A General Formula for Duration

Topics: Bond, Bond duration, Zero-coupon bond Pages: 46 (11605 words) Published: December 3, 2012
Chapter Nine
Interest Rate Risk II

Chapter Outline


Duration: A Simple Introduction

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 Interest Rate Risk
• Duration and Interest Rate Risk Management on a Single Security • Duration and Interest Rate Risk Management on 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


Appendix 9A: The Basics of Bond Valuation

Appendix 9B: 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

Solutions for End-of-Chapter Questions and Problems: Chapter Nine

***signed to the questions 2 3 16 20

1.What is the difference between book value accounting and market value accounting? How do interest rate changes affect the value of bank assets and liabilities under the two methods? What is marking to market?

Book value accounting reports assets and liabilities at the original issue values. Current market values may be different from book values because they reflect current market conditions, such as interest rates or prices. This is especially a problem if an asset or liability has to be liquidated immediately. If the asset or liability is held until maturity, then the reporting of book values does not pose a problem.

For an FI, a major factor affecting asset and liability values is interest rate changes. If interest rates increase, the value of both loans (assets) and deposits and debt (liabilities) fall. If assets and liabilities are held until maturity, it does not affect the book valuation of the FI. However, if deposits or loans have to be refinanced, then market value accounting presents a better picture of the condition of the FI. The process by which changes in the economic value of assets and liabilities are accounted is called marking to market. The changes can be beneficial as well as detrimental to the total economic health of the FI.

***2.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 weighted-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.

***3.Two bonds are available for purchase in the financial markets. The first bond is a two-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 (R) 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 = $1,000Coupon rate = 10%Annual payments R = 8%Maturity = 2 years
Time Cash Flow PV of CF PV of CF x...
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