A Penny Saved is a Penny Earned: Less Expensive Zero Coupon Bonds

Abstract

This paper introduces a more general modeling world than available under the classical no-arbitrage paradigm in finance. New research questions and interesting related econometric studies emerge naturally. To explain in this paper the new approach and illustrate first important consequences, 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 main reason for the existence of less expensive zero coupon bonds is the strict supermartingale property of benchmarked savings accounts under the real world probability measure, which the calibrated parameters identify under the proposed model. We provide intuition and insight on the strict supermartingale property. The less expensive zero coupon bonds provide only one first example that is indicative for the changes that the new approach offers in the much wider modeling world. 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.