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abstract: '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.'
author:
- '[^1]'
- '[^2]'
- '[^3]'
bibliography:
- 'biblio.bib'
title: |
    [A Penny Saved is a Penny Earned:\
    Less Expensive Zero Coupon Bonds]{}
---

**Key words:** Forex, benchmark approach, benchmarked risk minimization, stochastic volatility, long term securities.

**JEL Classification:** C6, C63, G1, G12, G13

Introduction
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This paper aims to draw the 