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Modified duration and convexity with semiannual compounding

Abstract

Both duration and convexity are a function of the curvilinear bond price: yield relationship. While duration measures the slope of the price:yield curve at a given yield-to-maturity, convexity measures the change in duration at this yield-to-maturity. Three shortcomings exist in the presentation of bond price volatility in financial education. First, modified duration and convexity should be used together as measures of bond price volatility. Second, these measures of bond price volatility should properly reflect semiannual compounding. Third, simple linear models for modified duration and convexity should be generally adopted in financial education literature.

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References

  • Alexander, Gordon J., andWilliam F. Sharpe.Fundamentals of Investments. Englewood Cliffs, NJ: Prentice Hall, Inc., 1989.

    Google Scholar 

  • Bierwag, Gerald O. Duration Analysis: Managing Interest Rate Risk. Cambridge, MA: Ballinger Company, 1987.

    Google Scholar 

  • Brealey, Richard A., andStewart C. Myers.Principles of Corporate Finance, 4th ed. New York: McGraw-Hill, Inc., 1991.

    Google Scholar 

  • Brooks, Robert, andMiles Livingston. “A Closed-Form Equation for Bond Convexity”.Financial Analysts Journal 45, no. 6 (November/December 1989): 78–79.

    Article  Google Scholar 

  • Brooks, Robert. “Relative Impact of Duration and Convexity on Bond Price Changes”.Financial Practice and Education 2, no. 1 (Spring/Summer 1992): 93–99.

    Google Scholar 

  • Caks, John, William R. Lane, Robert W. Greenleaf, andReginald G. Joules. “A Simple Formula for Duration”.Journal of Financial Research 8, no. 3 (Fall 1985): 245–249.

    Google Scholar 

  • Cheney, John M., andEdward A. Moses.Fundamentals of Investments, St. Paul MN: West Publishing Company, 1992.

    Google Scholar 

  • Chew, I. Keong, andRonnie J. Clayton. “Bond Valuation: A Clarification”.The Financial Review 18, no. 2 (May 1983): 234–236.

    Article  Google Scholar 

  • Chua, Jess H.. “A Closed-Form Formula for Calculating Bond Duration”.Financial Analysts Journal 40, no. 3 (May–June 1984): 76–78.

    Article  Google Scholar 

  • Cooper, S. Kerry, andDonald R. Fraser.The Financial Marketplace, 3d ed. Reading, MA: Addison-Wesley Publishing Company, 1990.

    Google Scholar 

  • Dunetz, Mark L., andJames M. Mahoney. “Using Duration and Convexity in the Analysis of Callable Bonds”.Financial Analysts Journal 44, no. 3 (May/June 1988): 53–72.

    Article  Google Scholar 

  • Francis, Jack Clark.Investment: Analysis and Management, 4th ed. New York: McGraw-Hill, Inc., 1986.

    Google Scholar 

  • Donald R. Fraser, Benton E. Gup, andJames W. Kolari.Commercial Banking: The Management of Risk. Minneapolis/St. Paul: West Publishing Company, 1995.

    Google Scholar 

  • Gardner, Mona J., andDixie L. Mills.Managing Financial Institutions: An Asset/Liability Approach. 3d ed. Fort Worth, TX: The Dryden Press, 1994.

    Google Scholar 

  • Grantier, Bruce J.. “Convexity and Bond Performance: The Benter the Better”.Financial Analysts Journal 44, no. 6 (November/December 1988): 79–81.

    Article  Google Scholar 

  • Horvath, Philip A.. “A Measurement of the Errors in Intra-Period Compounding and Bond Valuation: A Short Extension”.The Financial Review 23, no. 3 (August 1988): 359–363.

    Article  Google Scholar 

  • — “A Pedagogic Note on Intra-Period Compounding and Discounting”.The Financial Review 20, no. 1 (February 1985): 116–118.

    Article  Google Scholar 

  • Johnson, Lewis D.. “Convexity for Equity Securities: Does Curvature Matter?”.Financial Analysts Journal 46, no. 5 (September/October 1990): 70–73.

    Article  Google Scholar 

  • Kahn, Ronald N., andRoland Lochoff. “Convexity and Exceptional Return”.The Journal of Portfolio Management 16, no. 2 (Winter 1990): 43–47.

    Article  Google Scholar 

  • Kidwell, David S., Richard L. Peterson, andDavid W. Blackwell.Financial Institutions, Markets, and Money. 5th ed. Chicago, IL: The Dryden Press, 1990.

    Google Scholar 

  • Koch, Timothy W. Bank Management. 2d ed. Fort Worth, TX: The Dryden Press, 1992.

    Google Scholar 

  • Kolb, Robert W. Investments. 3d ed. Miami FL: Kolb Publishing Company, 1992.

    Google Scholar 

  • Kolb, Robert W., andRicardo J. Rodriquez Principles of Finance, 2d ed. Lexington, MA: D.C. Heath and Company, 1992.

    Google Scholar 

  • Lindley, James T.. “Compounding Issues Revisited”.Financial Practice and Education 3, no. 2 (Fall 1993): 127–129.

    Google Scholar 

  • Lindley, James T., Billy P. Helms, andMahmoud Haddad. “A Measurement of the Errors in Intra-Period Compounding and Bond Valuation”.The Financial Review 22, no. 1 (February 1987): 33–51.

    Article  Google Scholar 

  • Livingston, Miles.Money and Capital Markets. 2d ed. New York: New York Institute of Finance, 1993.

    Google Scholar 

  • Macaulay, Frederick Robertson.Some Theoretical Problems Suggested by the Movement of Interest Rates, Bond Yields and Stock Prices in the United States Since 1856. New York: National Bureau of Economic Research, 1938.

    Google Scholar 

  • Madura, Jeff.Financial Markets and Institutions. 2d ed. Saint Paul, MN: West Publishing Company, 1992.

    Google Scholar 

  • Moser, James T., andJames T. Lindley. “A Simple Formula for Duration: An Extension”.The Financial Review 24, no. 4 (November 1989): 611–615.

    Article  Google Scholar 

  • Nawalkha, Sanjay K., Nelson J. Lacey, andThomas Schneeweis. “Closed-Form Solutions of Convexity and M-Square”.Financial Analysts Journal 46, no. 1 (January/February 1990): 75–77.

    Article  Google Scholar 

  • Rich, Steven P., andJohn T. Rose. “A Note on Finance Principles, Bond Valuation, and the Appropriate Discount Rate”.Financial Practice and Education, 1, no. 2 (Fall/Winter 1991): 99–101.

    Google Scholar 

  • Rose, Peter S. Commercial Bank Management: Producing and Selling Financial Services. Homewood, IL: Irwin, 1991.

    Google Scholar 

  • Money and Capital Markets: The Financial System in the Economy. 4th ed. Homewood, IL: Irwin, 1992.

    Google Scholar 

  • Rose, Peter S., andDonald R. Fraser.Financial Institutions: Understanding and Managing. 3d ed. Homewood, IL, Irwin, 1988.

    Google Scholar 

  • Ross, Stephen A., Randolph W. Westerfield, andJeffrey F. Jaffe.Corporate Finance. 2d ed. Homewood, IL. Irwin, 1988.

    Google Scholar 

  • Saunders, Anthony.Financial Institutions Management: A Modern Perspective. Burr Ridge, IL: Irwin, 1994.

    Google Scholar 

  • Schnabel, Jacques A.. “Is Benter Better? A Cautionary Note on Maximizing Convexity”.Financial Analysts Journal 46, no. 1 (January–February 1990): 78–79.

    Article  Google Scholar 

  • Sinkey, Jr.,Joseph F. Commercial Bank Financial Management in the Financial-Services Industry. 4th ed. New York: Macmillan Publishing Company, 1992.

    Google Scholar 

  • Taylor, Richard W.. “The Valuation of Semiannual Bonds Between Interest Payment Dates”.The Financial Review 23, no. 3 (August 1988): 365–368.

    Article  Google Scholar 

  • Tse, K.S. Maurice, andMark A. White. “The Valuation of Semiannual Bonds Between Interest Payment Dates: A Correction”.The Financial Review 25, no. 4 (November 1990): 659–662.

    Article  Google Scholar 

  • Weston, J. Fred, andThomas E. Copeland.Managerial Finance. 9th ed. Fort Worth, TX: The Dryden Press, 1992.

    Google Scholar 

  • Winkelmann, Kurt, “Uses and Abuses of Duration and Convexity”.Financial Analysts Journal 45, no. 5 (September/October 1989): 72–75.

    Article  Google Scholar 

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Steven Cole, C., Young, P.J. Modified duration and convexity with semiannual compounding. J Econ Finan 19, 1–15 (1995). https://doi.org/10.1007/BF02920210

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  • DOI: https://doi.org/10.1007/BF02920210

Keywords

  • Interest Rate
  • Bond Price
  • Financial Education
  • Interest Rate Risk
  • Modify Duration