Non-Negativity of Nominal and Real Riskless Rates, Arbitrage Theory, and the Null-Alternative Cash

Jochen Wilhelm and Bernhard Nietert

No 11, Passauer Diskussionspapiere, Betriebswirtschaftliche Reihe from University of Passau, Faculty of Business and Economics

Abstract: Pragmatic-world nominal riskless rates are non-negative. However, conventional arbitrage theory has yet to develop a theoretical justification of this phenomenon. – We define the null-alternative cash as an investor holding onto cash and refraining from investment and consumption ("doing nothing"); we use the null-alternative cash to prove that both nominal spot and nominal forward rates are non-negative and that prices of zero-coupon bonds do not increase with increasing maturity. In a positive inflation environment, however, both real spot and real forward rates might well become negative, but prices of zero-coupon bonds still do not increase with increasing maturity.

Keywords: arbitrage theory; inflation; non-negativity of spot and forward rates; short selling constraints (search for similar items in EconPapers)
JEL-codes: G10 G12 (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:zbw:upadbr:11

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