A note on approximating bond returns allowing for both yield change and time passage

A number of papers through the years have addressed the price-yield relationship, the approximation of bond returns and the associated components of price sensitivity. Typically, the research has been focused around the concept of duration and convexity to explain the price sensitivity of a bond to changes in its yield. Fixed income portfolio managers, however, are also interested in what happens to bond prices over a certain investment horizon, i.e. how time passage affect bond returns together with yield changes. Chance and Jordan [1996] examines this in a very neat way by a second order Taylor series expansion around the current market yield