GLOBAL CURRENCY MOVEMENT AND

GENERALIZED RULE INDUCTION

A. G. MalliarisM. E. Malliaris

Loyola University Chicago

Northeast Decision Sciences Institute, Montreal, Canada, April 13-15, 2011

MOTIVATION

• If it is possible to isolate some assets that have consistent patterns of movement, then this knowledge can be used in two ways:

to make money if one has moved and the other has not moved yet, or,

to build a more diverse portfolio by not including both in the basket.

INTRODUCTION

• Are there certain currency markets that move up or down together sufficiently often for us to form a conclusion about their inter-relationships?

• This paper investigates the relationships among directional movement of eight major currencies around the globe.

• Data over ten years was studied to see if there are movement rules among these currencies that might be stable over time.

ASSOCIATION ANALYSIS

• Association analysis is a popular data mining method that originated with the study of market baskets to see which items people purchased at the same time.

• Association analysis generates a set of rules of the form IF A THEN B

ASSOCIATION ANALYSIS

• The set of rules that is generated also depends on the values of support and confidence.

• Support: percent of times that some combination of inputs (also called antecedents) occurs in the data set.

• Confidence: when the antecedent combination does occur, reflects the percent of time that the output, or consequent, is also true.

METHODOLOGY

• Generalized Rule Induction is an association analysis methodology that was introduced in 1992 by Smyth and Goodman

• GRI is an effective, parsimonious method for detecting relationships in a large set of variables

OTHER APPLICATIONS OF ASSOCIATION ANALYSIS

• These methods continue to be popular for approaching problems in finance, for example:

• time series databases• stock selection• forecasting time series• co-movement in international stocks

DATA

• January 2000 through July 2009 • Downloaded from Bloomberg.• These prices were split into two disjoint sets for

training and validation. • Data from January 1 2000 to June 30 2008 was

used as the training set (2215 rows)• July 1 2008 to July 21 2009, used as the validation

set (276 rows). • To study the simultaneous market movements, all

data was transformed into “Up” or “Down”

THE EIGHT CURRENCIES

Original data was daily cash closing prices for the price of 1 US Dollar in the foreign currency that day

Australian Dollar, Japanese Yen British Pound, Euro, Swiss Franc Canadian Dollar, Mexican Peso, Brazilian Real

RELATIVE MOVEMENT

In order to view them all in a similar scale, the Mexican Peso has been multiplied by 10 and the Japanese Yen by 100 for the graph.

PROBLEM SETUP

• The Generalized Rule Induction methodology was run using the SPSS product Clementine

• There were two runs of the model• In the first run of GRI, the Australian dollar and

Japanese Yen were used as inputs with the Euro, the Swiss Franc and the British Pound as possible outputs.

• Following this run, the Australian dollar, Japanese Yen, the Euro, the Swiss Franc and the British Pound were used as inputs, with the Mexican Peso, the Brazilian Real and the Canadian dollar as outputs.

RESULTS

• The GRI models generated a total of 151 rules. • Here we show a selection of 18 of those rules

where the validation set results supported the training set results, sorted by the market of the consequent.

• Each rule displays the antecedent and consequent followed by the support and confidence in both the training and validation data sets.

BRAZILIAN REAL

BRITISH POUND

CANADIAN DOLLAR

EURO

MEXICAN PESO

SWISS FRANC

PAIR-WISE UP AND DOWN MOVEMENTS

• In addition to rule generation, Clementine allows us to generate a picture of pair-wise relationships among non-numeric data variables using a web graph.

• Stronger relationships, that is, ones that occur more often, have darker lines connecting them.

• This graph does not combine up and down movement in the various markets as we can do with GRI, but it does give us some indications of places we might expect rules to be generated.

DOWN and UP, PAIRWISE

CONCLUSIONS

• Today, the daily volume of currency transactions in currency futures, forwards, swaps and options dominates all other types of trading volumes.

• Whether currencies move together or independently is a matter of importance for investors wishing to spread the impact of their portfolio decisions.

• The results of this study suggest that there is reason to believe that co-movement among some specific markets exists over relatively long periods of time.