On the yield to maturity of a coupon bond

Abstract

The article is devoted to one of the main characteristics of the bond-the yield to maturity. The subject of the study is the type of yield to maturity indicator. It is known, that there are two approaches to determining the yield to maturity of a bond: the nominal interest rate and the effective interest rate method. The relevance of the study is due to the fact that, as preliminary comparison has shown, these two approaches to determining the yield to maturity may be unequal in research. The purpose of this paper is to conduct a study of the dependence of the research results on the type of yield to maturity indicator. For this purpose, the problem of the dependence of the interest rate risk of a bond on the number of coupon payments per year was chosen. The literature contains reports on the dependence on the frequency of coupon payments over the term a bond that evaluates interest rate risk. The problem of the dependence directly of the interest rate risk of a bond on the number of coupon payments per year has not been considered in the literature. The task was set to determine which of the two approaches to determining the yield to maturity allows us to obtain results for interest rate risk that are consistent with the dependence of the duration of the bond on the number of coupon payments per year. Methods of differential calculus are used to solve the problem. As a result, it was proved that the use of the yield to maturity determined by the effective interest rate method allows us to obtain results consistent with the dependence of the duration of the bond on the number of coupon payments per year. The results obtained by using the yield to maturity determined by the nominal interest rate method do not agree with the dependence of the duration of the bond on the number of coupon payments per year. It is concluded that the yield to maturity determined by the nominal interest rate method in research may lead to incorrect results, in contrast to the yield to maturity in the form of an effective interest rate. Results of the work can be useful to both the bond issuer and the investor, as well as in theoretical studies of investments in bonds.