STOCK MARKET ANNUAL RETURNS PATTERNS, DAY-OF- THE-WEEK EFFECT, AND VOLATILITY: EVIDENCE FROM THREE LATIN AMERICAN FINANCIAL MARKETS,

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1 STOCK MARKET ANNUAL RETURNS PATTERNS, DAY-OF- THE-WEEK EFFECT, AND VOLATILITY: EVIDENCE FROM THREE LATIN AMERICAN FINANCIAL MARKETS, Chiaku Chukwuogor-Ndu Ph.D. 1 Eastern Connecticut State University USA ABSTRACT This paper analyzes the financial markets trends in the three largest Latin American economies namely Argentina, Brazil and Mexico for the period A set of parametric and nonparametric tests is used to test equality of mean returns and standard deviations of the returns across the-days-of-the-week. The results indicate extreme volatility in annual closing price changes, drastic indexes growth, and the presence of the-day-of-the- week only in the BVSP index, Brazil and insignificant daily returns volatility in the three markets. These results are at variance with some earlier findings and consistent with others. Key words: returns, volatility, standard deviation, anomalies, day-of-the-week effect, kurtosis, skewness INTRODUCTION Issues relating to emerging markets and their economies deserve greater scholarly attention than has been the case. For example, in 1997 we witnessed the collapse of many Asian economies and their emerging financial markets; the Russian crisis in 1998; the Brazilian currency crisis in 1999; the catastrophic collapse of the Argentine financial system, currency and even government in African emerging markets are not immune to this trend. Whereas there has been no crisis to quote, the population of most countries in Africa has suffered continuous decline in economic well being. Any crisis in one emerging economy and its market generates a contagion effect of possible crises in other emerging economies and markets as a result of the so called investors nervousness. The instant withdrawal of short-term and long-term portfolio 1 Chiaku Chukwuogor-Ndu is an Associate Professor of Finance at the Department of Business Administration, Eastern Connecticut State University, 83 Windham Street, Willimantic CT 06268, U.S.A. Contact details for all questions are: Tel: , Fax: , E- mail: nduc@easternct.edu. 1

2 investments and cessation of foreign direct investment flow not only to the country under severe economic and financial stress but to most emerging economies and to the emerging markets in the region in particular. This reaction contributes significantly to the stunted growth of emerging economies and their markets and the volatile nature of the market returns. Liberalization and increased foreign investments at the local emerging markets have led among other benefits to greater trade and liquidity, and greater corporate financing through stock and bond issuing, both at the local and international markets. It is also believed that globalization and the drive toward liberalization of the capital and financial markets, the speculative and erratic nature of some short term capital flows and the inability of the emerging countries governments and the International Monetary Fund to design and implement regulatory structures appropriate to the circumstances are responsible to the continuous occurrence of national financial and economic crises. Even if this is the case, there has been no concerted effort to address these issues. This paper attempts to document recent financial markets trends in the three largest Latin American economies, namely Argentina, Brazil and Mexico for the period There may be scholarly merit in studying longer periods of data. However long-term data that encapsulates archaic data that relate to periods of good performance can distort the overall results giving misleading picture and interpretation of recent trends. As a result of these deficiencies in using long-term data, we chose to focus on more recent trends in this study. The rest of the paper is organized as follows. Section II provides the data and methodology. Section III contains the literature review. Section IV contains the empirical results and Section V summarizes and concludes the paper. DATA AND METHODOLOGY We use the daily closing values of three selected Latin American stock market indices from January 2 nd, 1997 to December 31st 2004 to determine the daily returns, day-of-the-week effect and volatility of returns. We further use the average annual returns to depict the annual trends in stock market returns. The financial markets studied are: Merval (MERV) index, Argentina; Bovespa (BVSP), Brazil and IPC GRAL (MXSE), Mexico. The daily stock returns for these selected Latin American stock indices are calculated as follows: In (P t/p t-1) * (1) Where P t is the stock index at date t. Except for the returns on Monday, any returns that are preceded by a holiday were excluded. This exclusion was done in previous studies to avoid speculation that observed day-of-the-week-effect could be partially due to these non-trading days. To determine the nature of the volatility of returns, the distributions of daily returns are analyzed using such measures as variance, standard deviations, kurtosis, skewness and coefficient of variation. The results were substantiated by parametric and non-parametric tests. Since the result of the normality test indicates that the distributions of the returns are non normal, we use the non-parametric test, the Kruskal-Wallis to check for the results on equality on mean returns. The Kruskal-Wallis statistic is as follows: k 2 12 RJ 3n (2) N N 1 n j1 j 2

3 where: k = number of samples; n j = number of values in j th sample; N = n j =total number of values; R j = sum of ranks in the sample when N values are ranked together (the statistic is approximately Chi-square distributed degrees of freedom equal to k-1). To test for the equality of variance across the days of the week, we employ the Bartlett s homogeneity test.. The test criterion is as follows (Snedecor and Cochran, 1970). 2 2 M v a ln s ln si (3) 2 Where a = the number of samples; v = degree of freedom; s = s 2 / 2 a ; s i j = estimate of the 2 from sample i; then, the quantity M/C is distributed approximately as a Chi-square distribution with degrees of freedom equal to (a-1). The above test is for the case when all groups have the same degrees of freedom. When the degrees of freedom differ, as with samples of unequal sizes, the test criterion is as follows as follows: 2 2 Vi ln s v i ln si M (4) C (5) i 2 3 a 1 v i v 2 where s v isi / v i ; 2 si is an estimate of the 2 from sample I; a = the number of samples; v i = the degree of freedom of samples i. The quantity M/C is distributed approximately as a Chi-square with degrees of freedom equal to (a-1). In our case, as we have five weekdays in a week, degrees of freedom are four. However, as Bartlett s test of homogeneity of variance is sensitive to non normality in stock return distribution, the Levene s (1960) test is also employed to check the results on equality of variance. In measuring the variation within a class, Levene s test uses the average of the absolute deviations instead of the mean square of deviations. This avoidance of squaring makes the test criterion much less sensitive to non-normal distributions (Snedecor and Cochran, 1976). The Levene s statistic is as follows: J J n j N J 2 2 D. j D.. / Dij D. j x F n j (6) j1 j1 i1 J 1 where D R M ; R ij is the return for week I and weekday j for j =1, 2,., J and J =5 if ij ij the last trading day of the week is a Friday.. j LITERATURE REVIEW The presence of anomalies in returns of common stocks has intrigued researchers since the last century challenging the appropriateness of the Capital Asset Pricing model (CAPM) and the whole theory of market efficiency. 3

4 Day-of-the-week-effect in stock returns in the US Market has been documented by a large number of studies. For instance, in the US stock market the mean Monday stock return has been found to be negative or significantly lower than the non-monday return. Many studies have shown that in addition, mean stock return on Fridays is significantly high relative to other days. See for example Cross (1973), French (1980) and Jaff, Westerfield and Ma (1989), Gibbons and Hess (1981), Lakonishok and Levi (1982), Rogalski (1984), Keim and Stambaugh (1984), Smirlock and Starks (1986), Harris (1986), Lakonishok and Smidt (1988), Mehdian and Perry (2001), among others document the Monday effect or other daily anomalies in the US stock market. Jaff and Westerfield (1985a, b) found a negative Monday effect in Canada and the UK but a negative Tuesday effect in Japan and Australia. Condoyanni et al. (1987) confirms these findings on the Japanese and Australian markets. Kato (1990) also finds that the Tuesday return is negative and Wednesday and Saturday returns are strongly positive in Japan. Jaff, Westerfield, and Ma (1989) drew attention to this phenomenon when they provided international evidence. Findings relating to the linkage between bad Fridays and the Monday effect are robust internationally. Bad Friday refers to a decline of the market on the Friday usually preceding a Monday with increased stock selling pressure. This phenomenon of the day-of-the-week has also been documented in relation to the emerging markets of Asia. Wong et al. (1986) find the existence of a significant day-of-the-week and seasonal effect for the Singapore market during the period In addition they find that the pattern is similar to that of the U.S. market but is different from that of Japan and Australia because the lowest return occurs on Monday and is negative. The highest return occurs on Friday and is positive. Wong et al. (1986) also find that the negative Monday returns occur during February through November of the year. The average daily returns in January are also higher than that for other months but the turn-of the year effect in Singapore is not significant at all. Kim (1988) reports results for Japan and Korea that are similar to that of Jaff and Westerfield (1985a, b). Aggarwal et al. (1989) also confirm the existence of the day-of-the-week effect in some Asian markets including Hong Kong, Korea, Taiwan, Japan and Singapore. Ho (1990) performs a comprehensive study on seasonalities in ten Asia-Pacific markets and finds a strong day-of-theweek effect for most of the Asian markets and there are more day-of- the-week variations in the non-january months than in January. Ho (1990) also finds it hard to reject the hypothesis that the day-of-the-week variations in the Asia-Pacific markets are similar to that of the U.S. Market after adjusting for time-zone differences. This phenomenon is especially true for smaller markets. Using a non-parametric test, Wong et al. (1992) further confirm the day-of-the-week effect in Singapore, Malaysia, Hong Kong and Thailand. Using the Levene test, Ho et al. (1994) find the existence of day-of-the week variations in volatility with Monday returns having the highest volatility, in most of the emerging Asian stock markets including Hong Kong, Malaysia, Singapore and Taiwan, with the exception of South Korea whose highest volatility occurred on Tuesday. In a recent study, Chen, Kwok and Rui (2001) examined the day-of-the week effect in the stock markets of China and found negative returns on Tuesday, after In a more recent study, Chukwuogor-Ndu (2004), the stock markets of seven Asian countries show negative Monday returns. These markets are those of China, Indonesia, Malaysia, Japan, Singapore, South Korea, and Thailand. The result of this study supports the existence of the day-of-the-week effect in stock returns in six countries namely: China, India, Japan, Philippines, Singapore, South Korea and Taiwan. Empirical research findings suggest the nature of market efficiency that exist in the Latin American Financial markets is not certain or changes according to prevailing economic conditions. It seems that in the presence of liberalization and increased foreign investments in the Latin American Markets, these markets became more efficient and moved away from weak efficiency, apparently towards semi-strong efficiency, Aguilera (2002); Arbelaez and Urrutia (1998); de la Uz (2002); Neriz Jara (2001); Zablotsky (2001). In a recent study, of the seasonal anomalies in seven Latin American countries, namely Argentina, Brazil, Chile, Colombia, 4

5 Mexico, Peru, and Venezuela, Cabello and Ortiz (2003), find that in nominal, real and dollar terms, daily seasonal anomalies are present in all Latin American equity markets. They used closing index prices for the seven Latin American markets: Brazil and Mexico , Argentina , Columbia , Chile , Peru and Venezuela They further find that in nominal terms, Monday is the worst performing day for five of the seven markets, namely Argentina, Brazil, Chile, Mexico, and Venezuela. These markets show negative Monday returns. With respect to volatility, Ortiz and Arjona, (2000) find that the Latin American equity markets remain small and highly volatile; moreover, volatility is time dependent. EMPIRICAL RESULTS A. Annual Stock Returns Analysis Extreme volatility in annual closing price changes and drastic growth characterized the LAFM during the period. For example between 1997 and 2004, the MXSE index, Mexico grew by 284 percent; the BVSP index, Brazil by 272 percent and the MERV index, Argentina by 112 percent. Extra ordinary annual gains include and percentage changes for the BVSP index, Brazil in 1999 and 2003 respectively; percentage change for the MERV index, Argentina in 2003; and and percentage changes for 1999 and 2004 respectively for the MXSE index, Mexico. The LAFM indexes also experience some severe declines in value during the period. In 1998 and 2001, the MERV index, Argentina declined percent and percent. In 1998, the BVSP index, Brazil declined percent and in 1999, the MXSE index, Mexico declined by percent. The declines experience in 1998 and 1999 coincided the Brazilian financial crisis and devaluation of the Brazilian Real. Similarly the declines in 2001 and 2002 coincided with the period of the Argentine financial crisis. However the indexes gained more momentums than declines during the period. Table 1 contains the annual closing index values, annual percentage and period percentage changes. Figure 1 depicts the annual percentage changes. Table 1 Annual Closing Index Values, Annual Percentage and Period Percentage Changes Index/Country/A nnual Percentage changes MERV, Argentina Annual Percentage changes Period Percentage change in closing values na BVSP, Brazil

6 Annual Percentage changes MXSE, Mexico Annual Percentage changes na na Figure 1. Annual Percentage Changes in Index Closing Prices Percentage Changes Years Merval MERV Index, Argentina Bovespa BVSP Index, Brazil MXSE IPC GRAL Index, Mexico B. Daily Stock Returns Analysis and Day-of-the week Effect All the Monday returns are negative. All the other days returns are positive for Mexico, positive for Argentina and Brazil except on Thursday. This observation indicates a strong presence of the day of the week effect. Table 2 contains the Descriptive statistics of the daily returns of the stock markets of Argentina, Brazil and Mexico. 6

7 Table 2 Daily Returns: Basic Statistics of the LAFM For the Period January 2 nd December 31 st, Name of Country/Index Monday Tuesday Wednesday Thursday Friday Argentina (MERV) Mean Median Maximum Minimum Standard Dev Skewness Kurtosis Variance Coefficient variation of Observations Brazil (BVSP) Mean Median Maximum Minimum Standard Dev Skewness Kurtosis Variance Coefficient variation of

8 Observations Mexico (MXSE) Mean Median Maximum Minimum Standard Dev Skewness Kurtosis Variance Coefficient of variation Observations Maximum returns occur for Argentina and Mexico on Wednesday and on Friday for Brazil. Argentina and Mexico show lowest returns on Monday, while Brazil shows lowest return on Thursday. Argentina experienced the highest standard deviation (SD) on Monday, while the highest SD occurs for Brazil and Mexico on Thursday. Table 3 contains the summary of maximum and minimum means and standard deviations of returns of the LAFM. Table 3 Summary of Maximum/Minimum Returns/Standard Deviations of the LAFM for the Period January 2 nd December 31 st, Name of Country/Index Argentina (MERV) Maximum return/sd * ** Day of Occurrence Wednesday/ Monday * ** Minimum Return/ S D Day of Occurrence Monday/ Tuesd ay Brazil (BVSP) * ** Mexico (MXSE) * ** Friday/Thursd ay Wednesday/T hursday * ** * ** Thursday/Wed nesday Monday/Friday 8

9 *= mean returns ** = standard deviation of returns As the skewness and kurtosis statistics of the returns for each day are generally well above zero and 3 respectively, normality of the returns is rejected. This is confirmed by the results of the W Test for normality shown on Table 4 below. For all the stock markets, the null hypothesis that states that the sample is normally distributed is rejected. As a result, we use nonparametric tests for further analysis. To substantiate the evidence of the day-of-the-week effects shown in Table 3, the Kruskal-Wallis test is carried out to test the null hypothesis of equality of mean returns across the days of the week. Ho: There is no difference in the returns across the days of the week; H1: There a difference in the returns across the days of the week. If the null hypothesis is rejected, this means that there is a day-of-the-week effect. As shown in Table 4, the values of the χ 2 -statistics are significant at 5% level for the BVSP index, Brazil but are not significant for MERV index, Argentina, and the MXSE index Mexico. We there reject the null hypothesis for Brazil and accept it for Argentina and Mexico. These results do not support the existence of the day-of-the-week effect on stock returns in Argentina and Mexico. These results seem more consistent with earlier findings of Arbelaez and Urrutia (1998); de la Uz (2001); Neriz Jara (2001) and Zablotsky (2001) where they find evidence of semi-strong efficiency in the Latin American markets. C. Volatility of Returns The standard deviation, variance and coefficient of variation of the returns indicate a high degree of volatility with the stock market of Mexico showing the least volatility. Most of the daily returns are skewed with all Monday returns skewed to the left. The deviations were generally skewed to the right for Brazil and to the left for Argentina and Mexico. The MERV index, Argentina showed the highest daily standard deviation of on Monday. That of the BVSP index Brazil was on Thursday, and the MXSE, Mexico of on Thursday. The daily standard deviations were highest for the Argentine stock market, followed by the Brazilian stock market. The coefficients of variation, though high were lower than expected because of the generally high daily returns. In testing the equality of variance we use both the Levene s test and the Bartlett s test because the non-normality of the distribution has been established. It has been found that Bartlett s test tends to reject the hypothesis of homoskedasticity more often in the case of nonnormal or leptokurtosis distributions. The results of both the Levene s test and Bartlett s test show that in none of three Latin American countries can the homoskedasticity hypothesis be rejected. See Table 4. Table 4 Results of Test of Normality, Equality of Means/Variance across Day-of-the-Week Effect of the LAFM for the Period January 2nd, 1998-October 31 st, Index/Countries Kruskal-Wallis W Test for Normality Levene s Bartlett's Test 9

10 (MERV) Argentina Chisquare Test P Value Statistics R Statistics P Value Statistics P Value (BVSP)Brazil (MXSE)Mexico These results are at variance with some earlier findings and are consistent with others. The results contradict the findings of Aguilera (2002); Arbelaez and Urrutia (1998): de la Uz (2001); Neriz Jara (2001) and Zablotsky (2001), which indicate that in the presence of liberalization and increased foreign investments in the Latin American Markets, these markets became more efficient and moved away from weak efficiency, apparently towards semi-strong efficiency. This is not the case with our findings. The markets are inefficient according to the tenets of capital market efficiency. The strong presence of the day of the week effect means that returns are easily predictable. Compared to the results of some earlier, there exists higher returns and greater volatility. These results are consistent with the findings of Ortiz and Arjona, (2000) indicating that with respect to volatility, the Latin American equity markets remain small and highly volatile; moreover, volatility is time dependent. CONCLUSION There was evidence of the day-of-the-week effect as all Monday returns are negative. However the result of the Kruskal-Wallis s equality of mean returns across the days of the week test are significant at 5% level for the BVSP index, Brazil but are not significant for MERV index, Argentina and the MXSE index Mexico. These results do not support the existence of the day-of-the-week effect on stock returns in Argentina and Mexico. These results seem more consistent with earlier findings of Arbelaez and Urrutia (1998): de la Uz (2001); Neriz Jara (2002) and Zablotsky (2001) where they find evidence of semi-strong efficiency in the Latin American markets Extreme volatility in annual closing price changes and drastic growth characterized the LAFM during the period. The standard deviation, variance and coefficient of variation of the returns indicate a high degree of volatility with the stock market of Mexico showing the least volatility. The results of both the Levene s test and Bartlett s test show that in none of three Latin American countries can the homoskedasticity hypothesis be rejected. These findings are consistent with earlier findings of Ortiz and Arjona, (2000). The period of 1997 to 2004 covered in this study encompasses the periods of the Argentine and Brazilian financial crises, 2002 and 1999 respectively. Many Latin American countries floated their currencies during this period. In addition, there was the Asian financial crisis in 1997 and the Russian financial crisis in 1998 with their possible contagion effect in other emerging markets. A study of the macro economic changes may shed more light on the volatility and growth experienced in these LAFM. 10

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