Rentestrukturen og Forventningshypoteserne: En Betragtning Under Usikkerhed (The Yield-Curve and the Expectation Hypothesis)

Abstract

In this paper we analyse the relationship between the 4 different Expectation Hypothesis that has been suggested in the litterature. These 4 Expectation Hypothesis are: 1) The unbiased expectation hypothesis (UEH); 2) The return-to-maturity expectation hypothesis (RTM-EH); 3) The yield-to-maturity expectation hypothesis (YTM-EH) and 4) The local expectation hypothesis (LEH).In a deterministic setting it is shown that all the 4 Expectation Hypothesis are identical. However, In a world of uncertainty, they impose different hypothesis about the future Yield-Curve. It is in this connection - in continuous-time - shown that the only Expectation Hypothesis with does not violate the risk-free arbitrage argument is LEH.The market price of risk is also being analysed and proof is being presented that show that in order for the LEH to be valid it is required that the market price of risk is 0 (zero). Furthermore, it is being shown that one cannot freely define the market price of risk as there exist an interactive relationship between the market price of risk and the variance in the bond-price that need to be satisfied in order to be consisting with the risk-free arbitrage argument.