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CHAPTER 6 INTEREST RATE RISK: THE DURATION MODEL Chapter outline Calculating Duration A General Formula for Duration The Duration of a Six-Year Eurobond The Duration of a Two-Year Australian Treasury Bond The Duration of a Zero-Coupon Bond The Duration of a Consol Bond Features of Duration Duration and Maturity Duration and Yield Duration and Coupon Interest The Economic Meaning of Duration The Six-Year Eurobond The Consol Bond Semi-annual Coupon, Two-Year Maturity Treasury Bond Duration and Immunisation Duration and Immunising Future Payments Buy Five-Year Maturity Discount Bonds Buy a Five-Year Duration Coupon Bond Interest Rates Remain at 8 Per Cent Interest Rates Fall to 7 Per Cent Interest Rates Rise to 9 Per Cent Immunising the Whole Balance Sheet of an FI The Duration Gap for a Financial Institution Duration Gap Measurement and Exposure: An Example Immunisation and Regulatory Considerations Applying the Duration Model to Real-World Fl Balance Sheets Duration Matching Can Be Costly Immunisation is a Dynamic Problem Large interest rate changes and convexity Calculation of CX The problem of the flat term structure The Problem of Default Risk Floating Rate Loans and Bonds Instructor’s Resource Manual t/a Financial Institutions Management 2e by Lange, Saunders, 1

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Demand Deposits and Savings Deposits Instructor’s Resource Manual t/a Financial Institutions Management 2e by Lange, Saunders, 2
Answers to end-of-chapter questions QUESTIONS AND PROBLEMS 1. What is the price of a newly tendered five-year Treasury bond with a coupon of 7 per cent and a yield of 7.05 per cent? (Hint: All Treasury notes and bonds pay interest semi-annually.) The price of the Treasury note (per \$100 face value) is: P = 3.5 1- 1 (1.03525) 0.03525 100 (1.03525) 99.792 10 10 + = 2. (a) What are all of the promised cash flows on a \$1000 one-year loan yielding 10 per cent p.a. that pays interest and principal quarterly? (b) What is the present value of the loan if interest rates are 10 per cent p.a.? (c) What is the present value of the loan if interest rates are 8 per cent p.a.? Solutions (a) Cash flows at the end of the first quarter are: Principal payment = \$250 Interest payment = (0.10/4)(\$1000)= \$25 CF 1 4 = \$275 Cash flows at the end of the second quarter are: Principal payment = \$250 Interest payment = (0.10/4)(\$750) = \$18.75 CF 1 2 = \$268.75 Cash flows at the end of the third quarter are: Principal payment = \$250 Interest payment = (0.10/4)(\$500) = \$12.50 CF 3 4 = \$262.50 Cash flows at the end of the year are: Principal payment = \$250 Interest payment = (0.10/4)(\$250) = \$6.25 CF 1 = \$256.25 (b) PV 1 4 = \$275/(1.025) = \$268.29 Instructor’s Resource Manual t/a Financial Institutions Management 2e by Lange, Saunders, 3

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PV 1 2 = \$268.75/(1.025) 2 = \$255.80 PV 3 4 = \$262.50/(1.025) 3 = \$243.76 PV 1 = \$256.25/(1.025) 4 = \$232.15 PV = PV 1 4
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