output and interest rate movements. Her results suggest a negative β1 coefficient when the
central bank pursues interest rate smoothing. Moreover, Mark and Moh (2007) develop a
continuous-time model of UIP in which central banks’ policies to contain interest differen-
tial within a certain band can lead to forward premium bias. They are able to corroborate
the empirical evidence that forward premium bias intensifies during periods in which cen-
tral banks are intervening. In addition, Anker (1999) documents that a pure interest rate
smoothing policy of a central bank cannot account for the observed forward premium bias
in its entirety. Baillie and Osterberg (2000) estimate the effect of interventions in the for-
eign exchange market by central banks on the level and variance of ex post deviations from
the UIP condition within a FIGARCH framework. They report for the U.S. and Germany
that these interventions drive excess currency returns over the UIP-implied level for some
certain sub-periods.6
Limits to speculation hypothesis (LSH) suggests that investors engage in a specific
trading strategy only if that strategy yields a sufficiently large excess return per unit of
risk (Sharpe ratio). This hypothesis suggests the possibility of a band of inaction in which
the forward premium bias does not imply a profitable opportunity to exploit (Lyons, 2001;
Sarno et al., 2006). This implication of LSH is confirmed by Villanueva (2005). In particular,
Villanueva documents that spot exchange rate undershoots in response to a positive interest
differential shock, which is possibly due to the aforementioned band of inaction.
When rational risk-neutral agents care about real rather than nominal returns on finan-
cial assets, then the no-arbitrage condition for the forward exchange market becomes
Et " F St+k # = 0.
πt,t+k
where πt,t+k is the k-period domestic inflation. Under the assumption that all the variables
are log-normally distributed, the basic estimable UIP equation (3b) becomes:
δ k st+k = β0 + β 1 f fk - st + θ1 vart (st+k) + θ2 covt (st+k, πt+k) + ut+k (6)
where the variance and covariance terms arise from Jensen’s inequality, and ut+k is white
noise. Yet, many researchers have reported insignificant Jensen’s inequality terms (JIT),