EMU probability calculators are useless if European term structures contain little information regarding future interest rate changes. However, as discussed in Gerlach and Smets (1997a,b), Hardouvelis (1994), and Bekaert, Hodrick and Marshall (1997), European term structures tend to
for n-month Eurodeposit rates Rtn (n = 3, 6) relative to the forward rates Finferred from n-month and 2n-month Eurodeposit rates. Short-maturity forward rates are definitely informative with regard to future short-term rates, but the unbiasedness hypothesis is rejected for about half of the countries. Table 1B shows that intra-European forward spreads relative to the German forward rates do even better when forecasting of future interest rate differentials, with only 3 regressions out of 18 rejecting the unbiasedness hypothesis. there
As discussed in Gerlach and Smets (1997a,b), part of this greater consistency with the expectations hypothesis is undoubtedly attributable to the greater past predictability of European interest rate changes. Speculative attacks on the weaker currencies participating in the European Monetary System generate temporarily high short-term interest rates for those currencies, and sharply inverted term structures that correctly predict future interest rate declines once the currency is devalued.10 The expectations hypothesis fares less well for the DM, pound, and dollar, which were typically less constrained by exchange rate targets over 1977-98.
A past ability of term structures to forecast largely predictable changes in interest rates primarily associated with currency crises does not guarantee good forecasting performance for the future. A currency union is a European exchange rate regime previously experienced only by Belgium and Luxembourg, while the interest rate consequences of failing to achieve union could be difficult to forecast. Nevertheless, it is reassuring that there are no strong grounds a priori for rejecting the use of forward spreads as a forecast of future interest rate differentials.
Divergences between inferred and conditional probabilities
As indicated above in equations (3) – (5), equilibrium bond pricing theory does not in general predict that forward rates should be unbiased predictors of future short-term interest rates. There are three potential sources of bias. First is the interest rate risk premium (or term premium) when going from conditional to “risk-neutral” bond pricing probability measures. Second is the use of forward rates rather than bond prices, inducing biases indicated in equation (4). Third is a currency conversion issue when comparing forward rates from different currencies.
According to equation (3), EMU probabilities inferred from bond prices are “risk-neutral” (or risk-adjusted) probabilities computed under the probability measure Et :
Equivalently, fEMU g Prob*[EMU] is the current futures price on an Arrow-Debreu contract that pays off conditional upon EMU occurring. If the difference between EMU and no-EMU is associated with a major difference in investment opportunities, hedging against those differences could create a significant divergence between conditional probabilities and Arrow-Debreu futures prices.