The Distribution of Foreign Exchange Price Changes: Trading Day Effects and Risk Measurement--A Reply

This study investigates the nature of price changes in a variety of major and minor foreign exchange markets. The results suggest that the log of price changes over one (trading) day intervals seems to follow a non-normal stable distribution function. Different measures of location (and to lesser extent scale) are present for different days of the week. Dollar denominated price changes are high on Mondays and Wednesdays and low on Thursdays and Fridays for all currencies. The Wednesday-Thursday result is consistent with the settlement procedures used in foreign exchange transactions in the dollar. The Friday-Monday result is consistent with an increase in demand for the dollar prior to the weekend. THIS STUDY OFFERS SOME previously unavailable results on the nature of price changes in a certain set of speculative markets. In particular, this is a study of the distributional characteristics of daily and weekly price changes for a number of major and minor foreign exchange markets. The results document the existence of non-normal stable distributions for price changes in foreign exchange markets. These price change distributions differ by day of the week in ways that are only partly attributable to the institutional structure of the market. The results of the study are interpreted within the context of understanding how foreign exchange markets operate, and within the context of prior studies of stock market data concerned with summarizing the probability distribution of price changes for different intervals, including days of the week. Since Bachelier's [1] original treatise that contained the proposition that speculative market prices follow a process that could be described by a normal distribution, there have been numerous alternative attempts to describe the stochastic processes which characterize speculative market prices. These studies have not resulted in any generalized description of the probability distribution of price changes in such markets. Indeed, the evidence suggests substantial differences in the process among various types of financial instruments. The failure to achieve consensus can be traced to the lack of robustness in the statistical procedures employed to estimate processes and to differences in the underlying institutional or economic arrangements which are unique to that market. The possibility of differences in the information set used to assess value or differences in technology for transmitting information makes it important to secure additional

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