Český finanční a účetní časopis 2024(2):43-50 | DOI: 10.18267/j.cfuc.594

The Macaulay duration of a perpetuity bond in the period between coupon payments

Bohumil Stádník
Vysoká škola ekonomická v Praze, Fakulta financí a účetnictví, katedra bankovnictví a pojišťovnictví

In this paper, we deal with the derivation of the mathematical equation for the Macaulay duration of a perpetuity (hereinafter referred to as "Mac. duration") bond in the period between coupon payments. According to our findings, this equation is not included in the commonly available literature and is limited only to the equation for calculating Mac. duration at the moment when exactly one full coupon period remains before the payment of the nearest coupon. In a mathematical derivation, we come to a conclusion, which is consistent with financial intuition, that the Mac. duration of the perpetuity does not depend on the size of the coupon, but is dependent on the internal rate of return of the perpetuity and decreases as the moment of payment of the nearest coupon approaches.

Keywords: Macaulay duration of perpetuity; The price of perpetuity in the period between coupon payments
JEL classification: G10, G23

Received: June 7, 2024; Accepted: June 11, 2024; Prepublished online: July 3, 2024; Published: July 1, 2024  Show citation

ACS AIP APA ASA Harvard Chicago Chicago Notes IEEE ISO690 MLA NLM Turabian Vancouver
Stádník, B. (2024). The Macaulay duration of a perpetuity bond in the period between coupon payments. Czech Financial and Accounting Journal, 2024(2), 43-50. doi: 10.18267/j.cfuc.594
Download citation
  • BibTeX (.bib)
  • Bookends (.ris)
  • EasyBib (.ris)
  • EndNote (.enw)
  • EndNote 8 (.xml)
  • ISI WoS (.isi)
  • Medlars (.medlars)
  • Mendeley (.ris)
  • MODS (.xml)
  • Papers (.ris)
  • RefWorks (.txt)
  • RefManager (.ris)
  • RIS (.ris)
  • MS Word (.xml)
  • Zotero (.ris)
    • Open full article

    References

    1. CALDA, E., 2013. Součet nekonečné aritmeticko-geometrické řady. Matematika-fyzika-informatika. Vol. 22, no. 4, s. 250-252. Dostupné z: https://www.mfi.upol.cz/index.php/mfi/article/view/59.
    2. FABOZZI, F. J., 1999. Duration, Convexity, and Other Bond Risk Measures. Hoboken: Wiley.
    3. ODVÁRKO, O., 1995. Matematika pro gymnázia: Posloupnosti a řady. Praha: Prometheus.
    4. RADOVÁ, J., J. MÁLEK a P. DVOŘÁK, 2009. Finanční matematika pro každého. 7. aktualizované vydání. Praha: Grada.
    5. STÁDNÍK, B., 2015. Trhy dluhopisů. Praha: Oeconomica.

    This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.


    Return to the content