap009 - Chapter Nine Interest Rate Risk II Chapter...

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Chapter Nine Interest Rate Risk II Chapter Outline Introduction Duration A General Formula for Duration The Duration of Interest Bearing Bonds The Duration of a Zero-Coupon Bond The Duration of a Consol Bond (Perpetuities) Features of Duration Duration and Maturity Duration and Yield Duration and Coupon Interest The Economic Meaning of Duration Semiannual Coupon Bonds Duration and Immunization Duration and Immunizing Future Payments Immunizing the Whole Balance Sheet of an FI Immunization and Regulatory Considerations Difficulties in Applying the Duration Model Duration Matching can be Costly Immunization is a Dynamic Problem Large Interest Rate Changes and Convexity Summary Appendix 9A: Incorporating Convexity into the Duration Model The Problem of the Flat Term Structure The Problem of Default Risk Floating-Rate Loans and Bonds Demand Deposits and Passbook Savings Mortgages and Mortgage-Backed Securities Futures, Options, Swaps, Caps, and Other Contingent Claims 83
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Solutions for End-of-Chapter Questions and Problems: Chapter Nine 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 84
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b. How does the change in the current YTM affect the duration of this coupon bond? Increasing the yield-to-maturity decreases the duration of the bond.
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This note was uploaded on 08/30/2011 for the course AFF 2401 taught by Professor Unknown during the Three '10 term at Monash.

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Chap009 - Chapter Nine Interest Rate Risk II Chapter...

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