Статистичний аналіз дохідності державних облігацій з використанням економетричних моделей: макроекономічні та інвестиційні аспекти

Abstract

Abstract. Introduction. The yield to maturity of government bonds changes over time and depends on a number of external and internal factors. In recent years, the gap between the yield to maturity of bonds of developed countries and countries with relatively low credit ratings has been increasing. Inflation and the level of central banks key rates are important factors that cause fluctuations in the yield of government securities. The yield of government bonds is affected by the terms to maturity. Taking into account the ratio of yield and risk, the longer the maturity of government bonds, the higher the yield should be. But in practice, this dependence can be different, especially in periods of financial crises. All of the above makes relevant the task of analyzing the variation of yield to maturity of government bonds of different countries at the current stage of economic development, as well as the dependence between yield to maturity and the level of inflation on the examples of certain countries and impact on the yield to maturity of government bonds of central bank key rates. The research used such scientific methods as analysis and synthesis of results, logical-analytical methods, methods of descriptive statistics and econometric models. Purpose. The purpose of the paper are improving the approach to the analysis of the yield to maturity of government bonds of various countries and the analysis of the influence of central bank rates on the level of yield to maturity of government bonds. Results. The yield to maturity of government bonds and the rates of central banks of different countries are analyzed. The inverse relationship between the terms to maturity and the level of yield to maturity of government bonds is shown on the examples of the USA and Ukraine. For different samples, taking into account the level of the credit rating of the countries, the analysis of average yield to maturity, dispersion, standard deviation, range of variation, coefficients of oscillation and variation was performed. A high positive correlation was found between the yield to maturity of government bonds and the level of central bank rates. A regression models analysis of the influence of central bank rates on the yield to maturity of government bonds was performed. The linear regression, logarithmic regression and polynomial regression models were constructed. The most qualitative model was chosen on the basis of the coefficient of determination. Conclusions. It was found that developed countries have low (in some countries in certain periods – negative) central bank rates and a low level of yield to maturity. Countries with low credit ratings have high central bank rates and much higher yields. The examples of the USA and Ukraine show an inverse relationship between the yield to maturity and terms to maturity, which indicates the discrepancy between the level of yield and the risk of government bonds in the conditions of financial crisis. A high coefficient of variation for the entire sample of countries indicates a significant dispersion of the data. The average yield to maturity is much higher for countries with relatively low credit ratings and high yield to maturity. The standard deviation differs by more than 8 times for countries with low credit rating, and the range of variation is more than 7 times. Oscillation coefficients and coefficients of variation are also significantly higher for countries with low credit ratings and high yield. All this indicates that for countries with a high credit rating and a low yield, the variation is smaller, the population is more homogeneous, and the average value is more reliable. The linear correlation coefficient indicates a sufficiently high positive correlation between the yield to maturity of government bonds and central bank rates. The results of the regression analysis show that, of all the considered models, the influence of the central bank interest rate on the yield to maturity of government bonds with a maturity of 10 years is best described by the polynomial regression model of the third degree, which has the maximum coefficient of determination. The practical value of the methodical approach to the analysis of the yield of government bonds is that it can be used to assess the influence of various factors on the yield of bonds, as well as to analyze the dynamics of the yield indicators of certain countries' bonds.