Improving the quantification of interest rate risk

Abstract

The value of Macaulay duration, probably the most widely used quantification method for measuring interest rate sensitivity of bonds, could roughly be financially interpreted as a percentage change of the bond price if the parallel shift of the interest rate equals 1 percentage point along the entire zero-coupon curve and the initial bond price is equal to 100%. T he main problem of its practical application lies in the fact that parallel curve shift is a very rare case, and we are more often concerned with predicting short-term rate shifts and considering their consequences for the rest of the yield curve and thus also for bonds with longer maturities. Therefore, it is useful to find a certain value that represents a quantification of the impact of short rate shifts on bond prices with respect to the parameters of bonds. So, the main contribution of this financial engineering research is to design a measure that can be used in the same way as Macaulay duration, but as a response to the change of the short interest rate, for example: in the equation for changing ΔP of a bond, in the equation of the volatility ratio of two bonds, or in the equation for bond portfolio sensitivity. Such a measure is still lacking in finance. We refer to this measure as the “short rate-shift duration”. Since the effect of the short rate shift on the entire yield curve, and thus especially on the price of long-term bonds, is very difficult to predict analytically, we use empirical data to calculate the duration value of the short-term shift and also to calculate its values for the USD and EUR interest markets.