Heterokedastic behavior of the Latin American emerging stock markets

International Review of Financial Analysis 10 (2001) 287 – 305

Heterokedastic behavior of the Latin American emerging stock markets Edgar Ortiza,*, Enrique Arjonab a

Universidad Nacional Auto´noma de Me´xico, Me´xico City, Me´xico b Colegio de Posgraduados, Me´xico, Montecillo, Me´xico

Abstract Few studies on emerging markets have been devoted to examine the nature of their volatility. This work analyzes the time series characteristics of six major Latin American equity markets: Argentina, Brazil, Chile, Colombia, Mexico, and Venezuela. Non linear dependency and autoregressive conditional heterokedasticity are studied. The work includes several GARCH(p.q) models, including their exponential and GARCH – in – mean extensions. Weekly data for the 1989-1994 period from the International Financial Corporation is used. Not a single (G)ARCH model was found to depict volatility of these markets. Different models are more appropriate for each country. The best models seem adequate; the models reject autocorrelation, the distribution of the residuals is normal is all cases but one, the series are integrated, and heterokedasticity is rejected. The presence of heterokedasticity and autocorrelation in the major Latin American stock exchanges reflects their thinness and the presence of inefficiencies which reflect in time dependent high volatility. D 2001 Elsevier Science Inc. All rights reserved.

1. Introduction Sophisticated research on the emerging capital markets has been possible during the last few years due to the impressive growth and internationalization of some of these markets, spurred by financial liberalization and deregulation and structural changes implemented in their economies. Rising interest in these markets has been also made possible due to the

* Corresponding author. Apartado 21-712, Col Coyoacan, Del Coyoacan, 64000 Mexico, D.F., Mexico. Tel.: +52-5-658-1949; fax: +52-5-658-1949. E-mail address: [email protected] (E. Ortiz). 1057-5219/01/$ – see front matter D 2001 Elsevier Science Inc. All rights reserved. PII: S 1 0 5 7 - 5 2 1 9 ( 0 1 ) 0 0 0 5 7 - 6

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availability of important data banks. Continuous and reliable time series about emerging markets activity has led to important studies to characterize the characteristic of these markets. Originally, ‘‘financial repression’’ and the lack of information limited the study of emerging capital markets to descriptive studies and policy oriented papers. Important models about financial intermediation and economic growth were also put forth, strongly suggesting financial liberalization to promote the participation of the capital markets in the savings and investments processes of the developing nations.1 Structural changes and financial liberalization policies undertaken by many countries during the last decade, along with economic and financial globalization, promoted an accelerated growth of stock exchanges along the world. Some ‘‘emerging’’ markets rose in importance and brought the attention of both practitioners and scholars. This led to an increased interest in determining the opportunities of investing in those markets to enhance portfolio returns.2 The increased availability of information about these markets soon led to more serious empirical studies, beginning timidly with some inefficiency studies.3 Currently, the financial literature gives account of studies dealing with comovements, dynamic linkages, co-integration, seasonal effects, and other phenomena from the emerging markets.4 Nevertheless, in relative terms, the literature on emerging markets is still scanty. Moreover, there are few studies identifying their stochastic behavior particularly concerning volatility. ARCH, ARCH-M, and GARCH and EGARCH-M models have been used to study these markets by Chiang, Jeon, and Oh (1996), Errunza, Hogan, Kini, and Padmanabhan (1994), Islam and Rodriguez (1997), Koutmos et al. (1993), Liu and Ming-Shiun (1997), Ortiz and Soldevilla (1997), and Thomas (1995). Complementing this research, this work attempts to study the time-series characteristics of six major Latin American stock markets: Argentina, Brazil, Chile, Colombia, Mexico, and Venezuela. Nonlinear dependency and autoregressive conditional heterokedasticity are studied. Traditionally, stock market returns have been carried out assuming homokedasticity. Following recent advances in the financial literature, this paper examines heterokedastic behavior of these six Latin American markets. The study includes several GARCH( p,q) models including their exponential and GARCH-in mean extensions.5

1

Development financing theory is extensive. A comprehensive treatment on this issue, emphasizing capital markets can be found in Ortiz (1993). That article also has a fine bibliography on this matter. 2 See Aggarwal and Schirm (1995), Avgustinous, Lonie, Power, and Sinclair (1997), Barry and Rodriguez (1998), Hartmann and Khambata (1993), and Shachmurove (1998). Works on returns and international diversification to emerging stock markets also emphasize exchange rate issues. See, for example, Ghosh and Ortiz (1998), Hauser and Yaari (1994), and Soenen and Schrepferman (1997). 3 Recent works with this focus are Aggarwal and Leal (1996), Agrawal and Tandon (1994), Arbelaez and Urrutia (1998), Butler and Malaikah (1992), and Leal and Ratner (1994). 4 See, for instance, the works by Alford and Lustier (1996), Arshanapalli and Doukas (1996), and Shachmurove (1996). 5 ARCH models were originally developed by Bollerslev (1986), Engle (1982, 1983), Engle and Kraft (1983), and Miljoh (1985). ARCH-M modeling was proposed by Bollerslev (1987) and Engle et al. (1987); the models for Generalized Autoregressive Conditional Heterokedasticity were introduced by Bollerslev (1986, 1990) and Taylor (1990). The exponential versions of the GARCH models were originally proposed by Nelson (1991).

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The study includes weekly data from 1989 to 18994, period when stock markets for the area grew significantly as a result of strong adjustment programs and financial liberalization policies implemented by the governments of Latin America in response to their debt crisis (Edwards, 1995); their explosive growth during that period also constitutes the roots for the financial crisis that ensued in those countries, beginning with the December 1994 macro peso devaluation. The paper is organized in five sections, including this introduction. Section 2 describes briefly some institutional characteristics of the Latin American stock exchanges. Section 3 presents the basic stochastic characteristics of the return series for the Latin American stock markets, both in terms of dollars and in terms of their local currency. Section 4 presents the models characteristics and the main results for the autoregressive models. Section 5 is a brief conclusion.

2. Institutional characteristics of the regions’ stock markets Table 1 summarizes the main long trend institutional characteristics of the seven major Latin American stock markets.6 It is worth mentioning that the number of companies listed in these markets is small and, in some cases, it has even decreased. This decrease can be attributed mainly to thin and infrequent trading, and in some cases due to mergers and acquisitions. As far as the number of companies is concerned, the Brazilian (Sao Paolo) market is the largest, with 544 companies listed. The Chilean market, a small country, is the second most important in this category, reflecting its maturity, for its growth process began in the 1970s. Concerning market capitalization, the Latin American exchanges registered an impressive growth throughout the years, albeit with a sharp decline in the early 1980s. The most impressive growth is that of the Mexican stock market. In 1980, total market capitalization was of US$12.994 billion. Due to the debt crisis, market capitalization decreased sharply to US$1.710 billion by 1982. Recuperation was almost steady during the following years, beginning an explosive growth in 1989. Then, market capitalization amounted to US$22.2250 billion. This explosive growth continued during the following 4 years, greatly influenced by foreign portfolio investments in that market (Cabello, 1999, 2001). Thus, by 1993, market capitalization increased to US$200.671 billion, a 12.6 times increase from the low levels of 1982. Due to the peso crisis in December 1994, market capitalization declined to US$130.246 billion by the end of that year. However, in spite of that fall, it is obvious that a structural change took place in the Mexican stock market during the late 1980s and early 1990s. This structural change appears to be a common fact among the Latin American capital markets, as suggested by Table 1. For instance, the Brazilian stock market had a total capitalization value of US$9.221 billion in 1980. By 1994, market capitalization had increased to US$189.289 billion becoming that year the largest

6

This table includes information about the Peruvian market, too. Because weekly time series for this market were available for only 2 years, we excluded it from this study.

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Table 1 Latin American emerging capital market trends (billion dollar) 1980 Number of listed firms Argentina 278 Brazil 426 Chile 265 Colombia – Mexico 259 Peru – Venezuela – Market capitalization Argentina 3864 Brazil 9221 Chile 9400 Colombia 1605 Mexico 12,994 Peru – Venezuela 2657 Deal value Argentina 1089 Brazil 5383 Chile 548 Colombiaa 187 Mexico 3262 Peru – Venezuela 60 Comparative index Argentina 1.00 Brazil 1.00 Chile 1.00 Colombia 1.00 Mexico 1.00 Peru
Venezuela 1.00

1981

1982

1983

1984

1985

1986

1987

263 477 242 – 229 – –

248 493 212 193 206 – 98

238 505 214 196 163 – –

236 522 208 180 160 – 116

227 541 228 102 157 159 108

217 592 231 99 155 177 108

206 590 209 96 190 197 110

2056 12,574 7050 1399 10,100 1371 2441

974 10,261 4395 1322 1719 685 2415

1386 15,100 2599 857 3004 546 2792

1171 28,994 2106 762 2197 397 –

2037 42,768 2012 416 3815 760 1128

1591 42,096 4062 822 5952 2322 1510

1591 16,900 5341 1255 8371 831 2278

454 6185 375 332 4181 – 47

231 5938 163 93 781 – 82

389 4884 65 65 1112 – 59

277 9960 51 47 2160 – 27

631 21,485 57 30 2360 38 31

309 28,912 298 49 3841 239 52

251 9608 503 80 15,554 301 148

1.92 2.13 0.76 1.69 0.66 1.00 0.93

4.67 3.50 0.68 1.34 0.47 1.00 1.07

36.50 30.13 0.57 1.02 1.71 2.40 1.37

233.83 163.75 0.63 0.83 2.82 7.00 1.98

1745.67 818.75 1.10 0.87 7.82 54.80 2.75

2082.08 1157.50 2.62 1.78 32.89 200.00 7.02

5506.50 1561.25 3.44 3.27 73.78 189.00 13.20

Source: Elaborated by authors from IFC, Emerging Stock Markets Factbook, 1990; 1995. a Includes Medelin stock exchange value.

Latin American stock market according to all indicators shown in the table. Indeed, as far as traded value is concerned, the Brazilian market is the largest stock market in Latin America. However, it is important to point out that traded value was rather low in Latin America, compared with market capitalization, i.e., ownership remains largely in a few hands reflecting corporate governance practices often limited to a tight circle of family and family friends.7 7 On this issue, see ‘‘Risk Management and Corporate Governance in Imperfect Markets’’ (Fischer, Ortiz, & Palasuirta, 1994).

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Table 1 (continued ) 1988

1989

1990

1991

1992

1993

1994

186 589 205 86 203 236 60

178 592 213 82 203 256 60

179 581 215 80 199 294 76

174 570 221 83 209 298 87

175 565 245 80 195 287 91

180 550 263 89 190 238 93

156 544 279 90 206 218 90

2025 32,149 6849 1145 13,784 – 1816

4225 44,368 9587 1136 22,550 931 1156

3268 16,354 13,645 1416 32,725 812 8361

18,509 42,759 27,984 4036 98,178 1118 11,214

18,633 45,261 29,644 5681 139,061 2630 7600

43,967 99,430 44,622 9237 200,671 5113 8010

36,864 189,281 68,195 14,028 130,246 8178 4111

593 17,979 610 63 5732 57 221

1916 16,762 866 74 6232 90 93

852 5598 783 71 12,212 99 2232

4824 13,373 1900 203 31,723 130 3240

15,679 20,525 2029 554 44,582 417 2631

10,339 57,409 2797 732 62,454 1672 1874

11,372 109,498 5263 2191 82,964 3080 936

34,485.83 5,977,014.12 18,357,500 148,800,000 111,895,833 171,726,667 132,130,000 41,352.50 770,187.50 3,145,000 75,970,000 847,562,500 46,931,250,000 544,237,500,000 4.60 7.58 11.67 24.84 27.33 39.16 54.25 3.35 3.75 5.36 1.38 1.92 2.88 3.42 147.70 292.50 439.04 999.51 1228.46 1817.20 1658.78 1720.00 67,388.60 5,160,000 20,000,000 74,580,000 186,100,000 282,980,000 12.99 9.25 60.09 98.51 66.78 3.36 4.53

The explosive rate of the Latin American stock markets reflects in the growth of their price indexes. The comparative index (1982 = 100) reveals the magnitude of the increased importance of those markets. However, it must be recognized that the growth of stock prices in the region were impacted by high inflation rates, which, for example, in the case of Argentina the inflation index surpassed 116, 184, 844, 564% points in 1994 alone (1982 = 100). Finally, it is important to note that in a world basis emerging capital markets increased in importance from a share of 5% of total market capitalization in 1989 to 13% by 1994. However, the share of the Latin American stock markets in relation to

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Table 2 Basic statistics Argentina Dollar

Brazil Local currency Dollar

Equivalent returns Mean 0.6347
2.7049*** S.D. 10.4677 11.3819 Skewness
0.8208*** 1.9429*** Kurtosis 12.6863*** 12.0589*** Jarque – Bera 1246.7220 1254.5550 Ljung – Box (6) 13.587** 35.421*** (12) 26.110*** 50.442*** (24) 45.700*** 69.411*** Unit root tests for log Pt ADF 0.8794 3.3947 PP 0.8428 2.4669 Unit root tests for Rt ADF
18.2557***
14.0984*** PP
18.2546***
14.7232***

Chile Local currency Dollar

0.4203
8.7700*
0.6709*** 5.4184*** 98.7971

5.2433*** 8.7249
0.5521*** 6.2794*** 154.6592

8.283
11.792*** 27.613** *

19.211*** 25.802*** 37.236**

0.7529 0.6334

10.2725 8.2447


15.4511***
11.0976***
15.4881***
11.6029***

0.6082*** 3.0704 0.3272*** 3.3581
7.1894

Local currency 0.7642*** 2.9351 0.3091*** 3.3239
6.2915

20.346*** 21.698*** 35.737**

29.407*** 31.909*** 44.350***

3.4267 2.7067

4.4699 3.4519


13.9650***
12.9123***
14.2788***
13.2001***

All returns are in percentages: Rt = log( Pt/Pt
1)100. The sample period is 1989.2 – 1994.11; 312 monthly price observations. Ljung – Box (n) is the n
lag Ljung – Box statistics for the returns series. It follows a chi-square distribution with n degrees of freedom. McKinnon critical values for the ADF and PP statistics are
2.5722,
1.9406, and
1.6162 at the 1%, 5%, and 10% levels, respectively. * Denote significance at the 10% level. ** Denote significance at the 5% level. *** Denote significance at the 1% level.
Indicates significance levels above 10%.

total emerging markets capitalization remained basically unchanged: 14% in 1989 and 14.5% in 1994.8

3. Comparative stochastic characteristics Table 2 summarizes the main stochastic characteristics of the six major Latin American stock markets, using an AR(1) process. The data includes weekly returns from January 1989 to November 1994. A total of 313 price index observations constituted the original database obtained from the Emerging Markets Data Base (EMDB) from the International Financial Corporation. Results include dollar and local currency returns. However, the

8

Emerging Markets Fact Book, various issues, 1990 – 1995.

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Table 2 (continued ) Colombia Dollar

Mexico Local currency

Dollar

Venezuela Local currency

Dollar

Local currency

0.6460*** 3.9161 1.3216*** 9.3182*** 605.8739

0.9387*** 3.7619 1.5639*** 10.8927*** 931.0177

0.5830*** 3.0804
0.2669* 3.1643
4.0280

0.7171*** 2.9552
0.3004* 3.2427
5.4233

0.2574** 5.6131 0.3571** 4.7559*** 46.4153

0.7443** 5.2250 0.4472** 4.8402*** 54.0782

28.212*** 57.897*** 68.303***

42.162*** 74.891*** 84.703***

14.460** 18.696* 26.145


17.556*** 22.557** 28.709


20.422*** 30.362*** 40.645**

28.195*** 35.125*** 48.809***

2.8551 2.2163

4.2501 3.1345

3.1358 2.5309

4.0719 3.2144

0.6475 0.4884

2.3399 1.7892


14.9367***
15.4003***


13.5985***
14.1825***


14.2328***
14.5249***


13.9558***
14.3882***


14.9231***
15.1351***


13.773***
14.0131***

application of the GARCH–EGARCH models in the following sections are presented only for dollar returns. A comparative analysis of the stochastic characteristics of these markets shows that mean monthly dollar returns were always lower than local currency returns in all cases. Moreover, with the exception of Argentina, in all other five Latin markets, returns were more volatile in dollars than in local currency, as shown by their standard deviation. Another important fact that outspans about returns and volatility of these emerging capital markets is their wide differences. In local currency, the markets of Brazil and Argentina were the most profitable, offering returns of 5.2% and 2.7%, respectively, which contrasts sharply with returns under 1% offered by the other markets. It is worth noting that the lowest monthly returns for the period were offered by the Mexican stock exchange (0.71%), in spite of its exponential growth during the period brought about by financial liberalization and deregulation. The Brazilian, Argentinian, and Venezuelan markets were the more volatile. Their standard deviations of 8.7, 11.3, and 5.2 points is extremely high compared with the more stable returns from the other countries with standard deviations

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around 3 points. It is worth noting the case of Venezuela because it offered the second lowest returns, but its standard deviation was high. In dollar terms, the story is somewhat different. The highest returns were offered by the stock markets from Colombia (0.64%), Argentina (0.63%), and Chile (0.60%). Venezuela offered the lowest returns in dollars, 0.26%. Concerning volatility, the standard deviation from Argentina is extremely high (10.4 points) followed by Brazil and Venezuela. Chile and Mexico presented the lowest standard deviation for returns in dollars among the six Latin American markets under analysis. In the case of Chile, this reflects the maturity of its economy and liberalized markets. In the case of Mexico, this rather reflects the overvalued peso policy sustained by the government during the period. In sum, risk levels and risk premia offered by the Latin American stock markets reflect the characteristics prevailing at each country. Higher distribution moments also present interesting characteristics. In regard to skewness, the returns in local currency from four countries, Argentina, Chile, Colombia, and Venezuela are skewed to the right; only the distributions from Brazil and Mexico are skewed to the left. The distributions in dollar terms do not follow a similar pattern. In the cases of the markets from Chile Colombia and Venezuela, the asymmetry is to the right, while, in the remaining three cases of Argentina, Brazil, and Mexico, their distributions are left skewed. Finally, concerning kurtosis, it is worth noting that in all cases the Latin American stock returns are leptokurtic. These two characteristics reflect in the lack of normality in five of six Latin American stock markets. According to the Jarque–Bera indicator, returns from the Latin American capital markets follow a N(0,1) distribution only for the Mexican case, both in local currency and dollar terms. Autocorrelation of returns is also a common problem in the Latin American stock markets. As shown in Table 2, the 6, 12, and 24 lag Ljung–Box statistic reject independence, in most cases at the .01 level, both for local currency and dollar returns. Unit root tests9 are also presented in Table 2, for the logarithm of the stock price and the logarithmic first-difference, i.e., returns. The Augmented Dickey–Fuller (ADF) and Phillips and Perron (1988) statistics are shown for the series in local currencies and dollars. The two statistics test for a unit root in the univariate representation of a time series. For a series Yt, the ADF tests (Dickey and Fuller, 1979) consist of a regression of the first difference of the series against the series lagged k times [Eq. (1)]: Dyt ¼ a þ ryt
1 þ

k X

bs Dyt
s þ et

ð1Þ

S¼1

where Dyt = yt
yt
1; yt = ln( Yt). The null and alternative hypotheses are: H0: r = 0; H1: r = 1. Acceptance of the null hypothesis implies nonstationarity. The Phillips–Perron (PP) (1988) statistic is an alternative 9

An excellent survey on unit root tests is available at Phillips and Xiao (1999).

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295

test of r = 1. There are not lagged difference terms. It is based on the following model [Eq. (2)]: Dyt ¼ m þ ryt
1 þ et

ð2Þ

Both the ADF and PP tests accept the hypothesis of a unit root in the logarithmic of the price time series. However, the hypothesis of a unit root in the returns series is rejected both for the dollar and local currency return series for all six Latin American markets. There is a strong rejection at the .01 level; the McKinnon critical corresponding sample critical values are
2.5722,
1.9406, and
1.6162 at the 1%, 5%, and 5% levels, respectively. Summing up, dollar returns are lower than local currency returns in all six Latin American stock markets. There is a wide difference in returns and volatility among these markets. Volatility is extremely high in some cases. The distribution of the return series of these markets does not follow a normal distribution; time dependency among returns is also present, which also suggests the presence of heterokedasticity. Finally, the logarithmic price series are not stationary, while the return series show stationarity according to the ADF and PP tests. These facts, coupled with the evolution of the Latin American capital markets since the early 1980s, and particularly since financial liberalization and deregulation was fully enforced during the late 1980s and early 1990s, identify thin and very volatile markets, sensitive to speculative attacks or capital reversals and prone to severe liquidity crisis.

Table 3 Mean returns time series models Argentina
1,
7,
9,
27,
31,
36,
52,
55,
58,
63,
85 Durbin – Watson 2.01 Akaike Info Criterion 3.56 Schwars Criterion 3.75 Log Likehood
707.70 Breusch – Godfrey F statistics 0.1025 Probability 0.7491 ARCH – LM test F statistics 20.3408 Probability 0.0000 White heterocedasticity test crost terms F statistics 2.7353 Probability 0.0000 Relevant lags

Brazil

Chile

Colombia


1,
13,
1,
5,
1,
2,
5,
29,
41,
74,
76,
8,
11,
64
85
16,
22
24,
61,
75 1.91 2.00 1.96 4.09 2.14 2.80 4.17 2.23 2.96
846.20
554.89
651.69

Mexico

Venezuela


1,
28,
1,
12,
31
13,
33,
53,
58
56

2.01 2.22 2.30
631.21

2.00 3.46 3.55
794.89

1.7638 0.1854

0.3113 0.5743

0.3166 0.5742

0.4199 0.5175

0.0772 0.7813

4.7098 0.0309

5.7922 0.0169

12.1444 0.0005

10.7552 0.0011

4.9867 0.0264

1.9240 0.0119

1.6378 0.0467

4.2538 0.0000

1.5916 0.0556

1.5639 0.0626

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4. GARCH modeling and empirical findings The stochastic characteristics of the six major Latin American markets strongly suggest that their stock returns are not independent and identically distributed. As in the case of the evidence shown for other markets, returns should be conditionally heterokedastic; the expected market premium for risk must be related to the predictability of volatility of returns, as shown for the cases of the US market (Akgiray, 1989; French, Schwert, & Stambaugh, 1987), and for the case of emerging stock markets in the case of Greece (Koutmos, Negakis, & Panayiotis, 1993), and Taiwan and Korea (Chiang et al., 1996). Furthermore, evidence for an earlier period confirmed heterokedasticity for five South American stock markets (Ortiz and Soldevilla) and recently for the case of Mexico (Ortiz & Arjona, 2000). Thus, to confirm heterokedasticity first was necessary to determine the mean assuming a constant stationary variance over time. This procedure is appropriate to identify the most relevant lags. Most studies skip this step because they find adequate to model the time series behavior regressing returns in terms of its most recent lag, t
1. However, in the case of the Latin American markets, time dependency might extend itself beyond the first lag. Further because of the lack of sound and continuous information about their economies and markets, and because of instabilities derived from noneconomic facts, there is also the possibility of irregular lag significance. Table 3 summarizes our empirical findings concerning relevant lags. They were obtained beginning with a Box–Jenkins analysis and then following an iterative process to find the most relevant lags and regression.10 The best empirical results according to the statistics shown in Table 3 reveal important differences among the Latin American stock markets, regarding the importance of past information. In all cases, lag one is important, but then many others, quite separate and distant are important in the determination of current returns. This is most evident in the case of Argentina and Colombia where lags
85 and
75 seem to have some importance to determine current returns. The irregularity of the lags included in the regression is also astounding. With few exceptions (lags
8,
12,
24, and
52), they could be attributed to some cyclical behavior. Thus, each market has its own characteristics, and inversionists draw past information according to such behavior. Further studies are necessary in this respect to determine the characteristics of market information released in these markets (like dividend announcements, earnings announcements, etc.), which is probably the reason for the ‘‘irregular’’ importance of some lags in the regressions examined here. Although the regressions reported in Table 3 were the best in terms of the Durbin Watson statistic, Akaike Criterion, Shwarz Criterion, and Log Likelihood Function, autocorrelation and the lack of homoskedasticity was detected as hypothesized. The Breusch–Godfrey statistics shown in Table 3 confirm the presence of autocorrelation. Similarly, the ARCH-LM and White Heterokedasticity Tests (cross-terms) confirm the presence of heterokedasticity.

10

For this purpose, an algorithm under construction by Enrique Arjona was tested.

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Once heterokedasticity was confirmed, our research focused on determining the best (G)ARCH models applicable to the case. Although we tested conventional ARCH models, GARCH and E-GARCH-M models proved to be the best. In the GARCH model, the conditional variance of a time series is analyzed as a random process, which is a function of time dependent on the following set of information (Eq. (3)): Vt
1 ¼ et
j ; yt
j ;

j ¼ 1; 2 . . . 1

ð3Þ

where et
j represents past stochastic disturbances and yt
1 is a vector of variables containing information about the variables relevant to the model. Here, the difference between the conditional and unconditional variance of a time series is implicitly recognized. The first one is a function of random variables in a specific manner; the second one is assumed to be a constant.11 A GARCH structure for the series Yt can be formalized by the following set of equations (Bollerslev, 1986) (Eq. (4)):12 Yt j Vt
1  N ðXt0 ; b; ht Þ ht ¼ f ðet
1 ; et
2 ; . . . ; et
q ; ht
1 ; ht
2 ; . . . ; ht
p ; aÞ

ð4Þ

et ¼ Yt Xt0 ; b here Xt0 represents the vector of independent variables; the mean of Yt is assumed to be a linear function of k exogenous and endogenous lagged variables; ht is the conditional variance, which depends on past innovations, as well as its own lags; b and a are vectors of unknown parameters of the mean and conditional variance, respectively; q is the order of the autoregressive structure; and et are the errors of forecasted estimates. The innovations et follow a conditional normal distribution, N(0,s2) and adopt the following functional form (Eq. (5)): ht ¼ a0 þ a1 ðLÞe2t
1 þ a2 ðLÞht
1

ð5Þ

where a0 is a constant; a1(L) and a2(L) are polynomials in the lag operator L; and h represents the autoregressive part of the conditional variance. Intuitively, an increase in the uncertainty of forecasts made by the agents for period t is extended to the following periods.13 The random variable market returns from a stock market (Engle, 1983) has both an unconditional mean and an unconditional variance nonstochastic for each period of time. In order to carry out a simultaneous estimation of the conditional mean and variance, the 11 The models ARCH-M (Engle et al., 1987) are a generalization of the ARCH models where the variance is an argument of the conditional mean. 12 Engle (1995) presents an excellent compilation on major theoretical developments and applications of GARCH modeling. 13 et captures the level of information available to agents not contained in the fundamental variables.

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Table 4 Garch models of the Latin American emerging stock markets Parameters b0 b1 f GARCH -M Variance equation ARCH a0 a1 GARCH g1 g2 g3 EGARCH d1 d2 d3 l1 l2 l3 f1 f2 f3 Unconditional mean Unconditional S.D. Durbin – Watson Akaike Criterion Schwarz Criterion Log Likelihood Likelihood ratio Ljung – Box (6) Ljung – Box2 (6) Jarque – Bera ARCH-LM test F statistics Probability

Argentina GARCH(1,3) 0.7891*** (2.58)
0.8325*** (
16.20)

4.3979** (2.16) 0.3941*** (4.30)


0.264*** (3.79) 0.3997*** (5.88) 0.3471*** (2.88)

Brazil GARCH-M(2,2)
5.0868* (
1.92)
1.0115*** (16.72) 0.7795*** (2.10)

21.7979** * (3.76) 0.0355a (0.66) 0.121** (1.86) 1.0799*** (7.15)
0.6149*** (
4.520)

Chile GARCH-M(1,3) 4.8911*** (3.06)
0.7979*** (
13.12) 1.5808*** (
2.60)

1.0501*** (3.97) 0.0692** (2.19) 0.6792*** (6.90) 0.8422*** (10.17)
0.7349*** (
7.0510)

0.1058 8.2000 2.0900 3.6300 3.8700
685.63

0.1183 11.1200 1.9100 4.1300 4.3000
841.27


0.0074 3.8400 2.0900 2.1400 2.3300
541.66

4.4843 2.8122 0.9193

1.5500 2.6900 0.3282

0.7661 2.6575 3.4420

0.0712 0.7897

0.0272 0.8691

0.0052 0.9420

Ljung – Box (6) and Ljung – Box (6) square statistics follow a chi-square distribution with n degrees of freedom. a Indicates significance level above 10%. * Denote significance at the 10% level. ** Denote significance at the 5% level. *** Denote significance at the 1% level. () Indicate t-values.

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Table 4 (continued ) Colombia EGARCH(1,1) Mexico GARCH(1,2) 0.5013*** (3.90)
1.1635*** (
3.45) 0.5014*** (3.90)

2.3913*** (11.33)

0.6325*** (3.37)
0.7909*** (
12.19)

1.3443** (1.98) 0.1245*** (2.38)
0.0919* (
1.70)

Venezuela EGARCH-M(3,3) Venezuela GARCH(1,1) 3.3912*** (
4.33)
0.8194*** (
11.95) 0.7430*** (3.99)

0.1317* (0.31)

0.0980* (0.32)
0.7931*** (
10.55)

2.2208a (1.41) 0.1377*** (2.89) 0.7921*** (9.50)

0.8153*** (9.43)

0.8861*** (7.06) 1.0134*** (3.69) 0.1613a (1.01) 0.1072** (1.79) 0.2827*** (2.90) 0.1913*** (3.17)
1.2899*** (
27.22) 0.1087** (1.63) 0.4447*** (12.78) 0.0069
0.0308 5.6100 3.9100 2.1400 2.0400 2.8700 2.2100 3.0900 2.3400
640.47
620.86

0.3730*** (6.05) 0.3644*** (4.02) 0.0780a (1.11) 0.0551a (1.12) 0.0364a (0.39) (0.0230)a (
0.40)
0.9361*** (
22.87) 0.7982*** (26.52) 0.8885*** (26.52)
0.0057 7.6100 2.1100 3.5300 3.7700
768.12


0.0057 7.6100 2.100 3.500 3.8300
784.06

3.9000 2.2700 2.7062

3.3600 5.2800 1.8050

1.9100 3.6500 1.2282

3.9900 4.6500 33.3211

0.7217 0.3964

0.9102 0.3409

0.4739 0.4917

0.0022 0.9617

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following parametrization is adopted for the returns in the Latin American equity markets (Eq. (6)): tt ¼ tet þ et ht ¼ a0 þ a1 ðLÞe2t
1 þ a2 ðLÞht
1

ð6Þ

et  Nð0; ht Þ where t is the return in the stock market—logarithmic variations in the stock market index for each market; ht is the conditional variance of returns; and tte is the average return of each stock market during the period under analysis.14 The variance is affected by three factors: an autonomous component, unanticipated returns, and the conditional variance from previous periods.15 An important variant of the above model is the GARCH-in mean specification of GARCH-M (Engle, Lillien, & Robins, 1987). Here, the conditional variance enters into the regression function for the conditional mean. Thus, the model can be specified as (Eq. (7)): yt ¼ xt ðb; s2t Þ þ et ; s2t ¼ a þ AðL; gÞ þ BðL; dÞs2t ;

ð7Þ et  N ð0; 1Þ

Finally, in the exponential GARCH model (Nelson, 1991), known as EGARCH( p,q), the conditional volatility is an asymmetric function of past shocks and the estimated risk premium is insignificant [Eq. (8)]: et ¼ ut st ; lnst2 ¼ w þ

^ q P i¼1

14

ai ½fUt
1 þ gð=ut
1 =
E=ut
1 Þ þ

q P k¼1

bk lns2t
k

ð8Þ

In the mean equation, returns have been adjusted by the mean of each series. An alternative model to estimate the conditional variance has been proposed by Nelson (1990). He presents a GARCH exponential model (GARCHQ), which attempts to overcome limitations identified in conventional GARCH models. Three limitations can be specified: (1) empirical evidence (Black, 1976) shows that stock market returns are inversely related to market volatility. GARCH models only take into account the magnitude, not the sign of unanticipated returns for the expected volatility. In this case, volatility tends to increase with ‘‘bad news’’ (lower returns than expected), and volatility tends to decrease with ‘‘good news’’ (excess positive returns); (2) GARCH models impose the restriction of nonnegativity to the variance parameters; and (3) GARCH problems do not consider fully the problem of the persistency of shocks upon the conditional variance. 15

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It is an unrestricted ARMA( p,q) model, placing no restrictions on the ai and bk parameters. This ensures that st2 is nonnegative. Thus, if af < 0, then the variance tends to fall when et
1 > 0; if af>0, then the variance term tends to rise when et
1 < 0. The log maximizing function for this model is [Eq. (9)]: LðQÞ ¼

T X


logðsÞ þ log f ðet =st 1QÞ

ð9Þ

t¼1

The sui generis stochastic characteristics of the six major Latin American stock markets led to the application of different models in each case. As shown in Table 4, each country required a different model. For simplicity, only the coefficient of the first lagged variable is shown. Surprisingly, in all the six markets, the evidence shows that one lag return has an impact on current returns. The b1 coefficients are negative in all cases and significant at the .01 level. Similarly, with the exception of Venezuela for the EGARCH(3,3) model, the (G)ARCH coefficients are also significant. The Ljung–Box for the return and the squared residual series accept independence in all cases. Similarly, the Jarque–Bera statistic accepts normality for all cases except for the GARCH(1,1) model applied for Venezuela. Finally, the ARCH-LM tests reject heterokedasticity. Thus, the GARCH equations improve the regression results obtained assuming homoskedasticity, and are therefore better predictors of stock market performance for the Latin American capital markets. Further study, however, is necessary, the difficulties of modeling the Latin markets with GARCH models is well depicted with the Venezuelan case. Table 4 shows for this case two alternative models; A GARCH(1,1) model and a EGARCH-M(3,3) model. Results are mixed. In the simpler GARCH(1,1) model, the ARCH–GARCH coefficients are significant at the .01 level. However, the b0 is not significant and, according to the Jarque–Bera statistic, the residual homoskedasticity is rejected. On the other hand, in the more complex model EGARCH-M(3,3), both the b0 and Jarque–Bera statistic are significant. However, although the model rejects heterokedasticity, four coefficients of the EGARCH equation are not significant. In short, due to the explosive growth of the Latin American stock exchanges, returns do not follow a normal distribution and homoskedasticity is rejected. Due to the sui generis characteristic of each market, it is not possible to find a common model to determine mean returns and risk. In most cases, the G(ARCH) models and their extensions were appropriate and all coefficient statistical significant. Only in the case of Venezuela, the best two models found are not completely satisfactory.

5. Conclusion The six major Latin American markets analyzed in this study experienced an explosive growth during the end of the 1980s and beginning of the 1990s. This growth reflects in the stochastic characteristic of this market. Dollar returns were consistently lower than local monthly returns during the 1989–1994 period. The standard deviation of the dollar returns

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was also generally higher than volatility measured in local currency. Major stochastic characteristics of the Latin American stock markets also revealed time dependency of returns, heterokedasticity, and lack of a normal distribution. Returns of this market during the period under analysis were asymmetric both in dollar and local currency terms. Both right skewed and left skewed patterns were discerned. In all cases, the distributions were leptokurtic. Assuming constant variance, the AR processes revealed the importance of several lags in addition to t
1. These lags were irregular, and, in some cases, distant; perhaps, revealing the lack of continuous and reliable information about economic activity and stock market activity in these markets. It probably also reveals irregular patterns of market information releases, because no significant cyclical patterns were found out. Due to the intrinsic characteristics of these markets, not a single (G)ARCH model was found to depict market activity from the six Latin American stock markets. A different model had to be applied in each case. The best models seem adequate and, according to several statistical tests, the models reject autocorrelation, the distribution of the residuals is normal (with the exception of one case), the series are integrated, and heterokedasticity is rejected. The presence of heterokedasticity and autocorrelation clearly suggests the existence of market inefficiencies in the Latin American stock exchanges, which reflects in high volatility. These markets became therefore very sensitive to poor macro policymaking, capital reversals, speculative attacks, and the behavior of international capital markets, with which they have established increasing investment ties. It is therefore not surprising that these markets during the mid- and late-1990s increased sharply their volatility and experienced severe downfalls, triggered mainly by domestic macroeconomic disequilibria, manifested particularly by severe balance of payments deficit and extreme fragility of the banking system due to adverse selection and moral hazard problems derived from poor planned liberalization policies, coupled with excessive government guarantees to baking deposits16; indeed, these disequilibria have frequently led to severe currency crisis and banking crisis, identified as ‘‘twin crisis’’ at the developing countries (Kaminsky & Reinhart, 1999). Furthermore, in this highly unstable environment, it is not surprising either that the Latin American stock exchanges, and those from other developing countries, would also become important mechanisms for transmission of the crisis to all sectors of the economy (Alford, 1995; Cabello, 1999; Ortiz, 2000a), generating with their negative behavior a ‘‘triplet crisis’’ (Ortiz, 2000b). Five lessons can be drawn from the volatile behavior of the Latin American stock markets: (1) liberalization policies must be well planned and implemented in their magnitude, quality, and sequencing; (2) the growth and internationalization of the Latin American stock markets show their high potential to become an effective mechanism to promote corporate and economic development; further, well though reforms are necessary to increase their efficiency, liquidity, credibility, and stability; (3) the availability of information, and limited 16

Aggarwal, Inclan, and Leal (1999) recently proved that acute changes in volatility at 14 international markets, including 10 emerging markets, were caused mainly by local events, during the period May 1985 – April 1995. They use an iterative cumulative sum of squares (ICSS) algorithm to identify the time period when shifts in volatility occur.

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state intervention should be further promoted to avoid asymmetric information and related problems of adverse selection and moral hazard at financial markets and financial institutions; (4) policies for prudential banking and financial institutions regulation should be enhanced; (5) government discipline is paramount to achieve stable economic growth and create a favorable real and financial investment environment.

Acknowledgments We thank Profs. Ephraim Clark, Vincent Dropsy, and Miguel Angel Mendoza for their helpful and constructive comments. The authors also benefited from research support provided by Programa de Apoyo a Proyectos de Investigacio´n e Innovacio´n Tecnolo´gica (PAPPIT) from Direccion General de Asuntos del Personal Academico from Universidad Nacional Auto´noma, ade Me´xico, Project IN 312-798.

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