Stock Return Autocorrelation, Day-of-The-Week and Volatility: An Empirical Investigation on Saudi Arabian Stock Market

Transcription

1 Stock Return Autocorrelation, Day-of-The-Week and Volatility: An Empirical Investigation on Saudi Arabian Stock Market Shah Saeed Hassan Chowdhury, Prince Mohammad Bin Fahd University 1 M. Arifur Rahman, University of Brunei Darussalam M. Shibley Sadique, Curtin Unversity, Sarawak, Malaysia Abstract There is overwhelming evidence of the presence of autocorrelation in stock returns in many previous studies. Since stock return correlation is related to predictability of stock prices, it is important to know the extent of autocorrelation and its underlying causes. Using daily individual stock price and index data, this paper examines the autocorrelation pattern in stock returns of the Saudi stock market for the period January 2004 through March The paper sheds light on how autocorrelation could be related to factors such as day-of-the-week, stock trading, performance on the preceding day, and volatility. Findings show that (i) there is significant positive autocorrelation in both individual stock and index returns (ii) average autocorrelation from individual stock return is almost always lower than autocorrelation of index return (iii) there is no clear relationship between autocorrelation and firm size or frequency of trading (iv) autocorrelation of returns following a high absolute return day is significantly higher than that following a low absolute return day and (v) previous day of the week (that is, last day or any other day of the week) does not influence autocorrelation of stock returns. When the whole period of study is divided into five sub-periods based on the volatility of the overall market, intensity of autocorrelation of returns is found to be lower in tranquil period than that in volatile period. JEL classification: G12, G14, G15 Key words: Autocorrelation; Saudi Arabian Stock Market; Volatility; Trade Volume; Feedback Trade Introduction Autocorrelation in stock returns indicate predictability. It is well-documented in finance literature that returns from indexes exhibit positive autocorrelation. Such phenomenon exists even for different data frequencies. However, this goes against the concept of market efficiency which predicts that stock returns are unpredictable and serially uncorrelated. 1 Shah Saeed Hassan Chowdhury is the corresponding author. He can be reached at schowdhury@pmu.edu.sa. 1

2 In the existing literature, there are three reasons for return autocorrelation. First, nonsynchronous trading may cause autocorrelation in the index returns (Scholes and Williams 1977; Lo and MacKinlay, 1988, 1990). Since stocks are traded at different point of time on a given day, returns computed from the index results is a mixture of stale and contemporaneous prices. Thus, some information of prior period is reflected in the next period, which results in spurious autocorrelation. Second, expected returns on stocks follow common positively serially correlated process. The autocorrelation in expected returns may induce autocorrelation in individual as well as index returns (Conrad and Kaul, 1988, 1989).Third, due to delay in the arrival of information and transactions costs and resultant hindrance to arbitrage, index autocorrelation occurs (Damodaran 1993; Sias and Starks 1994; Lesmond et al. 1997). Even if stocks are traded frequently, autocorrelation may exist because of delayed adjustment of information in the stock prices. Although informed trades will only trade after considering the spread between the fundamental value and market price and relevant costs, liquidity traders still trade albeit based on stale information. Finally, findings of Sentana and Wadhwani (1992), Shiller (1984), and Bange (2000), among many others, provide the evidence of role of feedback traders to create autocorrelation in stock returns. For all the theoretical models based on index returns there is an assumption that individual stocks do not suffer from autocorrelation problems. Campbell et al. (1993) observe negative relationship between daily return autocorrelation computed from individual stocks and index and trade volume. Sentana and Wadhwani (1992) show how feedback traders may influence market in the presence of smart money and noise traders. They also find that intensity of positive feedback trading is greater after price declines than after price rises. Safvenblad (1997) report that conditional on high return index return autocorrelation is significantly positive while conditional on negative return such autocorrelation does not exist. Safvenblad (2000) shows that both index and individual stocks exhibit high autocorrelation for the Swedish stock market. Non-trading may induce autocorrelation in the returns of individual stocks, but in case of index returns it can be reasonably expected that cross-autocorrelation dominates the autocorrelation of individual stocks. Koutmos and Saidi (2001) show that positive feedback trading also occurs in emerging Asian stock markets. They also point out that feedback trade occurs during the period when market declines and volatility rises. They argue that the main reason for positive feedback is the negative autocorrelation in stock returns. Positive feedback 2

3 traders are those who buy when stock price goes up and sell when stock price goes down. Negative feedback traders do exactly the opposite. Presence of positive (negative) feedback is detected by the negative (positive) autocorrelation in stock returns. Other reasons that could induce positive autocorrelation are time-varying expected returns, nonsynchronous trading and transaction costs. This paper studies the autocorrelation structure of Saudi stock market. We select Saudi Arabian stock market because of at least three important reasons. First, to the extent that the theoretical predictions as well as existing empirical evidence are concerned, the emerging markets are likely to represent a favorable environment for autocorrelation. Stock returns in these markets are likely to be autocorrelated mainly due to the presence of information asymmetry, uninformed individual investors, non-synchronous trading, underdeveloped financial analysis industry, and possibly other behavioral aspects such as tendency to herd. In a very recent study Rahman et al. (2013) show that the investors in the Saudi stock market are highly prone to herd behavior, which may induce predictability and autocorrelation in stock returns. Saudi stock market trades only in common stocks, there is no derivatives market, and short-selling is strictly prohibited. Non-resident non-gcc foreign investors are not allowed to own and trade directly in Saudi stocks. Domestic individual investors account for more than 92 percent of stock turnover (Arab Monetary Fund, 2011). Saudi investors have the tendency to trade very aggressively. Individual investor accounts have a very high level of churn (turnover/net investment) 118 times compared to the mutual funds 30 times (NCB Capital, 2008). Therefore, unlike many other emerging markets, Saudi market presents a natural ground to test the autocorrelation behavior of mainly domestic individual investors. The participation of uninformed small investors may make the stock prices adjust partially to new relevant information, contributing to the presence of autocorrelation. Since individual investors are the dominating players, by focusing on the Saudi stock market, our study is expected to provide us a vivid picture of individual investors contribution to autocorrelation in stock returns. Secondly, the government is actively considering opening up the Saudi stock market to the global investors within next few years (Saadi 2012, March 21; Hankir 2012, February 22). Since this market is relatively unknown to foreign investors, it is important for them to understand the stock price behavior of this market. An understanding of the behavior of stock price would necessarily require an understanding of the investment strategies of currently active 3

4 investors (Lakonishok et al. 1992). Thus, this study may prove very timely especially for the prospective global investors interested in the Saudi stock market. Thirdly, to best of our knowledge, this is the first paper that uses both individual stocks and index returns to investigate autocorrelation in the Saudi market. Considering the fact that only index returns were used in almost all the previous studies and this is the first investigation of autocorrelation structure of Saudi stock returns using both individual and index returns, this paper is going to add significantly to the extant literature on predictability of an emerging stock market. Use of return of individual stocks gives the opportunity to know how autocorrelation is formed from the level of individual stocks. All the theoretical models of index return autocorrelation assume the absence of autocorrelation of individual stocks. Thus, this study is able to show how individual stocks contribute to the index level autocorrelation. Previous Literature: Presence of Autocorrelation in Stock Returns Regardless of return frequencies, previous studies indicate significant presence of positive autocorrelation in index returns (Stoll and Whaley 1990; Lo and MacKinlay 1990). 2 However, when autocorrelation is estimated for individual stocks, results vary. Using individual returns, Atchison et al. (1987) find no autocorrelation on average whereas Chan (1993) reports autocorrelation in the returns of large firms. Bohl and Reitz (2002) show that there is significant number of feedback traders in the German stock market and that the positive feedback traders are responsible for the negative autocorrelation in index returns during high volatile periods. Relatively recently, for the UK stock market index and individual stocks, McKenzie and Kim (2007) give the evidence of relationship between autocorrelation and trade volume, volatility, and the day-of-the-week. They find negative relationship between volatility and autocorrelation. Increase in volatility caused by increase in stock prices produces more autocorrelation than volatility caused by decrease in stock price. Although there is huge research on the use of autocorrelation to find the efficiency of emerging markets, these predominantly focus on predictability and do not examine autocorrelation structure of stock returns. Some of these are noteworthy here. Claessens et al. (1995) find significant first-order autocorrelation in stock market returns in Chile, Columbia, 2 Even, high trading frequency such as five minutes shows the presence of positive autocorrelation in index returns (Chan et al., 1991). 4

5 Greece, Mexico, Pakistan, the Philippines, Portugal, Turkey, and Venezuela. Harvey (1995) uses monthly data to show that 12 of the 20 emerging markets in his sample have monthly autocorrelation of more than 10% and eight of them have more than 20%. Altay (2006) gives evidence of the presence of positive feedback trading in Istanbul stock market. Moreover, this market shows negative feedback when there is higher return volatility and there is stronger positive feedback in down market relative to up market. Bohl and Siklos (2008) document that positive feedback trading in emerging markets is stronger than that in mature ones. They also show that autocorrelation for both mature and emerging market returns are usually higher in volatile periods in comparison to tranquil periods. Autocorrelation literature on Saudi stock market also focuses on efficiency issues. Some of them deserve to be mentioned. In one of the early studies on Saudi market, Butler and Malaikah (1992) find no evidence in favor of random walk. A study by Dahel and Labbas (1999) examines the Saudi Arabia, Bahrain, Oman and Kuwait stock markets for efficiency and their results suggest that these markets are efficient in the weak-form as the random walk hypothesis cannot be rejected. Al-Kholifey (2000) finds that 61% of the firms under consideration exhibit statistically significant serial correlation. Al-Abdulqader (2002) tests the Saudi market efficiency using weekly closing prices of 45 individual stocks for the period 1990 through Returns of 51% of the firms show significant autocorrelation. Abraham et al. (2002) report evidence in favor of weak-form efficiency in the Bahraini, Kuwaiti and Saudi stock markets. Al-Khazali et al. (2007) use weekly data of market index returns of Bahrain, Kuwait, Oman and Saudi Arabia to report that all these markets follow random walk. Onour (2009) tests the weak-form efficiency on the Saudi stock market using unit root tests and variance ratio. The findings of the tests reject the hypothesis of random walk behavior at all levels of stock prices. Al Ashikh (2012) also rejects market efficiency of Saudi stock market. Ibnrubbian (2012) reports the presence of significantly positive correlations in the Saudi stock market during recent time. He attributes the positive sign to slower price corrections to new information. Data and Methodology The sample consists of daily stock price index data of 152 firms listed in Tadawul. Returns are defined as the log difference of two daily consecutive stock prices times 100. We cover the 5

6 period from January 2004 through March All the data for return index and market capitalization are collected from Datastream. For the purpose of analysis, data are grouped based on the market capitalization, number of non-trading days as a percentage of total number of possible days of trade, and volatility of returns. We consider both individual stocks and index data to investigate autocorrelation of returns. The basic regression model to estimate autocorrelation is given by. (1) This equation can be estimated for index as well as for individual stocks, which can then be used to compute the average estimate of autocorrelation. Regression model given in (1) can be modified with two interactive dummy variables to examine any asymmetric effect in autocorrelation. With the modification equation (1) will become, (2) where ( is a dummy variable for low (high) returns/absolute returns. Absolute return is used as a proxy for volatility. Moreover, ( is also used as the dummy variable for Saturday through Tuesday (Wednesday). It is noteworthy that Saudi stock market is open Saturday through Wednesday. Saudi market is fully closed on Thursday and Friday. In a very influential paper, Sentana and Wadhwani (1992) show that during the period of higher volatility autocorrelation rises and this phenomenon is completely supported by the finance theory because higher volatility increases the risk for smart money. In such a case, smart money is watchful whereas the other group called feedback traders dominate the trading and create autocorrelation in stock returns. 3 They argue that at low level of volatility negative feedback dominates, which is shown by positive autocorrelation in stock returns. Moreover, as volatility rises, demand for portfolio insurance-type strategies leads to positive feedback, which is shown by negative autocorrelation in stock returns. Since short sale is not allowed, findings could be completely different for Saudi market. Goyal and Santa-Clara (2003) estimate monthly variance of stock i as follows 3 Shiller (1984) gives the idea of how market trading can be influenced by two groups of traders smart money who trades on fundamentals and ordinary traders who basically trade on fads and fashion. 6

7 where is the number of trading days in month t and is the return of stock i on day d. The last term in the equation uses the methodology of French et al. (1987) to adjust for the autocorrelation in daily stock returns. Goyal and Santa-Clara (2003) compute the variance of the market by averaging the stock variances across firms on a given month. Their measure is where is the number of stocks that exist in month t. We have used the methodology of French et al. (1987) and Goyal and Santa-Clara (2003) to estimate 20-day rolling variance for the whole period. Figure 1 identified five different sub-periods either volatile or tranquil periods based on 20-day rolling variance. This volatility series helps us find the volatile and tranquil period of Saudi stock market. Analyses of Results Table 1 provides the autocorrelation of individual stock and index returns. Autocorrelation is significant for both of them, but not that much strong. Panel A gives the evidence of autocorrelation when firms are sorted by size. All size firms show positive autocorrelation in their returns. Large firms are supposed to be more liquid and number of non-trading days as a percentage of total number of days for large firms should be less for small firms. It is interesting to observe that there is no clear relationship between autocorrelation and firm size and stock trade. The reason is probably the fact that big portion of large firm stocks in Saudi Arabia are often held by few people who do not trade much. Since trading is a channel through which information is passed to the investors, we sort the firms based on the percentage of non-trading days. Results show that highly traded firms (i.e., lower non-trading days) exhibit higher autocorrelation in returns than others two types. 7

8 Table 1. First autocorrelation of stock returns Sample Index returns Stock returns No. of stocks Non-trading days (%) a Panel A: Firms sorted by size Large ** ** (4.09) (3.49) Medium ** ** (3.50) (2.89) Small ** ** (5.77) (9.41) All ** ** (2.94) (6.77) Panel B: Firms sorted by percentage of trade High ** ** (6.05) (6.49) Medium ** ** (5.17) (6.84) Low ** (4.10) (0.54) The regression model is b. t-statistics are reported in the parenthesis. a Non-trading days as percentage of total number of possible trading days. b Average of individual regression estimates. ** Significantly different from zero at 5% level. Panel A of Table 2 gives the autocorrelation estimates following high/low return on the previous trading day. Autocorrelation of index returns is significantly higher after low return day than that after a high trading day. However, there is weak evidence of autocorrelation for stock returns and there is no asymmetry in response to last trading day. The difference in autocorrelation between stock returns and index returns suggest that cross-autocorrelation may be an important factor for index return autocorrelation. Panel B presents the autocorrelation estimates following high/low absolute return (i.e., volatility) on the previous day. This shows how autocorrelation in returns reacts to volatility of returns on the last trading day. There is high autocorrelation when there is higher volatility on the last trading day. The difference of estimates of autocorrelation is highly significant for the indexes of all size firms. Just like Panel A, for the individual stocks the autocorrelation in less in magnitude and the difference of estimates is not significant. 8

9 Table 2. First autocorrelation conditional on preceding day s return and absolute return for firm sizes Index returns - Stock returns a a - Panel A: Previous day produced low or high return Large ** ** ** ** (6.19) (-0.14) (4.65) (2.12) (3.12) (-1.08) Medium ** ** ** (4.20) (1.30) (2.80) (1.20) (3.18) (-0.28) Small ** ** ** ** (7.05) (1.08) (4.39) (6.82) (6.17) (0.97) All ** ** (4.39) (-0.20) (-3.26) (4.08) (6.24) (-0.53) Panel B: Previous day produced high or low absolute return Large.0588 ** ** ** ** ** (2.51) (4.49) (-3.11) (4.65) (2.62) (-0.68) Medium ** ** ** ** (2.05) (4.87) (-3.87) (2.94) (0.92) (-0.73) Small ** ** ** ** ** (3.86) (5.49) (-3.40) (9.42) (3.37) (-0.68) All ** ** ** ** (3.88) (4.68) (-2.67) (3.08) (0.17) (1.00) Regression model is. ( is a dummy variable for low (high) returns/absolute returns. t-statistics are reported in the parenthesis. a Average of regression estimates. Significance tests given in the parentheses tests whether the mean estimate is significantly different from zero. b Difference of the average of regression estimates. Significance tests given in the parentheses tests whether the mean difference of estimates is significantly different from zero. ** Significantly different from zero at 5% level. b Higher volatility implies higher cost of pricing error. Koutmos (1997) and Safvenblad (2000) find lower index return autocorrelation conditional on higher volatility on the preceding day and higher index return autocorrelation following a day of positive return. Table 3 examines these issues for Saudi stock market. There is evidence of highly significant positive autocorrelation in stock returns conditional on high volatility on the preceding day. This phenomenon is supported by herding behavior found in a recent study by Rahman et al. (2013). 9

10 Table 3. First autocorrelation conditional on preceding day s return and absolute return for firms sorted by percentage of non-trading days Index returns a a - Stock returns a a - Panel A: Previous day produced low or high return High ** ** ** ** (5.94) (4.65) (0.84) (7.88) (0.66) (5.22) Medium ** ** ** ** (5.68) (4.97) (0.97) (6.83) (0.61) (4.62) Low ** ** ** (-0.63) (2.00) (-1.59) (4.38) (1.43) (2.38) All ** ** ** ** (4.08) (6.24) (-0.53) (6.87) (0.99) (4.47) Panel B: Previous day produced low or high absolute return High ** ** ** (3.84) (6.45) (-4.40) (6.25) (1.31) (-0.96) Medium ** ** ** ** (2.89) (6.23) (-4.51) (6.97) (1.66) (1.57) Low ** ** ** (2.57) (4.29) (-2.86) (0.55) (1.49) (-1.28) All ** ** ** ** (3.88) (4.68) (-2.67) (7.15) (1.00) (-0.27) b Regression model is. ( is a dummy variable for low (high) returns/absolute returns. t-statistics are reported in the parenthesis. a Average of regression estimates. Significance tests given in the parentheses tests whether the mean estimate is significantly different from zero. b Difference of the average of regression estimates. Significance tests given in the parentheses tests whether the mean difference of estimates is significantly different from zero. ** Significantly different from zero at 5% level. Table 4 shows autocorrelation of returns conditional on day-of-the-week. Boudoukh et al. (1994) document that index autocorrelation is high between Friday (last trading day) and Monday (first trading day) returns. In the same line of reasoning, autocorrelation may be high between Wednesday and Saturday since Tadawul is closed on Thursday and Friday. Panel A shows that all size indexes including All have significant positive autocorrelation conditional on other days of the week. For the stock returns, the intensity of autocorrelation is not that strong. This is probably the case of negative feedback trading where traders do not really care about closing their profit taking before the weekend. This finding is a clear deviation from the findings of Boudoukh et al. (1994). The reason may be the fact that Tadawul is mainly dominated by 10

11 individual traders, who behave differently from institutional investors in many ways. Results do not qualitatively change much when portfolios are created based on trading. Table 4. First autocorrelation conditional on day-of-the-week Index returns Stock returns Sat.-Tue. Wed. - Sat.-Tue. a Wed. - Panel A: Firms sorted based on size Large ** ** ** (4.80) (-0.75) (2.61) (2.63) (1.58) (0.02) Medium ** ** (4.59) (0.16) (2.87) ** (1.86) (2.59) (0.05) Small ** ** ** ** (5.86) (1.08) (1.46) (10.67) (2.25) (4.15) All ** ** ** (5.75) (0.46) (1.89) (5.69) (3.24) (1.34) Panel B: Firms sorted based on percentage of trade High ** ** ** ** (6.40) (0.57) (2.16) (7.19) (2.23) (1.63) Medium ** ** ** (4.44) (0.09) (1.72) (6.60) (2.88) (1.15) Low ** (5.37) (0.64) (1.61) (0.08) (0.45) (-0.22) Regression model is. ( is a dummy variable for Saturday through Tuesday (Wednesday). It is noteworthy that Saudi stock market is open Saturday through Wednesday. Market is fully closed on Thursday and Friday. t-statistics are reported in the parenthesis. a Average of regression estimates. Significance tests given in the parentheses tests whether the mean estimate is significantly different from zero. b Average of difference of regression estimates. Significance tests given in the parentheses tests whether the mean difference of estimates is significantly different from zero. ** Significantly different from zero at 5% level. b Table 5 presents the nature of autocorrelation during period of volatility and tranquility. Sentana and Wadhwani (1992) document that index return autocorrelation becomes significantly highly negative during the period of crash of the U.S. market in Contrary to their findings, results show that positive correlation exists for all the sub-periods. However, it is observed that the intensity of autocorrelation in volatile period is higher than that in tranquil period. 11

12 Table 5. First autocorrelation of stock returns in volatile and tranquil periods Sample Index returns Stock returns No. of stocks Non-trading days (%) a Panel A: Period 01/01/ /30/2006 (Tranquil Period) Large (0.15) (-1.69) Medium (0.72) (0.12) Small (1.59) (-1.47) All (-1.99) Panel B: Period 01/30/ /30/2007(Volatile Period) Large (1.90) (3.70) ** Medium ** (2.36) (1.97) Small ** ** (2.72) (7.16) All ** 152 (5.73) Panel C: Period 03/30/ /30/2008(Tranquil Period) Large (1.23) (1.19) Medium (0.51) (1.71) Small (1.32) (1.30) ** (2.52) Panel D: Period 09/30/ /28/2009 (Volatile Period) Large ** (1.28) (4.55) Medium ** (1.32) (5.68) Small ** (1.99) (9.19) All ** (11.06) Panel E: Period 03/01/ /30/2012 (Tranquil Period) Large ** (0.44) (2.34) Medium ** (1.07) (2.31) Small ** (1.91) (3.54) b 12

13 All ** (4.08) The regression model is. t-statistics are reported in the parenthesis. a Non-trading days as percentage of total number of possible trading days. b Average of individual regression estimates. ** Significantly different from zero at 5% level. Conclusion Using daily individual stock price and index data, this paper examines the autocorrelation pattern in stock returns of the Saudi stock market for the period January 2004 through March The paper focuses on how autocorrelation could be related to factors such as day-of-the-week, stock trading, performance on the preceding day, and volatility. Findings show that there is significant positive autocorrelation in both individual stock and index returns and average autocorrelation from individual stock return is almost always lower than autocorrelation of index return. There is no clear relationship between autocorrelation and firm size or frequency of trading. Surprisingly, autocorrelation of returns following a high absolute return day is significantly higher than that following a low absolute return day. Contrary to the findings of Sentana and Wadhwani (1992), previous day of the week (that is, last day or any other day of the week) does not influence autocorrelation of stock returns. This paper also divides the whole period of study into five subperiods based on the volatility of the overall market. Results show that intensity of autocorrelation of returns is lower in tranquil period than that in volatile period. 13

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