%0 Journal Article
%A Fabozzi, Frank J.
%A Xu, Yuewu
%T Higher-Order Durations with Respect to Inflation and Real Rates and Their Portfolio Management Applications
%D 2012
%R 10.3905/jfi.2012.21.4.069
%J The Journal of Fixed Income
%P 69-79
%V 21
%N 4
%X This study considers duration measures of any order with respect to inflation and real rates for both nominal bonds and real bonds (i.e., inflation-indexed bonds, or TIPS). The authors demonstrate that these duration measures, as well as the analysis of fixed-income portfolios, take a particularly simple form when examined from the viewpoint of continuously compounded rates. They show that, although the durations of all orders for nominal bonds with respect to inflation and real rates are exactly equal to the usual durations with respect to the nominal rates, the durations of all orders for TIPS with respect to inflation is exactly zero and the duration of all orders for TIPS with respect to real rates can be calculated in the usual way. Under general (non-infinitesimal) changes in the term structures of inflation and real rates, they derive the formulas for the percentage changes in bond prices using higher-order duration measures. Applications to portfolio management such as hedging (or speculating) on the inflation rate using portfolios of nominal bonds and TIPS are discussed.
%U https://jfi.pm-research.com/content/iijfixinc/21/4/69.full.pdf