Variance Ratio Tests of the Random Walk Hypothesis for European

The European Journal of Finance 9, 290-300 (June 2003)

Variance ratio tests of the random walk hypothesis for European emerging stock markets GRAHAM SMITH* and HYUN-JUNG RYOO Department of Economics, School of Oriental & African Studies, University of London, Thornhaugh Street, Russell Square, London WC1H0XG, UK '[email protected]

The hypothesis that stock market price indices follow a random walk is tested for five European emerging markets, Greece, Hungary, Poland, Portugal and Turkey, using the multiple variance ratio test. In four of the markets, the random walk hypothesis is rejected because of autocorrelation in returns. For the Istanbul market, which had markedly higher turnover than the other markets in the 1990s, the stock price index follows a random walk. This contrasts with the results of earlier research, carried out for periods of lower turnover, which rejected the random walk hypothesis. Keywords: emerging markets, random walk hypothesis, stock prices, variance ratio tests

1. INTRODUCTION Equity markets play a central role in the pricing and allocation of capital and the pricing of risk and their efficiency can be assessed by examining the behaviour of equity prices. In markets that are weak-form efficient, equity prices completely reflect all of the information contained in the past history of prices and do not convey information about future changes in prices. If they did convey such information there would be profit-making opportunities for Investors and so markets would be imperfect. A widely used test of weak-form efficiency is to see whether equity prices follow a random walk - a test that can be used with individual equities or with stock price indices. Although there has been extensive research on the weak-form efficiency of stock markets, much of this has focused on developed markets. In emerging markets, the random walk hypothesis has been tested for Korea (Ayadi and Pyun, 1994), eight Asian markets (Huang, 1995) and four Latin American markets (Urrutia, 1995). There is very little work which has tested the random walk hypothesis for Euro- pean emerging stock markets. Those tests of the hypothesis that have been carried out consider the behaviour of either the prices of individual equities or aggregate stock price indices. Muradoglu and Unal (1994) used daily data for a sample of 20 stocks traded on the Istanbul Stock Exchange over the period from the beginning of 1988 until the end of 1991 and carried out tests of independence, randomness

The European Journal of Finance ISSN 1351-847X print/ISSN 1466-4364 online © 2003 Taylor & Francis Ltd http://www.tandf.co.uk/journals DO!: 10.1080/1351847021000025777 Tests of random walk hypothesis for European emerging niarkets 291 and normality and found equity prices did not follow a random v^ralk. Dockery and Kavussanos (1996) used monthly data on the closing prices of 73 equities quoted on the Athens stock market from February 1988 to October 1994 and rejected the random walk hypothesis. Dockery and Vergari (1997) employed variance ratio tests with weekly data from January 1991 until May 1995 on the Budapest Stock Exchange share price index. The hypothesis that the logarithm of the index follows a homoscedastic random walk was rejected but the heteroscedastic random walk null hypothesis was not rejected. In summary, the available evidence sug- gests that the random walk hypothesis is not rejected for the Hungarian stock market but is rejected for the Athens and Istanbul markets. This study employs the multiple variance ratio tests of Chow and Denning (1993) to test the random walk hypothesis for a sample of five European emerging markets. We use stock price indices for all of the markets for which data of an adequate time span and frequency are available: Hungary, Poland, Portugal, Greece and Turkey. This is the first paper to employ these tests, which control test size for multiple comparisons, for European emerging markets.

2= THE EQUJTY MARKETS Ihh rumber f.sf European emerging markets has grown rapidly. A small number of stock markets with roots in the 18th and 19th centuries were re-established or reorgaaized In the 1980s or early 1990s as new capital market structures were intro- duced through legi.siative changes. Also, several new exchanges were opened. In 1991 there were six, and by the end of 1997 there were 18 organized emerging mar- kers (see Tabie 1). With the exception of Russia, the markets are generally small. As a group, at the end of 1997 they accounted for 1.4% of world stock market cap- iiaiizclkin, 5,4% of European market capitalization and 14.3% of emerging stock market capitalization. However, they accounted for only 5.4% of emerging market turno/er by vaSue, 3.6% of European turnover and 0.7% of world turnover. The liquidity of individaal markets varies considerably. Not surprisingly, the newer ma^'kets are trequently the least liquid. However, eight of the 18 markets had 1997 Dqiiicity ratios above the global median of 35%. Against this general background, three i;ype.s of market can be identified: (•; Russia vvhicri has approximately 60 authorized stock and commodity exchanges. Trading began in 1990 and in the mid-1990s market growth was rapid. In 1997, the number of traded stocks almost doubled and Russia was the be.st performing emerging market in the world in that year. At the end of •997, it ranked 21st in the world by capitalization. Unfortunately, however, )x vvas the worst-performing emerging market in the following year. The market Sacks liquidity. A third of all equities are often not traded for periods of day.s and sonietimcs even weeks. In 1995 the turnover ratio was 2.5% and in 1997 19A%, placing it 53rd in the world ranking by turnover. (i;) A group of .?ix medium-size markets originally established before the 20th century although they may not have traded continuously: the Czech Republic, Greece, Hungary, Poland, Portugal and Turkey. (:i\) A group oi eleven small, new markets: Armenia, Bulgaria, Croatia, Cyprus, F.stonia, Latvia., Lithuania, Romania, Slovakia, Slovenia and the Ukraine. n$ 07 ctj CCCO o 2 COMCT CO Z CO

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^ Tests of random walk hypothesis for European emerging markets 293 Table 2. Markets included in the study Turnover US$ avg. Weight in IFCG annual growth rate Composite Index % 1991-1997^ 1997 Hungary 26.4 1.14 Poland 86.4 0.63 Portugal 26.2 2.52 Greece 37.7 1.66 Turkey 34.2 3.43 ^Calculated using OLS. Source: international Finance Corporation (1998).

In this study, five of the six medium-size markets are examined: Greece, Hungary, Poland, Portugal and Turkey.' An adequate time span of data is not yet available for the Cxech Republic. All of the markets examined are included in the IFC's Global (IFCG) Composite index and have experienced rapid increases in turnover during the 1990s (.see Table 2).

3. METH0D0L0C3Y: MULTIPLE VARIANCE RATIO TESTS Variance ratio tests have been widely used and are particularly useful for examining the behaviour of stock price indices in which returns are frequently not normally distributed. These tests are based on the variance of returns and have good size and power properties against interesting alternative hypotheses and in these respects are superior to many other tests (Campbell et at., 1997). Sup- pose s, is the natural logarithm of a stock price index and consider the following random walk with drift process

S, = Si.,, + 11+^1 (1) or

r. S5 AS( = fi, + e, (2) in which p, is an arbitrary drift parameter, r, is continuously compounded returns and €,• is a random disturbance term. The {e^} satisfy E[6f] = 0 and E[ef €,-g] = 0, g 7^ 0, for al! f. This hypothesis does not necessarily imply that returns are either normally or identically distributed. Lo and MacKinlay (1988,1989) provide tests of the random walk null hypothesis under the alternative assumptions of homoscedastic and heteroscedastic disturbances. Variance ratio tests focus on the property that under a random walk with uncor- related increments in s,, the variance of these increments increases linearly in the observation interval,

Var(s, - Sf_^.) = q Var(s, - Sf^j) (3)

' Further information about these markets is avaiiabie on request from the corresponding author. 294 G. Smith and H-J. Ryoo in which q is any positive integer. The variance ratio is given by (,W) ^ Var(s, - s,_i) a2(l) where Rdq) is aq period continuously compounded return Rtiq) = rt + rt-i + --- + r,_,+i - St - St-q (5) and under the null hypothesis VR(<7)=1. Lo and MacKinlay (1988) generate the asymptotic distribution of the esti- mated variance ratios and provide two test statistics, ZQij) and Z*{q), both of which have asymptotic standard normal distributions under the null hypothesis. Z(g) is derived under the assumption that the disturbances of Equation 1 are homoscedastic; Z*{q) treats them as heteroscedastic.^ This latter test statistic is not only sensitive to correlated changes in stock prices, but also robust to many genera! forms of heteroscedasticity and nonnormality and so is particularly useful with stock returns because often they are not normally distributed. Early work has tested individual variance ratios for a specific aggregation Inter- val, q. The random walk hypothesis, however, requires that VR(q) = I V q. Chow and Denning (1993) show how controlling test size facilitates the multiple variance ratio (MVR) test. For a single variance ratio test, under the null hypothesis MAq)=yR{q)-l = O (6) We consider a set of m tests {Mr{qi)\i = 1, 2,..., m} associated with the set of aggregation intervals {qi\i = 1, 2,..., m}. Under the random walk null hypothesis there are multiple sub-hypotheses Hoi:Mr((7,)==O for /=1,2, ...,m Hii: Mriqt) ^0 for any / = 1, 2,..., m (7) Rejection of any one or more Hoi rejects the random walk null hypothesis. Consider a set of Lo and MacKinlay test statistics {Z(qi)\i — 1,2,..., m}. Since the random walk hypothesis is rejected if any one of the VR((7,) is significantly different from one, we need only consider the maximum absolute value in the set of test statistics. The core of Chow and Denning's MVR test is based on Hochberg (1974) PR{max(|Z((7i)!,..., |Z(g^)i) < SMM(a; m:N)]>l-a (8) in which SMM(a; m; N) is the upper a point of the Studentized Maximum Modulus (SMM) distribution with parameters m and A^ (sample size) degrees of freedom. Critical values are provided by Miller (1981). Asymptotically, oo SMM(a: m; N) = Z^y2 (9) where Zu+/2 is standard normal with a+ = 1 — (1 — a) ^ Mixing and moment conditions are used to derive the heteroscedasticity-consistent variance ratio estimate (Lo and MacKinlay, 1988, pp. 48-49). Tests of random walk hypothesis for European emerging markets 295 With our sample size, we can make use of this last result and so use the standard normal distribution to calculate the critical values. The size of the MVR test is controlled for muitipie comparisons by comiparing the calculated values of the standardized test statistics, either Z(g,) or Z*(<7,), with the SMM critical values. If the maximum absolute value of, say, Z*{qi) is greater than the critical value at a predetermined significance level then the random walk hypothesis is rejected.

4. THE DATA AND THEIR PROPERTIES Our data are weekly beginning in the third week of April 1991 and ending in the last week af August 1998 (385 observations). They refer to Wednesdciys to minimize day oi-the week effects. The start of the period was determined by the availability ot 5i'3 index for Poland. For Greece we use the Athens Stock Exchange General Index wh:.ch covers approximately 75 companies and 76% of both stock market capitaiizatior) and turnover. The Budapest Stock Index (the BUX) is used for Hun- gary and comprises the 24 most liquid equities in the market. For Poland, the Warsaw Gener.2l Index (WIG) is used. This includes the shares of all companies Us Led on the main market. For Portugal, we use the Banco Totta & Azores (BT&A) Sha; e index. This consists of the share prices of approximately one-third of listed companies including those most heavily traded but excluding those with abnor- ma.l price variations. The Istanbul Stock Exchange National-100 Index is used for Turl:ey, This comprises stocks from the top 75% of companies by both market value and average daily traded value. The source of all data is Datastream. All indices are m focal currency and have market value weights. Table 3 reports descriptive statistics of weekly returns for the five European emerging markets and, for comparative purposes, the large developed markets of Lj^e UK aiid the USA. For the latter two markets we use the Fif-All Share and S'fa.:i;dard and Poors' Composite indices respectively. Average stock returns are po.?ltive for al! markets; the Istanbul market has the largest average weekly returns, Athens has the smallest. The summary statistics confirm that weekly returns in tt^ese ^'jjropean emerging markets are similar to those in the large developed market.? in that they are not normally distributed. Weekly returns are leptokurtic, that is, more sharp]y peaked about the mean than the normal distribution. Returns on the Warsaw stock exchange are negatively skewed; for all other emerging markets thfHy are positively skewed. Returns in larger European markets show similar departures fvorn norniality (Aparicio and Estrada, 2001).

5. RESULTS Table 4 reports the results of variance ratio tests on the logarithms of our eight stock price Indices for sampling intervals of 2,4, 8 and 16 weeks. For each interval, we report, the estimate of the variance ratio, VR(g), and the test statistics for i:he null, hypotheses of homoscedastic, Z{q), and heteroscedastic, Z*{q), increments random walks. Using the multiple variance ratio procedure, we focus on the maximum absolute value of the test statistics. With our sample sizes and CO CO CO CM 00 2 01 6 CO o o d CO CC) 1 1

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For four markets, Greece, Hungary, Poland, and Portugal, the results follow a similar pattern The hypothesis that the logarithm of the stock market price index tollov E a homoscedastic random walk is rejected. In principle, the rejection of this hypothesis could result from either heteroscedasticity or autocorrelation in the stock price index. In all four of these markets, however, the hypothesis of a heteroscedastic random walk Is also rejected. Therefore, autocorrelation of weekly increments in the natural logarithm of the stock market price indices results In the random walk hypothesis being rejected for all four of these markets ;.,o and MacKinlay (1988) show that for q = 2, estimates of the variance ratio

6. CONCLUSIONS This paper uses multiple variance ratio tests to examine the random walk hypothesis for five medium-size European emerging stock markets. In four of the markets, Greece, Hungary, Poland and Portugal, the hypothesis is rejected because returns have autocorrelated errors. In Turkey, however, the Istanbul stock market follows a random walk. Factors which may affect whether or not a stock market follows a random walk are discussed and liquidity is found to be important. Liquidity is much greater on the Istanbul market than in any of the o CO m in o CM

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