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The European Journal of Applied Economics

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Duration and Convexity of Bonds

Slobodan Čerović
  • Corresponding author
  • Singidunum University, Department of Tourism and Hospitality, 32 Danijelova Street, Belgrade, Serbia
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/ Marina Pepić / Stanislav Čerović / Nevena Čerović
  • University of Belgrade, Faculty of Economics, Master’s student 6 Kamenička Street, Belgrade, Serbia
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Published Online: 2014-05-08 | DOI: https://doi.org/10.5937/sjas11-4766


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.


Veliki uticaj koji promene kamatnih stopa imaju na uspešnost poslovanja, cinjenica da su svi tržišni ucesnici, više ili manje, izloženi kamatnom riziku, kao i velika volatilnost kamatnih stopa poslednjih godina, cine kamatni rizik jednim od najznacajnijih rizika. Kamatni rizik je nemoguce u potpunosti eliminisati, ali ga je poželjno svesti na najmanju mogucu meru. Kako bi se efikasno upravljalo kamatnim rizikom najpre se mora prepoznati i izmeriti izloženost ovoj vrsti rizika. Ovaj rad ima za cilj da ukaže na dve metode merenja kamatnog rizika - na trajanje i konveksnost. Koncept trajanja je dobar pokazatelj promene cene obveznice ali samo za male promene prinosa (kamatnih stopa). U slucaju vecih promena, trajanje daje precenjenu/potcenjenu aproksimaciju promenu cene obveznice, jer odnos cena obveznice prinos nije linearan. Zbog toga se prilikom merenja kamatnog rizika u obzir mora uzeti i konveksnost obveznice. Modifikovano trajanje i konveksnost uzeti zajedno daju najbolju aproksimaciju osetljivosti cene obveznice na promenu kamatnih stopa.

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

Ključne reči: Mekulijevo; modifikovano; efektivno; empirijsko novcano trajanje; trajanje portfolia; modifikovana i efektivna konveksnost; konveksnost portfolia


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About the article

Received: 2013-10-29

Accepted: 2013-11-25

Published Online: 2014-05-08

Published in Print: 2014-04-01

Citation Information: Singidunum Journal of Applied Sciences, Volume 11, Issue 1, Pages 53–66, ISSN (Online) 2217-8783 , DOI: https://doi.org/10.5937/sjas11-4766.

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© by Slobodan Čerović. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. BY-NC-ND 3.0

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