THE IMPACT OF COUPON PAYMENT FREQUENCY ON BOND DURATION

Abstract

In this paper we consider the impact of coupon payment frequency on the bond duration. The frequency of coupon payments per year is not among factors that have the key impact on the investment features of bonds. Scientists have already mentioned the impact of this factor on bond duration. However, no special research has been conducted. That is why the theory of investing in financial instruments with fixed income is incomplete. If we take into consideration that bond duration is a rather adequate measure of its interest rate risk, the solution to thisproblem is important from a practical point of view as well, as it allows to have a better understanding of factors that impact the interest rate risk of bonds.The problem is solved under certainty for fixed values of the bond’s key parameters. The main mathematicaltool is the expansion (of complex) functions in power series and actions with the series, such as addition and multiplication of series. We used the features of alternating series and convergent numerical sequences.The main result of this work is a mathematical proof that the bond duration depends on the frequency of coupon payments, which can be seen as a part of the theory of financial investments with fixed income. It is proved thatfor fixed values of the bond’s key parameters, when the frequency of coupon payments is increasing, the sequence of duration’s values is decreasing, which corresponds to the meaning of duration. We got the value of the limit of this sequence. The assertions were proved and confirmed by concrete calculations.Theoretical results - proved assertions about the impact of the frequency of coupon payments on duration - can be considered a contribution to the theory of investment in financial instruments with fixed income. The results can be used for the purposes of portfolio and long-term investment.