Financial futures and immunization

This paper investigates the ability of any portfolio that contains both bonds and financial futures contracts to immunize a lump sum liability having the same initial duration and value as the portfolio itself. An analysis of second order conditions shows that immunization against a local change in interest rates is possible only if the number of futures contracts lies within a critical interval; the endpoints depend on cash flow characteristics of the specific bonds and contract being combined. Immunization against any large change in rates is impossible if the portfolio contains any long position in futures but is achieved by some portfolios that contain short positions in futures.