Duration and convexity of bonds

Slobodan Čerović; Marina Pepić; Stanislav Čerović; Nevena Čerović

doi:10.5937/ejae11-4766

Slobodan Čerović Singidunum University
Marina Pepić National Bank of Serbia
Stanislav Čerović Singidunum University
Nevena Čerović University of Belgrade, Faculty of Economics

DOI: https://doi.org/10.5937/ejae11-4766

Keywords: Macaulay, modified, effective, empirical and dollar duration, duration of a portfolio, modified and effective convexity, convexity of a portfolio,

Abstract

The wide impact that interest rate changes have on business performance, the fact that all market participants are, more or less, exposed to interest rate risk, as well as high volatility in interest rates in recent years, make interest rate risk one of the most significant risks.
It is impossible to neutralize interest rate risk completely, but it is desirable to reduce it to a minimum. In order to effectively manage it, interest rate risk must first be identified and measured. This paper aims to show the two methods of measuring the interest rate risk - duration and convexity.
The concept of duration is a good indicator of changes in the price of bonds but only for small changes in the interest rates. In case of major changes, the duration gives overestimated/underestimated approximation of the bond price, because bond price-yield relationship is not linear. Therefore, when measuring interest rate risk, convexity of bonds must be taken into account. Modified duration and convexity taken together provide the best approximation of the sensitivity of bond prices to changes in interest rates.

References

Barber, J.R. (1995). A note on approximating bond price sensitivity using duration and convexity. The Journal of Fixed Income, 4(4), 95-98. doi: 10.3905/jfi.1995.408123.

Choudhry, M. (2005). Fixed-income securities and derivatives handbook: Analysis and valuation. Princeton, N.J: Bloomberg Press.

Fabozzi, F.J. (1996). Measuring and controlling interest rate risk. New Hope, PA: Frank J. Fabozzi Associates.

Fabozzi, F.J. (2000). Bond markets, analysis and strategies. Upper Saddle River, N.J: Prentice Hall.

Fabozzi, F.J., & Mann, S.V. (2005). The handbook of fixed income securities. New York: McGraw-Hill.

Fabozzi, F.J. (2007). Fixed income analysis. Hoboken, N.J: Wiley.

Hull, J. (2009). Options, futures and other derivatives. Upper Saddle River, N.J: Prentice Hall.

La Grandville, Olivier de. (2001). Bond pricing and portfolio analysis: Protecting investors in the long run. Cambridge, MA: MIT Press.

Mishkin, F.S., & Eakins, S.G. (2005). Financial markets and institutions. Boston: Addison Wesley.

Reilly, F.K., & Brown, K.C. (2003). Investment analysis and portfolio management. Mason, OH: South-Western/Thomson Learning.

Steiner, R. (1998). Mastering financial calculations: A step by step guide to the mathematics of financial market instruments. London: Financial Times.

Šoškić, D.B., & Živković, B.R. (2006). Finansijska tržišta i institucije. Beograd: Centar za izdavačku delatnost Ekonomskog fakulteta. (in Serbian).