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It is difficult to explain the persistent rejection of the simple efficiency hypothesis, and the finding of negative discount bias, moreoever, by recourse to explanations such as learning, peso problems and bubbles, because these are small-sample problems. 27 Appendix A. e. z = log Z ∼ N (µz , σz2 ), then E(Z ) = E[exp(z)] = exp(µz + 12 σz2 ). A1) where φ(z) is the normal probability density function, so that: E(Z ) = = = 1 √ σz 2π 1 √ σz 2π 1 √ σz 2π ∞ exp(z) exp −1 (z − µz )2 dz 2σz2 exp(z) exp −1 2 z − 2µz z + µ2z 2σz2 −∞ ∞ −∞ ∞ exp −∞ 1 = exp µz + σz2 2 −1 2 z − 2z µz + σz2 + µ2z 2σz2 1 √ σz 2π ∞ exp −∞ dz dz −1 z − µz + σz2 2σz2 2 dz .

32) which implies: var (ρt ) > var e k st+k . 33) says that the variance of the risk premium is greater than the variance of the expected depreciation. e. the predictable component of the excess return has a greater variance than the expected depreciation itself. Both of these inequalities follow from the finding of a small estimated slope coefficient (less than 1/2) in the regression of the rate of depreciation on the forward premium. Overall, therefore, regression evidence based on this approach suggests both that significant excess returns exist in the foreign exchange market, which can be predicted using current information, and that the variance of these predicted returns is larger than that of expected changes in the exchange rate.

Sq+1 | M 2 ) + lt−1L( st , st−1 , . . 68) where L( st , st−1 , . . , sq+1 | M2 ) and L( st , st−1 , . . , sq+1 | M1 ) represent the likelihood of the observed data given that the new or the old regime is in force respectively. The intuition behind this updating equation is as follows. 68) gives the posterior probability that there has been no regime shift. It combines the prior probability of a regime shift, (1 − lt−1 ), and of no regime shift, lt−1 , with the probabilities of observing the data given that a regime shift has or has not occured.