  In this paper we show how to hedge a zero coupon bond with a smaller amount
of initial capital than required by the classical risk neutral paradigm, whose
(trivial) hedging strategy does not suggest to invest in the risky assets. Long
dated zero coupon bonds we derive, invest first primarily in risky securities
and when approaching more and more the maturity date they increase also more
and more the fraction invested in fixed income. The conventional wisdom of
financial planners suggesting investor to invest in risky securities when they
are young and mostly in fixed income when they approach retirement, is here
made rigorous. The paper provides a strong warning for life insurers, pension
fund managers and long term investors to take the possibility of less expensive
products seriously to avoid the adverse consequences of the low interest rate
regimes that many developed economies face.
