Autocorrelation in Daily Stock Returns

This paper examines the roles of spread and gradual incorporation of common information in the explanation of the autocorrelation in daily stock returns. The study develops a theoretical model and provides empirical evidence using an innovative test procedure. The data used in the empirical study comes from the Center for Research in Security Prices (CRSP) daily return files for NYSE stocks. The development of the theoretical model predicts that the autocorrelation in stock returns is the sum of two terms. The spread is the source of a negative term, while the gradual incorporation of common information generates a positive term. In the case of daily stock returns, the model predicts that, taking into account the sign, the autocovariance can be positive, negative or approximately zero depending on the absolute values of the two terms. The results of empirical tests, which use a modified version of the statistic variance ratio, seem to indicate that both the spread and the gradual incorporation of common information are relevant to explain the dynamics of daily prices. This study examines, both theoretically and empirically, the autocorrelation in daily stock returns using an approach that takes into account the trading mechanism and the specific and common components of information. In the case of daily stock prices, the study proposes that the statistical properties of price changes depend on the interaction between the spread effects and the effects due to the gradual incorporation of common information. An important contribution of this study is providing an innovative test procedure that minimizes potential biases arising from unwanted factors. For each firm in the sample, and over the same period, this procedure compares two variance ratio statistics, as described in section V. Another important feature of the study is the application to individual daily stock returns, which requires a large amount of data, whereas most of the works on serial correlation analyse portfolio returns or longer time horizons. Other recent studies also examine the autocorrelation in short-term individual stock returns. This is the case of Avramov, Chordia and Goyal (forthcoming). However, they use a different approach and analyze weekly and monthly returns. Stock price changes reflect new market-level and firm-level information. It is likely that common information, which refers to the market-level information, has a significant impact on the dynamic properties of stock prices, because several empirical works found that stock price changes have informational implications for other assets in the same sector, market or even geographically separated markets, for example, Forbes and Rigobon (2002). Moreover, several studies suggest that the gradual incorporation of marketwide information causes serial correlation in short-term stock returns, for example, Chordia and Swaminathan (2000), Sias and Starks (1997), and Lo and MacKinlay (1990). In this study, the theoretical model uses the Glosten (1987) market microstructure framework, because microstructure models have been used to analyze stock transactions, O’Hara (1999) and Madhavan (2000). However, in order to incorporate into the model the assumptions described in the sections that follow, several modifications have had to be made to the Glosten (1987) framework. Given that the study focuses on the relevance of the information components and of the gradual incorporation of common information to the interpretation of the statistical properties of stock prices, then the stock price model must explicitly describe the incorporation of common and specific information. Another major modification is related to the composition of the spread, which is based on the empirical findings of Huang and Stoll (1997). Additionally, the study proposes a simple process of diffusion of information in a market operated by a competitive market maker. The model predicts that the autocovariance in stock returns is the sum of two terms. The spread is the source of a negative term, while the gradual incorporation of common information generates a positive term. In the case of daily stock returns, the model predicts that, taking into account the sign, the autocovariance can be positive, negative or approximately zero depending on the absolute values of the two terms. Several papers on serial correlation investigate the presence of abnormal returns using trading strategies, for example momentum and contrarian, that exploit the predictability of stock returns based on past returns. This study proposes that the statistical patterns in stock returns depend crucially on the time horizon. For example, several studies have found positive autocorrelation in medium-term stock returns, while long-term stock returns exhibit negative autocorrelation. Additionally, this study suggests that we can expect to find significant differences between the dynamic properties of individual stock returns and portfolio returns. The empirical tests in the study, which use daily returns, document a positive and substantial autocorrelation in stock index returns, while individual stock returns exhibit a weak autocorrelation. The empirical study examines the relationship between the autocorrelation in daily stock returns and the relevance of common information. The empirical tests use CRSP data on daily returns for NYSE stocks. The results of the theoretical model show that the autocorrelation in stock returns has two terms: the term related to the spread and the term due to the gradual incorporation of common information. The term related to the spread is negative while the other is positive, and the second term is expected to be higher when common information is more significant. In the study, the CRSP Index return is the variable used to represent the importance of common information. Therefore, the autocorrelation in daily stock returns is expected to be higher when the absolute value of the CRSP Index return is higher, because of the positive sign of the autocorrelation term associated with the incorporation of common information. As regards the meaning of high autocorrelation it is important to note that, in this study, a zero autocorrelation is higher than a negative autocorrelation. The choice of an appropriate statistic to test the serial correlation in stock returns is based essentially on the criterion proposed by Richardson and Smith (1994). They analyze a general class of test statistics that are linear combinations of the autocorrelations coefficient estimators, such as the variance ratio (Lo and MacKinlay), J-statistic (Jegadeesh) and multiperiod autocorrelation estimator (Fama and French). They found that, given an alternative distribution for stock returns, the most powerful test statistic places its relative weights on the autocorrelation estimators in a one-for-one correspondence with the magnitude of the true autocorrelation. The criterion suggests the use of the Lo and MacKinlay (1988) variance ratio, given that our theoretical model predicts that the magnitude of the autocorrelations is decreasing in the order of the autocorrelation. The Lo and MacKinlay variance ratio statistic is sensitive to serial correlation and robust to time-varying volatilities and deviations from normality, and has been used to detect deviations of stock returns from the random walk model. A main contribution of this study is providing an innovative test procedure that minimizes potential biases arising from unwanted factors. For each firm in the sample, and over the same period, this procedure compares two variance ratio statistics. However, this procedure implies the use consecutive and nonconsecutive observations whereas the Lo and MacKinlay (1988) statistic is based on consecutive observations. Therefore, a new expression for the estimator of the multiperiod variance, which uses overlapping observations, is proposed. To confirm the accuracy of this expression it is also shown that we can obtain the Lo and MacKinlay estimator in the case where there is no discontinuity in observations. The results of empirical tests seem to indicate that both the spread and the gradual incorporation of common information are relevant to explain the dynamics of daily prices. The first test applies the variance ratio statistic to the CRSP Index daily returns. The results of the test show that the autocorrelation in the Index return is positive and significant. When applied to individual stock returns, the tests show a weak autocorrelation. Moreover, the sign of the autocorrelation is not always the same, and frequently the absolute values of the autocorrelations do not lead to the rejection of the null hypothesis that the autocorrelations are different from zero. Another empirical test uses the median of the absolute values of the Index return to divide the individual stock return observations into two sets and, for each one of the two sets, the variance ratios in the daily individual stock returns are calculated. After that, tests are performed to investigate the null hypothesis that the mean variance ratio is equal between the two sets. The observed ANOVA Fstatistic and the probability p lead to the rejection of the null hypothesis, suggesting that the mean variance ratio is higher when common information is more relevant. This test uses 2-period variance. Similar tests were performed using 3-period variance and 4-period variance, leading to similar test results. Another test, which is based on the two-period variance, uses more extreme values of the CRSP Index return to split the stock returns into two sets. In this test the 66th percentile and the 33rd percentile are used to divide the return observations into two sets. This test leads to similar results. Assuming the results of the theoretical model that the autocorrelation in stock returns has two terms: the term related to the spread and the term due to the gradual incorporation of common informatio