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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 infor- mation 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 fol- lows 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 mar- kets. 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 mar- ket 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 c o "^^^ "^^r ^fci ^ *^ ^^1^ ^^ir ' <N»c4 in (2l CO T- in CO g ii cotBojcscBcscocdcocococo^- cocoeo^ ^5CM {CM CO c ll *Meoco h "*'-T-O CM tn 1 ^ cM<OT-r>- CO I o> CO in G) t- (/) o o o V CO m in o CO CM 1- CM T- CM CM T- Q. 2 w CO co •a <D b ° I c o 5 TJ CD .ffl O CO O) CM If) in N CM CM (O m CO co cDn h* CD CO "^ O y- O) CO o» T- T- in CM c I g CG i o O) D. C N •= o cococoinmK** CM o cococoocMcooooNO)'»-c\jo>'«OCMCOT>-C00in(0- CO CO CO CB 1 O =) CO CO s. UJ ^ 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 exam- ining 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.
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