An accurate formula for bond-portfolio stress testing
Purpose – The purpose of this paper is to derive an easy-to-implement and highly accurate formula to approximate the change in the bond price resulting from a change in interest rates. Design/methodology/approach – The bond price is raised to an infinitesimal power and the Taylor series expansion is applied. Then, using the well-known modified duration and convexity, the new formula is obtained as a limiting case. Findings – It is proved mathematically and illustrated by numerical examples that the new formula generates better results than both the traditional duration-convexity and the exponential duration approximation formulas. Originality/value – The new formula derived in this paper will be used by risk managers to perform stress-testing on bond portfolios.
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