Testing the Random Walk Behavior and Efficiency of the Gulf Stock Markets

Transcription

1 The Financial Review 37 (2002) Testing the Random Walk Behavior and Efficiency of the Gulf Stock Markets Abraham Abraham King Fahd University of Petroleum & Minerals Fazal J. Seyyed King Fahd University of Petroleum & Minerals Sulaiman A. Alsakran King Fahd University of Petroleum & Minerals Abstract Inferences drawn from tests of market efficiency are rendered imprecise in the presence of infrequent trading. As the observed index in thinly traded markets may not represent the true underlying index value, there is a systematic bias toward rejecting the efficient market hypothesis. For the three emerging Gulf markets examined in this paper, correction for infrequent trading significantly alters the results of market efficiency and random walk tests. The Beveridge- Nelson (1981) decomposition of index returns is done to estimate the underlying index. Keywords: infrequent trading, random walk, market efficiency, emerging markets, Gulf equity markets JEL Classifications: G12/G14/G22 Corresponding author: Department of Finance and Economics, King Fahd University of Petroleum & Minerals, P. O. Box 1181, Dhahran 31261, Saudi Arabia; Phone: ; Fax: ; seyyed@kfupm.edu.sa Abraham Abraham and Sulaiman Alsakran acknowledge financial support from King Fahd University of Petroleum & Minerals under project grant no. FIN/EQITY/219. Fazal J. Seyyed is grateful for financial support provided by King Fahd University of Petroleum & Minerals. The authors would also like to thank anonymous referees for their insightful comments and suggestions. 469

2 470 A. Abraham et al./the Financial Review 37 (2002) Introduction Efficient market theory and the random walk model have been at the center stage of debate in financial literature for several decades. The implications of market efficiency for investors, investment strategies, funds management, financial markets, and the economy are profound indeed and deserve the interest they have generated. A survey of efficient market studies by Fama (1970) provides overwhelming evidence to support an efficient market hypothesis for U.S. stock markets. In recent years, however, numerous departures from market efficiency in the form of anomalies have attracted attention of academics and practitioners alike. Evidence against the random walk hypothesis (RWH) for stock returns in the developed capital markets are reported by Fama and French (1988) and Lo and MacKinlay (1988), among others. Fama (1998) maintains that most return anomalies in the major stock markets are chance results that tend to disappear in the long term with a reasonable change in methodology, hence supporting the view that mature capital markets are generally efficient. The increasing globalization of the financial markets has heightened interest in emerging markets. Several studies have focused on predictability of return in the less mature emerging markets. Urrutia (1995), using the variance ratio test, rejects the RWH for the Latin American emerging equity markets of Argentina, Brazil, Chile, and Mexico, whereas the runs test indicates weak form efficiency. In contrast, Ojah and Karemera (1999) find that the Latin American equity returns follow a random walk and are generally weak-form efficient. Grieb and Reyes (1999) reexamine the random walk properties of stocks traded in Brazil and Mexico using the variance ratio tests and conclude that index returns in Mexico exhibit mean reversion and a tendency toward random walk in Brazil. These conflicting inferences possibly could be attributed to the effect of cross-sectional and temporal variations in the degree of infrequent trading in these emerging markets. This paper examines the random walk properties and weak form efficiency of three major Gulf stock markets Kuwait, Saudi Arabia, and Bahrain using the variance ratio test and the runs test for the period 1992 to A major difficulty in interpreting the results from tests on thinly traded markets is the confounding effect of infrequent trading on the observed index. Thus rejection of the RWH or the efficient markets hypothesis could simply be a result of having used the observed index an imprecise estimate of the true value of the index in the presence of nonsynchronous trading. Infrequent trading is widespread in most emerging markets and is particularly so in the case of the markets under examination here. A number of different approaches have been suggested to correct for infrequent trading. Stoll and Whaley (1990) use the residuals from an ARMA(p, q) regression as a proxy for the true index, whereas Bassett, France, and Pliska (1991) propose the use of a Kalman filter to estimate the distribution of the true index. In this paper, we employ a modified version of the Stoll and Whaley approach suggested by Jokivuolle (1995) to estimate the true unobservable index from the history of the observed index. The correction consists of decomposing the log of the observed index into its random and stationary components

3 A. Abraham et al./the Financial Review 37 (2002) using the Beveridge and Nelson (1981) methodology, in which the random component can be shown to equal the log of the true index. Separating the effects of infrequent trading allows us to draw definitive conclusions regarding market efficiency and random walks. For all three markets studied in this paper, the apparent weak form inefficiency observed can be attributed almost entirely to infrequent trading and disappears when one uses the estimated true index corrected for infrequent trading. For two of the three markets examined, the RWH cannot be rejected, and the departure from RWH is markedly attenuated for the third when the corrected indices are used in lieu of the observed indices. Butler and Malikah (1992) used serial correlation and runs tests to evaluate the weak form efficiency of the stock markets in Saudi Arabia and Kuwait. Their results indicate significant departure from random walk for the Saudi stocks and less pronounced but significant autocorrelations for many Kuwaiti stocks similar to other thinly traded markets. Al-Loughani (1995), using more robust statistical techniques on the Kuwait market index, concludes that the series exhibit stationarity but not random walk. The remainder of this paper proceeds as follows. Section 2 provides an overview of the Gulf stock markets. Analytical details of the Beveridge and Nelson decomposition to estimate the true index and the test methodologies for assessing the RWH and weak form efficiency are described in Section 3. Section 4 identifies the data sources, presents the empirical results, and contrasts the findings between the observed and the corrected indices. Section 5 concludes. 2. Overview of the Gulf equity markets The financial markets in the Gulf region are dominated by commercial banks. Stock markets are relatively small in terms of market capitalization, listed companies are few, most securities are infrequently traded, and trading volume is low. In addition, access to the Gulf markets for direct investment in equities, until recently, was only permitted to its nationals, with limited access to nationals from other states in the Gulf Cooperation Council (GCC). Increasing capital requirements to fund budget deficits and economic development has encouraged the regional states to launch capital market liberalization and broad-ranging structural reforms, allowing foreign investors greater access to the financial markets. In recognition of the growing importance of these markets, the IFC (International Finance Corporation) has recently included the equity indices of both Bahrain and Saudi Arabia in its emerging market database. The Saudi stock market, with 74 listed companies, is the largest stock market based on market capitalization ($43 billion in 1998) in the Gulf region. Trading in shares takes place over the counter through banks and is facilitated by an electronic trading system. Compared to other emerging markets, the overall share turnover ratio is low. Accessibility to foreign investors is very restrictive. Only recently, non-saudi investors have been allowed to invest indirectly through the purchase of mutual fund

4 472 A. Abraham et al./the Financial Review 37 (2002) shares. The Kuwait Stock Exchange is a centralized auction market, with 75 listed companies and a market capitalization of $18.5 billion in The market suffered a major setback as a result of the Gulf War in 1990, leading to a suspension of trading. It reopened for trading in September The Bahrain Stock Exchange has 42 listed companies, with a market capitalization of $7 billion in Electronic trading takes place on the exchange floor facilitated by the newly established clearing and settlement house. New legislation allows GCC investors an unrestricted stake, and non-gcc foreign investors up to a 49% stake, in listed companies. Although small by international standards, the Bahrain Stock Exchange is positioning itself to be a major player in the Gulf financial markets. 3. Methodology 3.1. Variance ratio test for random walk A consequence of informational efficiency is that asset returns should manifest properties of a random walk. An important property of the random walk process is that the variance of the increments to the random walk process linearly increases with the sampling interval. Lo and MacKinlay (1988) proposed a simple specification test for evaluating the random walk properties of asset prices. Specifically, if X t is a pure random walk, the ratio of the variance of the qth difference scaled by q to the variance of the first difference must approach unity. The variance ratio VR(q) is defined as: VR(q) = σ 2 (q) (1) σ 2 (1) where σ 2 (q)is1/q the variance of the q-differences and σ 2 (1) is the variance of the first differences. where: and where: σ 2 (q) = 1 m σ 2 (1) = nq i=q (X i X i q q ˆµ) 2 (2) ( m = q(nq q + 1) 1 q ) nq 1 (nq 1) nq i=1 (X i X i 1 ˆµ) 2 (3) ˆµ = 1 nq (X nq X 0 ) They develop test statistics both for homoscedastic and heteroscedastic increments. Because it is the heteroscedasticity in the data that is of interest, we use the more

5 A. Abraham et al./the Financial Review 37 (2002) robust heteroscedastic test statistic that uses overlapping intervals. The test statistic is: z (q) = VR(q) 1 N(0, 1) (4) [φ 1/2 (q)] where: q 1 [ ] 2(q j) φ (q) = 2ˆδ( j) q and ˆδ( j) = nq 3.2. Nonparametric runs test j=1 i= j+1 (X i X i 1 ˆµ) 2 (X i j X i j 1 ˆµ) nq i=1 [(X i X i 1 ˆµ) 2 ] 2 Yet another issue of interest in security markets is the informational efficiency or predictability of prices based on a given information set. Empirical work in this area has proceeded along a number of different lines, including the use of different information sets as predictors, examination of short-term versus long-term horizons, and the documentation of seasonal patterns that are inconsistent with established asset pricing models. The cumulative evidence on whether markets are efficient is rather mixed. Overall, however, weak form efficiency has held up as a reasonable working hypothesis. The runs test determines whether successive price changes are independent. Unlike its parametric equivalent, the serial correlation test of independence, the runs test does not require returns to be normally distributed. A run is a sequence of successive price changes with the same sign. If the return series exhibit greater tendency of change in one direction, the average run will be longer and the number of runs fewer than that generated by a random process. To assign equal weight to each change and to consider only the direction of consecutive changes, each change in return was classified as positive (+), negative ( ), or no change (0). The runs test can also be designed to count the direction of change from any base; for instance, a positive change could be one in which the return is greater than the sample mean, a negative change one in which the return is less than the mean, and zero change representing a change equal to the mean. The actual runs (R) are then counted and compared to the expected number of runs (m) under the assumption of independence as given in Equation (5) below, [ N(N + 1) 3 ] i=1 m = n2 i (5) N where N is the total number of return observations and n i is a count of price change in each category. For a large number of observations (N > 30), m approximately corresponds to a normal distribution with a standard error (σ m ) of runs as specified 2

6 474 A. Abraham et al./the Financial Review 37 (2002) in Equation (6). [ 3 σ m = ni 2 i=1 { } 3 ni 2 + N (N + 1) 2N i=1 3 i=1 n 3 i N 3 ] 1 2 The standard normal Z-statistic (Z = (R m)/σ m ) can be used to test whether the actual number of runs is consistent with the independence hypothesis. When actual number of runs exceed (fall below) the expected runs, a positive (negative) Z value is obtained. Positive (negative) Z value indicates negative (positive) serial correlation in the return series. (6) 3.3. Estimating the true index correcting for infrequent trading To separate the effects of infrequent trading, we apply a correction to the observed index by using a methodology that employs the Beveridge and Nelson (1981) decomposition of the index into its permanent and cyclical component. If we denote by X o t the log of the true unobservable index corresponding to Xt o, the log of the observed index, it can be shown that the permanent component of the log of the observed index equals the log of the true unobserved index. See Jokivuolle (1995) for a proof of this proposition. The notation follows Jokivuolle (1995). Specifically, the permanent component of the Beveridge and Nelson decomposition of an infinite order MA process 1 can be written as: X o t = X o t + Lim T [ T t ] Rt o ( j) (T t)µ, j=1 where ˆR o t ( j) is the optimal forecast of ˆR o t+ j made at time t, and µ is the slope of the ARMA process. Again following the notation in Jokivuolle (1995), letting yt o = ˆR o t µ, the permanent component can be written as: [ ] T t X o t = X t o + Lim ŷt o ( j) (7) T The decomposition can be implemented by using an algorithm provided by Newbold (1990) to evaluate the second term on the right-hand side. [ ] T t q p p ŷt o ( j) = ŷt o ( j) + (1 φ 1 φ p ) 1 φ 1 ŷt o (q j + 1) Lim T j=1 j=1 j=1 ŷ o t (i) = yo t+i i 0 j=1 i= j (8) 1 It is well known that any ARMA(p, q) process can be represented as an infinite order MA process.

7 A. Abraham et al./the Financial Review 37 (2002) Table 1 Summary statistics of Gulf stock markets weekly index returns (%) Saudi Arabia, Kuwait, and Bahrain, October 7, 1992, to December 30, 1998 Weekly returns are computed as R t = 100 ln( Pt P t 1 ). Saudi Arabia Kuwait Bahrain Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability Observations Number of observations differ because individual indices have missing observations corresponding to religious holidays. where p and q represent the order of the ARMA(p, q) process followed by the log of the observed index. 4. Data and Results 4.1. Data The data consist of weekly index values for the three major Gulf stock markets of Kuwait, Saudi Arabia, and Bahrain for the period October 1992 to December All indices used are value-weighted. The Kuwaiti data were provided by the Kuwait Investment Agency, a government organization overseeing the stock market; the Saudi Arabian data were obtained from SAMA (the Saudi Arabian Monetary Authority); and the Bahraini data were from the Financial Analysis Unit of the Bahrain Stock Exchange. Summary statistics for each of the markets considered are provided in Table 1. For the time period considered, the Saudi stock market experienced negative returns in contrast to the positive return in the other markets. All three markets exhibit significant deviations from normality as seen from the reported Jarque-Bera test statistic Results In this section we provide the results of our empirical analysis of the three Gulf equity markets. The results are presented in three parts. In the first part, details are provided for the indices corrected for infrequent trading using the Beveridge and Nelson (1981) methodology described in the previous section. In part two, the variance ratio test for the RWH for each of the markets is carried out and comparisons

8 476 A. Abraham et al./the Financial Review 37 (2002) Table 2 Estimated ARMA coefficients for Saudi Arabia, Kuwait, and Bahrain Index returns, October 7, 1992, to December 30, 1998 The Saudi Arabian and Kuwaiti Indices are modeled as: Rt o = µ + θεt 1 o + εo t, whereas the Bahraini Index is modeled as: Rt o = µ + φ Rt 1 o + θεo t 1 + εo t where Rt o is the log relative of the observed index levels. Coefficient (Standard Error) µ θ φ Saudi Arabia [MA(1)] (0.0013) (0.0545) Kuwait [MA(1)] (0.0011) (0.0551) Bahrain [ARMA(1, 1)] (0.0016) (0.0720) (0.1002) Indicates statistical significance at the 0.01 level. Indicates statistical significance at the 0.05 level. are made between the observed and the corrected true index. A nonparametric runs test is explained and the efficient markets hypothesis assessed in the context of infrequent trading in part three Estimating the true index The first step in the decomposition procedure lies in identifying the underlying process for each of the observed log relatives. Sample autocorrelations and partial autocorrelations of the log relatives were examined. The Saudi and Kuwaiti Indices exhibit a single significant spike in their autocorrelation at a one-week lag, with no additional lags that are economically meaningful. This supports the choice of a MA(1) process for Saudi Arabia and Kuwait. The Bahraini Index shows a slow decay in the autocorrelation coefficients indicative of a mixed ARMA process. Given that we are working with weekly data, an ARMA(1, 1) specification is taken as an economically meaningful representation for Bahrain. Thus for Saudi Arabia and Kuwait the observed index returns are represented as Rt o = µ + θεt 1 o + εo t, whereas for Bahrain we have Rt o = µ + φ Rt 1 o + θεo t 1 + εo t, where Ro t represents the log relative in the index level and µ the slope of the ARMA process. Estimated ARMA coefficients for each of the markets are reported in Table 2 and are highly significant. The corrected indices using Equation (8) from the previous section are generated as X o t + θε o t for Saudi Arabia and Kuwait and X o t φ ( µφ + φ Ro t + θε o t ) for Bahrain. A summary of descriptive statistics for the observed and the corrected indices is provided in the appendix Variance ratio test The RWH for each of the markets is tested using the variance ratio test described in Section 3. The variance ratio is computed for multiples of 2, 4, 8, and 16 weeks, with the one-week return used as the base. Results for the observed and the corrected indices are shown in Panels A and B of Table 3, respectively.

9 A. Abraham et al./the Financial Review 37 (2002) Table 3 Variance ratio estimates and heteroscedastic test statistics for the Gulf stock markets, Saudi Arabia, Kuwait, and Bahrain, October 7, 1992, to December 30, 1998 The variance ratios are defined as the ratio of (1/q)σq 2 to σ 1 2 for values of q = 2, 4, 8, and 16, where σ 2 i is the variance of the index return defined as ln(p t /P t i ). The heteroscedastic consistent test statistic is reported in parentheses. Panel B shows the results for the index, corrected for infrequent trading. Number of Weeks Market Panel A: Log relatives of the observed index levels Saudi Arabia (6.973) (6.096) (6.030) (5.869) Kuwait (2.879) (3.603) (5.752) (5.492) Bahrain (5.970) (10.558) (14.770) (17.422) Panel B: Log relatives of the corrected index levels Saudi Arabia ( 0.018) (1.461) (1.079) (1.747) Kuwait ( 0.630) (2.564) (3.006) (3.236) Bahrain ( 0.356) (0.111) (0.628) (1.272) Indicates rejection of the RWH at the 0.01 level. Indicates rejection of the RWH at the 0.05 level. When the observed indices are used, the RWH is strongly rejected for all three Gulf markets; the variance ratio increases with the aggregation interval for all three stock markets. In contrast, when the corrected indices are used, the RWH cannot be rejected for the Bahraini and Saudi markets. The RWH is rejected for the Kuwaiti market even after correcting for infrequent trading. It should be noted, however, that the departure from the null value of unity for the variance ratio is less pronounced even for Kuwait, once the index level is corrected for infrequent trading. Rebuilding after a protracted closure of two years following the Gulf war could to some extent explain Kuwait s persistent departure from the RWH for the sample period Runs test for weak form efficiency In this section we report results of weak form efficiency using the nonparametric runs test. Because the return data for the Gulf markets do not conform to the normal distribution (the Jarque-Bera test statistic is reported in Table 1), the runs test was considered more appropriate than a parametric serial correlation test. The skewness and kurtosis statistic for the Gulf markets indicate positive skewness of returns, which are significantly more peaked than a standard normal distribution. To test for the weak form efficiency, we examine in this section the independence of price changes using

10 478 A. Abraham et al./the Financial Review 37 (2002) Table 4 Results of runs test for the Gulf stock markets, observed vs. corrected index levels, Saudi Arabia, Kuwait, and Bahrain, October 7, 1992, to December 30, 1998 The runs test tests for a statistically significant difference between the expected number of runs vs. the actual number of runs. A run is defined as a sequence of successive price changes with the same sign. n(+)/n( )/n(0) represent the number of successive sequence of positive/negative/zero price changes. Panel B shows the results for the index, corrected for infrequent trading. Saudi Arabia Kuwait Bahrain Panel A: Observed Index Levels Observations (N) n(+) n( ) n(0) Expected runs (m) Actual runs (R) Standard error (σ m ) Z-statistic a a Panel B: Corrected Index Levels Observations (N) n(+) n( ) n(0) Expected runs (m) Actual runs (R) Standard error (σ m ) Z-statistic a Indicates rejection of the null that successive price changes are independent. the runs test. Results of the runs test are shown in Table 4, both for the observed indices and for the indices corrected for infrequent trading. In Panel A for the observed indices, the actual number of runs (R) in each of the Gulf markets can be seen to fall short of the expected number of runs under the null hypothesis of stock return independence. The resulting negative z values for the Gulf indicates positive serial correlation. The runs test results show that the successive returns for both Saudi Arabia and Bahrain are not independent at the 5% level (critical value of 1.96). The Kuwaiti market appears to be marginally efficient in the weak form, with 148 actual runs against an expected number of 161. When the indices are corrected for infrequent trading, the results are strikingly different. For all three markets, the expected and actual number of runs are so close as to be indistinguishable. 2 Based on the corrected indices, we cannot reject weak form 2 The runs test was also conducted using the sample mean as the base. Results obtained were essentially the same.

11 A. Abraham et al./the Financial Review 37 (2002) efficiency for any of the three equity markets. Correcting for nonsynchronous prices in this case leads to an absolute reversal in the inference on market efficiency. The results in this section make an important point in that infrequent trading and nonsynchronous prices can significantly affect the conclusions drawn from efficiency and random walk tests. Explicitly correcting equity indices for infrequent trading, as we did here, can therefore produce more robust tests of efficiency. 5. Conclusions It has been known for some time that infrequent trading makes inferences drawn from efficiency tests imprecise, particularly so for thinly traded emerging markets. However, researchers have continued to use the observed index levels in their analysis, and not surprisingly the extant literature on emerging markets has predominantly rejected the efficient markets hypothesis. To mitigate the confounding effect of nonsynchronous prices on efficiency and random walk tests, the true underlying indices for three Gulf equity markets are estimated by applying the Beveridge and Nelson (1981) decomposition to observed index levels. The RWH and market efficiency hypotheses are assessed using the variance ratio and the runs test. Consistent with results in the literature for similar emerging markets, both the RWH and weak form efficiency are rejected for the Gulf markets when the observed index levels are used. In contrast, inferences are reversed with the use of the corrected true indices. The corrected indices show that successive price changes are independent for all three markets, implying weak form efficiency. Similarly, we cannot reject the RWH for the Saudi and Bahraini markets. The Kuwaiti market, however, fails to follow a random walk even after the correction. Results presented in this paper have practical implications when assessing the efficiency of Appendix Descriptive statistics for the observed and estimated true index returns for Saudi Arabia, Kuwait, and Bahrain, October 7, 1992, to December 30, 1998 Saudi Arabia Kuwait Bahrain Observed Corrected Observed Corrected Observed Corrected Mean SD ρ 1 (a 1 ) 0.19(0.19) 0.0( 0.0) a 0.12(0.12) 0.02( 0.02) 0.18(0.18) 0.01( 0.01) ρ 2 (a 2 ) 0.01( 0.05) 0.0( 0.0) a 0.01( 0.01) 0.01(0.01) 0.18(0.15) 0.01(0.01) ρ 3 (a 3 ) 0.05(0.06) 0.05(0.05) 0.12(0.13) 0.13(0.13) 0.16(0.11) 0.01(0.01) ρ 4 (a 4 ) 0.04(0.02) 0.03(0.03) 0.08(0.06) 0.06(0.07) 0.17(0.11) 0.05(0.05) ρ 5 (a 5 ) 0.03(0.02) 0.01( 0.01) 0.02(0.01) 0.02(0.02) 0.13(0.06) 0.02(0.02) Correlation ρ i is the autocorrelation at lag i, and a i is the partial autocorrelation coefficient. Correlation measures the correlation between the observed and the corrected index returns. a First significant digit is in the third place of decimal.

12 480 A. Abraham et al./the Financial Review 37 (2002) thinly traded markets, where explicitly correcting for infrequent trading could serve to produce more robust test results. References Al-Loughani, N.E., Random walk in thinly traded stock markets: The case of Kuwait, Arab Journal of Administrative Science 3, Bassett, G.W., Jr, V.G. France, and S.R. Pliska, Kalman Filter estimation for valuing nontrading securities, with applications to the MMI Cash-Futures spread on October 19 and 20, 1987, Review of Quantitative Finance and Accounting 1, Beveridge, S. and C.R. Nelson, A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the business cycle. Journal of Monetary Economics 7, Butler, K.C. and S.J. Malaikah, Efficiency and inefficiency in thinly traded stock markets: Kuwait and Saudi Arabia, Journal of Banking and Finance 16, Claessens, S., S. Dasgupta, and J. Glen, Return behavior in emerging stockmarkets, World Bank Review, Fama, E., Efficient capital markets: A review of theory and empirical work, Journal of Finance 25, Fama, E., Market efficiency, long-term returns, and behavioral finance, Journal of Financial Economics 49, Fama, E. and K. French, Permanent and temporary components of stock prices, Journal of Political Economy 96, Grieb, T. and M.G. Reyes, Random walk tests for Latin American equity indices and individual firms, Journal of Financial Research 4, Jokivuolle, E., Measuring true stock index value in the presence of infrequent trading, Journal of Financial and Quantitative Analysis 30, Lo, A. and C. MacKinlay, Stock market prices do not follow random walks: Evidence from a simple specification test, Review of Financial Studies 1, Newbold, P., Precise and efficient computation of the Beveridge Nelson decomposition of economic time series, Journal of Monetary Economics 26, Ojah, K. and D. Karemera, Random walks and market efficiency tests of Latin American emerging equity markets: A revisit, The Financial Review 34, Stoll, H.R. and R.E. Whaley, The dynamics of stock index and stock index futures returns, Journal of Financial and Quantitative Analysis 25, Urrutia, J.L., Tests of random walk and market efficiency for Latin American emerging markets, Journal of Financial Research 18,