#### Report Number

1994-020

#### Abstract

An f-percent filter rule in a foreign exchange market calls for buying a foreign currency when its price has risen by f percent above a trough and holding until its price has fallen f percent from a peak. If the foreign exchange rate following a random walk, this is an unprofitable strategy. Since ex post filter rules continue to show positive gains on average, there must be a pattern in the data that makes these gains possible. Slight first-order autocorrelation, evident in the changes in actual exchange rates, is not strong enough by itself to account for the ex post filter-rule gains. We propose viewing changes in exchange rates as being generated by a short-run Markov switching model. This is a Markov chain (with states in which changes are positive and other states in which they are negative) embedded in substantial noise. When the probability is about 95 to 96 percent each day of staying in the current trend and when a very small propotion of the daily variance (e.g., about 3 to 4 percent) is attributable to the Markov chain, then implied exchange rate patterns (e.g., size of first-order autocorreclation) and simulated filter rule statistics (e.g., days holding a foreign currency and gains from the trades) are consistent with statistics generated by actual exchange rate movements. Furthermore, an investment strategy using an optimal Bayesian updating rule with actual mark/dollar and yen/dollar data dominates the best filter rules.

#### Keywords

Exchange Rate, Monetary Policy

#### Date of this Version

1994