Interest Rate Risk of Zero-Coupon Bond Prices on Bombay Stock Exchange (BSE) –Empirical Test of the Duration, Modified Duration, Convexity and Immunization Risk

Abstract

Duration and convexity are important measures in fixed-income portfolio management and help develop methodologies in interest rate risk management. This article presents empirical test of duration and convexity of Zero-Coupon Bonds( ZCBs )at BSE in order to determine sensitivity of ZCBs prices on interest rate changes. The sensitivity of ZCBs in BSE on interest rate changes is tested and determined that convexity is more accurate measure as approximation of ZCBs prices changes than duration. The empirical results provide evidence that first duration is an increasing function of the interest rate and next there is no relationship between convexity and interest rate. The estimated percentage changes in ZCBs price using duration decrease by raising the percentage change in interest rate and we have non-parallel shift in lines for different level of duration. By non-parallel shifting of duration downward, the percentage change using only duration decreases and indicates higher negative difference and hence higher sensitivity at higher duration levels. As the interest rate increases the percentage change in ZCBs price using duration and convexity increases and again we have non-parallel shift in lines for different level of duration. By non-parallel shifting of duration upward, the percentage change using both duration and convexity increases and indicates higher positive difference and hence higher sensitivity at higher duration levels and by non-parallel shifting of duration downward, the percentage change using both duration and convexity decreases and indicates higher negative value and hence higher sensitivity at shorter duration levels. Also it has tested empirically whether convexity is return enhancing or return diminishing. Results of empirical tests over time periods under consideration show ZCBs convexity to be either significantly or negatively related to ex ante ZCBs returns. Further, the magnitude of ZCBs convexity is shown to be related indirectly and significantly to the immunization risk inherent in a bond portfolio. The main goal of this study is to determine how non-linear estimation models fit in case of ZCBs that are traded on BSE and to verify whether they offer reliable results compared with linear regression model on BSE. Also the most relevant contribution of the paper is to obtain a better curve estimation during the time period of March, 2009 -June, 2012 for duration and convexity exposures that contribute to the marginal increment of the coefficient of determination and the construction of a best nonlinear regression model that overcomes the linearity models.

Keywords: duration, convexity, corporate bonds, interest rate risk

JEL Classification: G1, G12