COMPARISON OF CURRENCY CO-MOVEMENT BEFORE AND AFTER OCTOBER 2008

Transcription

1 COMPARISON OF CURRENCY CO-MOVEMENT BEFORE AND AFTER OCTOBER 2008 M. E. Malliaris, Loyola University Chicago, 1 E. Pearson, Chicago, IL, mmallia@luc.edu, A.G. Malliaris, Loyola University Chicago, 1 E. Person, Chicago, IL, tmallia@luc.edu, ABSTRACT This paper considers foreign currency markets and discusses how currencies can be used as investment, hedging and speculative instruments. These three financial activities take place because certain fundamentals relationships exist between and among currencies that persist despite the surrounding uncertainty. To uncover such relationships and to examine their robustness over time and across various currencies, Apriori association analysis is performed on two sets of data, prior to the September 2008 financial crisis and after. This paper focuses specifically on the directional movement of eight major currencies in these two time periods and investigates whether there are any Apriori rules common to both periods. We then look at the performance of several of these rules in each time period, on both training and validation sets. INTRODUCTION The daily volume of currency transactions in currency futures, forwards, swaps and options dominates all other types of trading volumes. This volume is driven by globalization that includes trade and foreign direct investments, global portfolio diversification, global hedging and speculation and global banking, among other factors. Changes in information and communication technologies have accelerated the processing and transmission of data and ideas to a level far beyond our capabilities of a decade or two ago. Global financial imbalances have also played an important role in the volume and behavior of currencies. Substantial trading surpluses in China, Germany and Japan have been transferred in countries with balance of payments deficits such as the U.S. Global banks have facilitated the transfer of funds from subsidiaries in countries with large saving to countries with low saving and attractive investment opportunities. Also, the establishment of sovereign funds by surplus countries has contributed to the movement of currencies. Increased financial globalization has offered important opportunities for portfolio diversification. There is a wide spectrum of financial risks that include firm specific risks, industry wide risks and country risks. Several macroeconomic policies such as monetary policy, fiscal policy and level of regulation are included in country risks, among several other factors. The growth in the size and complexity of international financial markets has been one of the most striking aspects of the world economy over the last decade. Lane and Milesi-Ferretti [6] document the increase in gross holdings of cross-country bond and equities for a large group of countries. They describe this as a process of financial globalization. Economists and policy makers have

2 speculated on the implications of financial globalization for the design of monetary policy. Most central banks now either explicitly or implicitly follow a policy of inflation targeting. Under this policy, price stability, appropriately defined, is the principal goal of monetary policy. Campbell et al. [3] considered an equity investor who chooses fixed currency weights to minimize the unconditional variance of her portfolio. Such an investor wishes to hold currencies that are negatively correlated with equities. Their first novel result is that at one extreme, the Australian dollar and the Canadian dollar are positively correlated with local-currency returns on equity markets around the world, including their own domestic markets. At the other extreme, the euro and the Swiss franc are negatively correlated with world stock returns and their own domestic stock returns. The Japanese yen, the British pound, and the US dollar fall in the middle, with the yen and the pound more similar to the Australian and Canadian dollars, and the US dollar more similar to the euro and the Swiss franc. When considering currencies in pairs, Campbell et al. found that risk-minimizing equity investors should short those currencies that are more positively correlated with equity returns and should hold long positions in those currencies that are more negatively correlated with returns. When considering seven currencies as a group, they found that optimal currency positions tend to be long on the US dollar, the Swiss franc, and the euro, and short on the other currencies. A long position in the US-Canadian exchange rate is a particularly effective hedge against equity risk. This brief discussion points to the conclusion that certain global currencies have received great significance the past few decades. When we also consider the creation of the euro this significance becomes even greater since several important national currencies such as the German marc, the French franc, the Italian lira and several others were replaced by the euro. This global significance translates into a search for the pricing of these currencies and for understanding of their co-movement. The challenge becomes even greater since currencies are priced one in terms of another. One may view the issue of pricing currencies as a comparison of all economic and financial fundamentals between two nations. Instead of pricing currencies, in this paper we study the directional behavior of leading currency prices over two periods prior to and following the crash of October It is well known that the Global Financial Crisis of has impacted all financial markets very pronouncedly. The initial crash of the credit markets with the collapse of the values of mortgage backed securities and housing values quickly expanded to global equity, bond and currency markets. Global banks experienced substantial losses in their portfolios of asset backed securities, the Fed moved aggressively to reduce interest rates and establish several credit facilities to supply much needed liquidity. Foreign currency markets experienced substantial volatilities. The Global Financial Crisis started in August of 2007 but no one at that time had any accurate assessment of how the crisis would evolve. After Lehman Brothers filed for Chapter 11 bankruptcy protection on September 15, 2008, the intensity of the crisis amplified. Our main goal is to find whether or not there are any relationships among currency movements that have remained stable prior to and following the crash, using October 1 as our dividing date. If price movements are not random but follow patterns, such information may allow economists to better

3 evaluate the overall impact of leading currencies in the global economy. They can also be used as a basis for formulating speculative, hedging and carry trade strategies. Mandelbrot and Hudson [8] give a detailed description of the presence of non-linear determinism in financial markets. Empirical evidence of chaotic dynamics in financial data such as stock market indexes, foreign currencies, macroeconomic time series and several others have been performed by various researchers, Kyrtsou and Vorlow [5] recently, and in much more detail earlier by Brock, Scheinkman and LeBaron [9] and Brock and Malliaris [2]. However, this paper will study co-movements in currency markets before and after October 2008, and ask Is there stability in patterns of directional co-movement of major currencies before and after this time period? DATA AND METHODOLOGY Data for eight currency prices, the Australian dollar, the Japanese yen, the Euro, the Swiss franc, the British Pound, the Canadian dollar, the Mexican peso, and the Brazilian real, was retrieved from the Bank of Canada nominal noon exchange rates, which are published each business day at about 12:30 ET and were downloaded from year-converter/ Each original number is the amount of the currency equal to one US dollar on that day at that time. The data covered a time period beginning in November 2005, and ending in September During the week that began on October 6, 2008, the Dow Jones fell over 18% and the S&P 500 fell more than 20%. This crash was followed by declines in other markets around the world. The month of October 2008 is thus a dividing time in our data set. We removed this month, dividing the data set into two distinct pieces: Before (October 2008) and After. Each data set contains over 700 days of data. The Before and After sets were further subdivided into training and validation sets with the validation set being the last 252 days of each set. The validation sets thus occur entirely after the training sets and are completely disjoint. This type of disjoint, temporally following, and lengthy validation set is the most difficult for a model to perform well on and will thus be a very good judge of the rules stability. The training sets were used to generate rules of directional movement for the currencies. The validation sets were used to judge the robustness of rules on entirely new data. The four sets are named Before Training, Before Validation, After Training, and After Validation. The beginning and ending dates for each set are shown in Table 1. Table 1. Data Sets Set Name Begin Date End Date # Rows Before Training 11/1/2005 9/28/ Before Validation 10/1/2007 9/30/ After Training 11/3/2008 9/17/ After Validation 9/20/2010 9/19/

4 The data was originally downloaded as numeric values. These were converted into categorytype data that represented the direction of movement of the respective currency relative to the US dollar. The values used were Up, Even, and Down. Though association analysis originated with the study of market baskets to see which items people purchased at the same time, it has been generalized to look at questions of what occurs together. It is often in an exploratory way to discover interesting relationships in the data that may be analyzed further. For an in-depth discussion of association analysis techniques, see Hand et al [4], or Berry and Linoff [1]. The methodology used to generate rules on these currencies was Apriori Association Analysis, run in IBM s SPSS Modeler data mining package. Association analysis generates a set of rules of the form IF A THEN B where variables used in the modeling process may occur either after the IF or after the THEN. The set of rules that is generated also depend on the user-supplied minimum values of support and confidence. Support refers to the percent of times that some combination of inputs (also called antecedents) occurs in the data set. This forms the IF part of the statement. When the antecedent combination does occur, confidence reflects the percent of time that the output, or consequent, is also true. This is the confidence of the THEN part of the rule. There are several major association analysis techniques, for example, Apriori, Generalized Rule Induction (GRI), and Carma. These vary in the way they search for interesting rules within a large, and generally sparse, data set. In this problem, support and confidence were set to 7% and 65%, respectively. That is, for any rule to be generated, the IF part must occur in the training data set at least 7% of the time, and when the IF part is there, the THEN part must be true at least 65% of the time. RESULTS Using the settings for support and confidence detailed above, the Before training set generated 2635 rules. The After training set generated 2643 rules. While there are many ways to look at the results from these training runs, we will focus on those rules that occurred in both of the training sets. These are the rules that have remained stable on both sides of the October 2008 crash. Of these two rule sets, 79 rules had identical antecedents and consequents. That is, 79 common rules of the form IF [antecedent] THEN [consequent] occur in both the Before and After training sets. From these 79, one rule with the greatest confidence in the Before training set for each possible market direction represented was selected for further analysis. There were eleven such rules. Not every market and direction combination generated a rule common to both sets. No rules were generated using the market direction EVEN since there are not enough days were this occurs for a rule to be created. These common rules are shown in Table 2. The antecedents contain multiple conditions, all of which must be true for the rule to be applicable. For example, Rule 1 states that if the Japanese yen was Down (relative to the US dollar) and the Mexican peso was Down and the Brazilian real was Down then the Australian dollar was Down.

5 Table 2. Rules common to both Before and After training sets Rule Antecedent Consequent 1 DirJpy = Down and DirMex = Down and DirBrz = Down DirAus = Down 2 DirMex = Up and DirSws = Down and DirAus = Down DirEur = Down 3 DirBrz = Up and DirSws = Up and DirMex = Down DirEur = Up 4 DirMex = Up and DirSws = Down DirJpy = Down 5 DirAus = Up and DirSws = Up and DirMex = Down DirJpy = Up 6 DirSws = Down and DirCan = Down and DirAus = Down DirPnd = Down 7 DirAus = Up and DirCan = Up and DirSws = Up and DirMex = Down DirPnd = Up 8 DirBrz = Up and DirMex = Up and DirEur = Down DirSws = Down 9 DirEur = Up and DirMex = Down DirSws = Up 10 DirSws = Up and DirCan = Down and DirAus = Down DirMex = Down 11 DirBrz = Up and DirCan = Up and DirSws = Up DirMex = Up Each of these eleven rules occurred in both the Before and After training sets, but with different values for support and confidence. Though the minimum values for these are set at run-time, the Modeler package calculates the actual values of support and confidence for each rule that occurred in the data set used for training. These are shown in Table 3. Notice that all confidence values are above 70%. This means that, when the If part of the rule was satisfied, the THEN part was true at least 70% of the time. However, a much harder test is the comparison on each validation set. Table 3. Values of support and confidence for each training set Rule Before Support Before Confidence After Support After Confidence The validation set data is from the year following the training set in each of the cases. These results on the respective Validation sets are shown in Table 4.

6 Table 4. Values of support and confidence for each validation set. Rule Before Support Before Confidence After Support After Confidence An easier way, perhaps to look at these numbers is in how they change from the training to the validation sets. This is summarized in Table 5. Table 5. Validation values minus Training values. Rule Before Support Before Confidence After Support After Confidence Here we can see that, in the rules generated with the Before training set, while the rules still had a usably strong percent of occurrence, the confidence on the validation set dropped in one direction for each of the represented markets. In contrast, the After training and validation sets differences show that all the drops in confidence occurred with consequents of the European currencies, the Euro, the British pound, and the Swiss franc. Rules with consequents relating to the Australian dollar, the Japanese yen, and the Mexican peso remained positively robust and grew stronger. CONCLUSIONS This paper considers foreign currency markets and discusses how currencies can be used as investment, hedging and speculative instruments. These three financial activities take place

7 because certain fundamentals relationships exist between and among currencies that persist despite the surrounding uncertainty. To uncover such relationships and to examine their robustness over time and across various currencies, an a priori association analysis is performed on two sets of data, prior to the September 2008 financial crisis and after. There are 11 rules that this paper identifies as most appropriate for further analysis. All 11 rules, if analyzed one at a time, confirm stable relationships among currencies that would allow hedging and speculative activities. For example, if certain currencies decline in a given day then certain other currency will also decline. Also, if certain currencies rise in a given day another currency will also rise. Between all three currencies rising or all three declining and as a consequence also observing a certain currency also rising or also declining, we have several mixed cases. For example if the Swiss franc and Australian dollar decrease while the Mexican Peso increases the rule suggests that the euro will also decline. Overall, it is confirmed in these rules that the euro, the Japanese yen and the euro move in the same direction most of the times; also it is confirmed that the Mexican peso and Brazilian real move together although the Canadian dollar also influences the Mexican peso. The British pound is influenced by, and in turn it influences, the Australian dollar. In conclusion, these rules demonstrate that stable and robust relationships exist among groups or pairs of currencies that in turn form the fundamentals for global banking and investment, hedging and speculative activities. REFERENCES [1] Berry, M. and Linoff, G. Data Mining Techniques, Second Edition, Indianapolis, IN: Wiley Publishing Inc., [2] Brock, W and Malliaris, A. Differential Equations, Stability, and Chaos In Dynamic Economics, Amsterdam, Netherlands: Elsevier Science, [3] Campbell, JY, Medeiros KS-de, Viceira LM. Global Currency Hedging. Journal of Finance, 2010, 65(1): [4] Hand, D., Mannila, H., and Smyth, P. Principles of Data Mining, Cambridge, MA: The MIT Press, [5] Kyrtsou C and Vorlow C. Modelling Nonlinear Comovements Between Time Series. Journal of Macroeconomics, 2009, 31(1): [6] Lane, P., and Milesi-Ferretti, G.M. The External Wealth of Nations: Measures of Foreign Assets and Liabilities for Industrial and Developing Countries. Journal of International Economics, 2001, 55, pp [7] Lane, P., and Milesi-Ferretti, G.M. The External Wealth of Nations Mark II. IMF Working Paper, No 06-69, [8] Mandelbrot, B. and Hudson, R. The (Mis)Behavior of Markets. New York, NY: Basic Books, [9] Scheinkman, Jose A and LeBaron, B. Nonlinear Dynamics and Stock Returns. Journal of Business, University of Chicago Press, 1989, 62(3), pages