Makeham's Formula: Some Applications in Fixed Income Analysis

30 Pages Posted: 16 Sep 2012

See all articles by Bjarne Astrup Jensen

Bjarne Astrup Jensen

Copenhagen Business School - Department of Finance

Date Written: September 14, 2012


Makeham's formula is an actuarial formula expressing the present value of a payment stream in terms of its repayments instead of the payments themselves. The formula is largely neglected in the finance literature, but -- as this paper shows -- it has a number of useful applications in fixed income analysis. We use Makeham's formula to decompose the return on a bond investment into interest payments, realized capital gains and accrued capital gains for a variety of accounting rules for measuring accruals in order to study the theoretical properties of these accounting rules, their taxation consequences and their implications for the relation between the yield before tax and the yield after tax. We also show how Makeham's formula produces short-cut expressions for the duration and convexity of a bond and facilitates the analytical calculation of the yield in certain cases.

Keywords: Makeham's formula, duration, convexity, yield after tax, tax, accued capital gains

JEL Classification: C63, G21

Suggested Citation

Jensen, Bjarne Astrup, Makeham's Formula: Some Applications in Fixed Income Analysis (September 14, 2012). Midwest Finance Association 2013 Annual Meeting Paper, Available at SSRN: or

Bjarne Astrup Jensen (Contact Author)

Copenhagen Business School - Department of Finance ( email )

Solbjerg Plads 3
Frederiksberg, DK-2000

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