Measuring Interest Rate Risk Using a Duration Vector

Abstract

The duration of a bond approximately measures the interest rate risk caused by parallel shifts of the yield curve. This paper uses a generalization of the duration suggested by Diebold et al. (2006a), that takes the variations of the level, the slope and the curvature of the yield curve into account. As the dynamics of the yield curve are well approximated using these three factors we obtain a reasonable risk assessment. Compared with other approaches that take non-parallel shifts into account the approach considered here is very intuitive as it is similar to the classical duration. A case study exemplifies that in addition to the level the risk factors slope and curvature matter. Actually, we find a risk reducing effect due to the positive correlation between the innovations to the level respectively the slope.

Keywords: Duration, duration vector, Factor duration, Interest Rate Risk

JEL Classification: B26, E43, G12