The unbiased expectations hypothesis states that forward rates are unbiased estimates for future short rates. Cox, Ingersoll and Ross  conjectured that this hypothesis should be inconsistent with the absence of arbitrage possibilities. Using the framework of Heath, Jarrow and Morton  we show that this is not always the case. The unbiased expectations hypothesis together with the existence of an equivalent martingale measure is equivalent to a certain condition on the volatilities of the forward rates.
term structure of interest rates expectations hypotheses