Subject:

Bank stocks
(Analysis)

Information technology (Analysis)

Information technology (Forecasts and trends)

Information technology (Analysis)

Information technology (Forecasts and trends)

Author:

Gu, Anthony Yanxiang

Pub Date:

05/01/2002

Publication:

Name: Academy of Accounting and Financial Studies Journal Publisher: The DreamCatchers Group, LLC Audience: Academic Format: Magazine/Journal Subject: Business Copyright: COPYRIGHT 2002 The DreamCatchers Group, LLC ISSN: 1096-3685

Issue:

Date: May, 2002 Source Volume: 6 Source Issue: 2

Topic:

Event Code: 010 Forecasts, trends, outlooks Computer Subject: Information technology; Market trend/market analysis

Product:

Product Code: 9912600 Information Systems & Theory

Geographic:

Geographic Scope: United States Geographic Code: 1USA United States

Accession Number:

179817644

Full Text:

ABSTRACT

Advances in communication and information technologies are expected to have significant impacts on stock return behavior. As a major aspect of the advances, higher information frequency tends to reduce autocorrelation and volatility, or make the market more efficient and relatively more stable. The generally random arrival of more frequent information and thus more frequently adjusted trading activities at smaller scales may explain the negative connection between autocorrelation and information frequency. Autocorrelation and volatility exhibit a positive, nonlinear relation when stock price fluctuates more than randomly. The relation between autocorrelation and trading volume is negative and nonlinear.

INTRODUCTION

The quantity of information has been growing geometrically for the last few decades and is expected to increase even more rapidly in the future. Information affects stock return behavior through its influence on investors' expectations. If the assumption of random arrivals of information is valid, then ceteris paribus, more frequent information should make their "shocks" more random and less heavy. Thus, one can hypothesize that greater quantity of information would help to increase market efficiency and reduce market volatility.

There are numerous financial or economic studies on whether stock price changes follow a random walk or whether the stock market is efficient by testing autocorrelation between stock returns and the related factors. For example, Fama (1970) raises the efficient market hypothesis and states that if the market is efficient in the weak form, the information on past prices or returns should not be useful in achieving abnormal returns. As one of the earliest studies on market efficiency, Fama (1965) investigates the behavior of the daily closing prices of the 30 Dow Jones Industrials and finds evidence inconsistent with weak form market efficiency. His serial correlation tests reveal that the first-order autocorrelation of daily returns is positive for 23 of the 30 firms, but his runs tests reveal no significant autocorrelation. Lo and MacKinlay (1988) find that weekly returns on portfolios of NYSE stocks show consistent positive autocorrelation and the autocorrelation is stronger for portfolios of small companies. Similarly, Conrad and Kaul (1988) find that daily and Wednesday-to-Wednesday returns are positively autocorrelated, and more so for portfolios of small stocks.

However, all of the previous studies have focused on whether stock price movements are random or whether the markets are efficient. There is no work relating the quantity of information on stock price behavior, though there are some studies on stock reactions to news. Campbell and Hentschel (1992) examine the impact of the size of news on stock price behavior, Ross (1989), Ederington and Lee (1993, 1995) look at the relation between news release and stock price and volatility. McQueen, Pinegar and Thorley (1996) analyze the reaction of stocks to good news and the cross-autocorrelation of portfolio returns.

This study explores the impacts of information frequency or quantity of information, on stock price behavior and examines the relation between volatility, firm size, trading volume, rate of return and autocorrelation. Information frequency or the number of news items about publicly traded banks during a specified period of time is used as an explanatory variable to estimate the impact of greater information quantity on the behavior of stock returns. A further understanding of the behavior of bank stocks and of the related factors can help bank investors develop better investment strategies.

The plan of the paper is as follows. In Section II, we estimate the autocorrelation between daily returns on the bank stocks and present the results. In Section III we analyze the relations between autocorrelation and information frequency, return volatility, bank size and trading volume, and discuss the implications. We provide a conclusion in Section IV.

II. DATA AND TESTS

The Data

The number of news items in the Wall Street Journal about bank
stocks is used in this study. The Wall Street Journal is generally
regarded as the most accurate, consistent, and popular source of
economic and financial news with adequate quantity. Other sources are
generally viewed as of lower authorities. Data on the number of news
items in the Wall Street Journal in 1998 is from The Wall Street Journal
Index, UMI 1999. Using bank stocks can avoid the unwanted effects of
different factors of different types of companies on the behavior of
their stocks. Among industries, banks provide the most similar products
and services, and their stock prices are generally affected by similar
macroeconomic factors in similar ways, such as the expected rate of
interest and GDP growth.

In the data set there are 177 bank stocks that traded for at least 250 days in the year of 1998. The list of the banks and their total assets as of the end of 1998 are from Thomson North American Financial Institutions Directory, Thompson Financial Publishing. Daily stock price and volume in the year of 1998 is from Yahoo.

The Variance-Ratio Test

Variance ratio and runs tests are performed to estimate autocorrelation between daily returns on the bank stocks. The use of a short (daily) horizon may reduce the cost of statistical imprecision.

Let [I.sub.t] represent the natural logarithm of a time series with nq + 1 observations. If [I.sub.t] is a pure random walk, the variance of its q-differences grows proportionally with the difference q (we test with q = 2). Hence, a random time series should exhibit a unit variance ratio. (1) A variance ratio that is greater than unity indicates positive auto-correlation and a variance ratio that is smaller than unity indicates negative auto-correlation. The variance-ratio, VR(q) is defined as:

VR (q) = [[sigma].sup.2](q)/[[sigma].sup.2](l) (1)

Where [[sigma].sup.2](q) is 1/q the variance of the q-differences and [[sigma].sup.2](1) is the variance of the first differences. And:

[[sigma].sup.2] (q) = 1/m [nq.summation over (t=q)] [([I.sub.t] - [I.sub.t-q] - q [??]).sup.2] (2)

where

m = q (nq - q + 1)(1 - q/nq)

and

[[sigma].sup.2](1) = 1/(nq - 1)[nq.summation over (t=1)] [([I.sub.t] - [I.sub.t-1] - [??]).sup.2] (3)

where

[??] = 1/nq ([I.sub.nq] - [I.sub.0])

[I.sub.0] and [I.sub.nq] are the first and last observations of the time series.

The asymptotic standard normal test statistics for the variance-ratio is derived by Lo and Mackinlay (1988) and modified by Liu and He (1991). Under the hypothesis of homoskedasticity the test statistic is:

z(q) = VR (q) - 1/[[phi](q)].sup.0.5] ~ N (0,1) (4)

Where,

[phi](q) = 2(2q - 1)(q - 1)/3q(nq)

The asymptotic standard normal test statistic for the heteroskedasticity-consistent estimator is:

[z.sup.*](q) = VR(q) - 1/[[[phi].sup.*](q)].sup.0.5] ~ N (0,1) (5)

where

[[phi].sup.*](q) = [q-1.summation over (j=1)][[2(q - j)/q].sup.2] [??](j)

and

[??](j) = [summation][([I.sub.t] - [I.sub.t-1] - [??]).sup.2][(I.sub.t-j] - [I.sub.t-j-1] - [??]).sup.2]/[summation][[([I.sub.t] - [I.sub.t-1] - [??]).sup.2]).sup.2]

The Runs Tests

The runs test is a non-parametric test used to detect the frequency of changes in the direction of a time series. As it is a non-parametric test, the runs test is not based on any finite-variance assumption and does not require an assumption about the distribution. Runs are defined here as the number of sequences of consecutive positive and non-positive (negative or zero) returns. The runs test tabulates and compares the number of runs in the sample against its sampling distribution under the random walk hypothesis. Suppose that each observation is independently and identically distributed. When the null hypothesis of randomness is true, according to Albright (1987), the mean or expected number of runs can be calculated as

E(R) = N + 2AB/N (6)

Where,

N = total number of positive and non-positive sequences in the sample, A = number of sequences of positive returns in the sample, and B = number of sequences of negative or zero returns in the sample

The standard error of number of runs can be calculated as

SE (R) = [square root of 2 AB (AB - N)/[N.sup.2](N - 1)] (7)

To test whether any apparent non-randomness is the result of chance alone, we use the statistic,

Z = R - E(R)/SE(R) (8)

Where,

R = number of actual runs in the sample.

The null hypothesis, [H.sub.0] (randomness) can be rejected at the a level if [absolute value of z] > [[alpha].z/2]. The test is a two-tailed test since there is evidence of non-randomness when R is too small or when R is too large. For a two-tailed test with [alpha] = 0.10, the tabulated z value we require is [z.sub.0.05] = 1.645, and with [alpha] = 0.05, the tabulated z value we require is [z.sub.0.025] = 1.96.

Negative z-values of the runs test, runs ratios less than unity and variance ratios greater than one indicate positive autocorrelation or that price increases and decreases in streams. Positive z-values or greater-than-unity runs ratios and variance ratios less than one indicate negative autocorrelation or that price movements change directions more frequently than random. The runs ratio is defined as the actual number of runs divided by the expected number of runs.

The tests reveal significant autocorrelation for most of the 177 bank stocks, which is supported by the z-values for the variance ratio and runs tests. Table 1 provides the descriptive statistics of the data and the estimated autocorrelation.

III. THE REGRESSION ANALYSIS AND IMPLICATIONS

Regression analysis is conducted to examine the impact of information frequency on market efficiency and the relations between bank size, return volatility, trading volume, and rate of return and autocorrelation. In the model, the dependent variable is the absolute value of the estimated variance ratio minus 1 and the absolute value of the estimated runs ratio minus 1. Using absolute value of the dependency measurements can measure the extent of deviation from randomness with the same scale, reveal both the direction and the magnitude of the effects of the independent variables on the level of autocorrelation. (Our purpose is to estimate the effects of the independent variables on deviation from efficiency, not on positive or negative autocorrelation. Since both positive and negative values of the dependent variables represent deviation from efficiency, and the independent variables, i.e., standard deviation, variance and volume, except return, all have positive values, using absolute values of the dependent variables can avoid possible distortion of the estimates. We have also used the actual values of the dependent variables but find no significant difference from using absolute values though.) Frequency of information (number of news items), annual average standard deviation and variance of consecutive two-day returns, bank size (total assets), average daily trading volume, and average rate of daily returns are used as explanatory variables. The annual average standard deviation of consecutive two-day returns is calculated as:

[sigma] = [N - 1.summation over (t=1)][square root of [([R.sub.t] - [bar.R]).sup.2]/N - 1 (9)

where,

[R.sub.i] is the rate of return of day i, [bar. R] is the average rate of return of day i and day i+1, and N is the total number of trading days in a year. Three reasons justify the use of standard deviation of consecutive two-day returns. First, it reflects the time-varying characteristic of volatility, hence the time-varying risk faced by investors. This point is stressed by some previous researchers (i.e., LeBaron, 1992, Campbell, et al, 1993, and Chiang, 1998) who use previous period's rates of return to approximate the changing variance in their GARCH models. Second, it is relevant because autocorrelation between returns of two consecutive days is being examined, and third, using it improves the regression, the coefficients of determination (r2) and the t-values are higher compared to that from using annual standard deviation of daily returns. The standard deviation and variance (s 2) are used as volatility measurements, we include both variables in the model to capture any nonlinearity that may exist in the relation between volatility and autocorrelation.

Table 2 presents the results of the regression analyses. Both models show that the number of news items has a significant negative impact on autocorrelation, or a greater number of news items tend to reduce autocorrelation hence increase market efficiency. This phenomenon may be explained by the generally random arrival of more frequent news. A greater number of generally random news items may lead to more frequently adjusted trading activities since investors make their trading decisions in response to news. If trading activities reflect the characteristics of news, i.e., generally random, more frequent, and less shocking, price changes should be more independent and less volatile. Hence, highly advanced communication and information technologies might be an explanation as to why advanced markets are more efficient and less volatile than less developed and emerging markets.

Autocorrelation is positively related to volatility for this data set, and the relation is nonlinear, which is indicated by the significant positive coefficients for standard deviation and the significant negative coefficients for variance. Figure I shows the relation between autocorrelation and volatility. The positive relation between autocorrelation and volatility that found by this study is generally contrary to previous reports while the non-linearity of the relation revealed in this study supports the finding of LeBaron (1992).

[FIGURE I OMITTED]

LeBaron (1992) tests daily and weekly data of the S&P composite index from January 1928 through May 1990, the Dow Jones Index constructed by Schwert (1990), and weekly returns of IBM Stock including dividends. The results of his research indicate that first-order autocorrelation is larger during periods of lower volatility and smaller during periods of higher volatility for both daily and weekly returns. And, the relation between volatility and autocorrelation may not be linear.

Non-trading may be an explanation for the relation between autocorrelation and volatility (Cohen, et al., 1980, 1986, and LeBaron 1992). Some stocks do not trade close to the end of day, which will cause positive correlation in the stock return as information arriving at the end of the day appears in these stocks on the following day. The level of this non-trading should be inversely related to overall trading volume. Since there is a strong positive relation between volatility and volume, non-trading, and therefore autocorrelation, would be higher during periods of lower volatility. Another explanation is the accumulation of news. If news items arrive slowly and in small bits, a trader's optimal behavior may be to "do nothing" until they have received enough information. This optimal non-trading may vary inversely with the level of volatility if this is related to the current rate of information flow.

However, there is no explanation about the positive relation between autocorrelation and volatility has been found from previous studies. A causation-result relation may not exist between volatility and autocorrelation, though several researchers revealed generally negative relations between the two phenomena. Notice that returns show negative autocorrelation when stock return movements change directions more frequently than random, and, returns exhibit negative autocorrelation when volatility is high. Sentana and Wadhwani (1992) examine hourly data around the period of the October 1987 crash, daily data of Dow Jones returns from 1885 to 1928, the S&P composite from 1928 to 1962, and the CRSP value-weighted portfolio from 1962 to 1988. They have reported: "when volatility is low, stock returns at short horizons exhibit positive serial autocorrelation, but when volatility is rather high, returns exhibit negative autocorrelation." Under such situations, the absolute value of autocorrelation and volatility should be positively connected. Examining the estimated autocorrelation provides such evidence. The daily returns on most of the stocks are negatively autocorrelated during the time period. Of the 177 stocks, 145 exhibit negative autocorrelation by runs ratio tests and 140-exhibit negative autocorrelation by variance ratio tests. Moreover, the negative autocorrelation estimates are substantially more significant than that of positive autocorrelation estimates, e.g., the heteroskedasticity-consistent z-values average -2.01 for the negative autocorrelation estimates and 0.86 for the positive autocorrelation estimates. Obviously, there is a difference between the methodologies adopted by previous studies and this one, i.e., time series and cross section, respectively. The difference in methodologies should not contribute to the contrary results.

The negative connection between number of news and autocorrelation and the positive connection between volatility and autocorrelation imply a negative connection between the number of news items and volatility. This confirms my hypothesis that other things being equal, more frequent information should reduce volatility because a greater number of news tends to coexist with small pieces of news, and more frequently informed investors would not take drastic actions. This result is consistent with the findings of Khoo et al. (1993) that increased information reduces the volatility of Equity REIT (real estate investment trust) returns, and partially supports what Campbell and Hentschel (1992) have found.

Bank size generally has negative effects on autocorrelation; the market for big bank stocks tend to be more efficient than that for small ones. The relation between bank size and autocorrelation may not be linear, which is indicated by the fact that the variable assets-2 fits the data better, yielding the greatest coefficients of determination (r2) and t-values. Figure II shows the relation between bank size and autocorrelation. Note that the polynomial trend lines for autocorrelation reach their peaks at the beginning of the third percentile, or around $550 million of total assets. A possible explanation for the non-randomness in price changes of small stocks is that the market for small stocks is very thin. In such a thin market, sophisticated traders may not be able to make price changes independent by profiting from any dependence in successive price changes or in the process of generating new information about a stock.

[FIGURE II OMITTED]

Figure III indicates the relation between bank size and number of news items. Usually, large banks have greater impacts on the economy and have large numbers of shareholders, hence incur more analyst reports and more news. Some very small banks may also have more news reports due to their extraordinary profits or loses. The polynomial trend line for number of news items reaches its minimum at the end of the third percentile, or around $700 million of total assets. Right to this point, the larger the bank, the greater the number of news items. This phenomenon provides further evidence for the negative impact of more frequent news on autocorrelation.

[FIGURE III OMITTED]

Figure IV indicates the negative relation between bank size and their stock price volatility. Small bank stocks tend to be more volatile while large ones are less volatile. This supports the negative relation between bank size and autocorrelation, and the positive relation between stock price volatility and autocorrelation. The chart shows an exception that two stocks of medium size banks are the most volatile, due to their specific events.

[FIGURE IV OMITTED]

Trading volume is significantly negatively connected to autocorrelation and the relation is not linear, or autocorrelation decreases at decreasing rates as trading volume increases. The negative and nonlinear relation is consistent to what Campbell, Grossman and Wang (1993) have found. They test daily returns on a value-weighted index of stocks on the New York Stock Exchange and the American Stock Exchange. The result of their study shows that for large stock indices and individual stock returns, the first order autocorrelation tends to decline as volume increase, i.e., it is lower on high-volume days than on low-volume days. The difference is that their study uses the variables, volume and volume (2), while this study uses volume (-1.5) that results in the greatest coefficients of determination ([r.sup.2]) and t-values (2). Generally, as shown in Figure V, large bank stocks have greater trading volumes. high trading volume can provide a "thick" market, in which sophisticated traders may be able to profit from any dependence in successive price changes or to profit in the process of generating new information about a stock, hence making price changes random.

[FIGURE V OMITTED]

The coefficients for the variable rate of return are not significant though positive, which may imply an unclear relation between rate of return and autocorrelation. If a stock market becomes more efficient, more liquid, and less volatile, the required rate of return should be lower due to lower risk level, which would lead to relatively higher price to earnings level. The record high P/E ratios of US stocks for the last few years may partially reflect the impacts of the technological advances, and the fact that investors' expected rate of growth is higher than their required rate of return.

Figure VI shows the relation between bank size and rates of return. The rates of return for large banks with total assets greater than $3,000 million tend to fluctuate closely around a norm, and the average rate of their returns is the highest. Rates of return for medium size banks with total assets ranging from $500 million to $3,000 million exhibit three patterns. About a third of them fluctuate around a norm but not as close as that of the large banks, a third of them are above normal, and a third of them are below normal. For small banks with total assets less than $500 million, the rates of return tend to be further above or below the norm. The polynomial trend line depicts the relation between bank size and rates of return.

[FIGURE VI OMITTED]

IV. CONCLUSION

This article has provided convincing evidence for the positive impact of information frequency on market efficiency, i. e., first-order autocorrelation is lower for bank stocks with more news items and higher for stocks with less news items. Stated differently, a greater number of news items tend to reduce autocorrelation, hence increase market efficiency. This phenomenon may be explained by the generally random arrival of more frequent news. Greater number of generally random news offers more complete and timely information, which can lead to more frequently adjusted trading activities as investors make their trading decisions in response to the news. If trading activities reflect the generally random characteristics of news, price changes should be more independent with greater number of news.

Contrary to previous reports, autocorrelation and volatility exhibit a positive, nonlinear relation. Volatile price changes usually exhibit negative autocorrelation between returns hence high volatility can coexist with high negative autocorrelation. The negative connection between autocorrelation and volatility implies a negative connection between information frequency and volatility. Investors adjust their trading activities more frequently at smaller scales in response to more frequent, hence less shocking information, which should make the market less volatile. Further tests are required to determine the potential causes for relations between autocorrelation and volatility.

The connection between trading volume and autocorrelation is significantly negative and the relation is nonlinear, or autocorrelation decreases at decreasing rates as trading volume increases. A possible explanation is that large daily trading volume can provide a "thick" market, in which sophisticated traders may be able to profit from any dependence in successive price changes or to profit in the process of generating new information about a stock, hence making price changes more independent. Generally, larger banks have more news reports, their stocks have greater trading volumes, and their price changes tend to be more efficient and less volatile.

Although good theoretical explanations for the phenomena revealed by this study have yet to be obtained, these results add to our knowledge and to our questions about just what affects the behavior of asset prices in the short run, and about the dynamics of information flow, trading activities, and price behavior.

ACKNOWLEDGMENT

I thank the reviewer, Robert Everett, Nader Asgary, Christopher Annala and Mary Ellen Zuckerman for helpful comments.

REFERENCES

Albright, S. Christian, (1987). Statistics for Business and Economics (Macmillan, New York).

Campbell, John Y., Sanford J. Grossman, and Jiang Wang, (1993). Trading Volume and Serial Correlation in Stock Returns, Quarterly Journal of Economics 3, 905-934.

Campbell John Y. and Ludger Hentschel (1992). No News is Good News: an asymmetric model of changing volatility in stock returns, Journal of Financial Economics 31, 281-318.

Chiang, Thomas C., (1998). Stock Returns and conditional Variance-Covariance: Evidence from Asian Stock Markets, Emerging Markets: Finance and Investments, J. Jay Choi and John Doukas Eds. Greenwood Publishing Group Inc., Westport CT. 1998.

Cohen, K. J., G. A. Hawawini S. F. Maier, R. A. Schwartz and D. K. Whitcomb, (1980). Implications of Microstructure Theory for Empirical Research on Stock Price Behavior, Journal of Finance 35, 249-257.

Cohen, K. J., S. F. Maier, R. A. Schwartz and D. K. Whitcomb, (1986). The Microstructure of Securities Markets. Englewood Cliffs, N. J.: Prentice-Hall.

Conrad, Jennifer and Gautam Kaul, (1988). Time-Variation in Expected Returns. Journal of Business, 61, 409-425.

Ederington, L.H. and J.H. Lee, (1993). How markets process information: News releases and volatility, Journal of Finance 48, 1161-91.

Ederington, L.H. and J.H. Lee, (1995). The short-run dynamics of the price adjustment to new information, Journal of Financial and Quantitative Analysis 30, 117-34.

Fama, Eugene F., (1965). The Behavior of Stock Prices. Journal of Business 38, 34 - 105.

Fama, Eugene F., (1970). Efficient Capital Markets: A Review of Theory and Empirical Work. Journal of Finance 25, 383-417.

Khoo, T., D. Hartzell and M. Hoesli (1993). An Investigation of the Change in real Estate Investment Trust Betas, Journal of the American Real Estate and Urban Economics Association, 21(2): 107-130.

LeBaron, Black, (1992). Some Relations Between Volatility and Serial Correlation in Stock Market Returns, Journal of Business LXV, 199-219.

Liu, C. Y. and J. He. (1991). A Variance-Ratio Test of Random Walks in Foreign Exchange Rates. Journal of Finance. 46, 773-785.

Lo, Andrew W. and A Craig MacKinlay, (1988). Stock Market prices Do Not Follow Random Walks: Evidence From a Simple Specification Test, The Review of Financial Studies 1, 41-66.

McQueen, G., M. Pinegar and S. Thorley, (1996). Delayed reaction to good news and the cross-autocorrelation of portfolio returns, Journal of Finance 51, 889-919.

Ross, S.A., (1989). Information and volatility: The no arbitrage Martingale approach to timing and resolution irrelevancy, Journal of Finance 44, 1-17.

Sentana, Enrique, and Sushil Wadhwani, (1992). Feedback Traders and Stock Return Autocorrelations: Evidence from a Century of Daily Data, Economic Journal CII, 415-425.

ENDNOTES

(1) For the variance-ratio method, see Lo and Mackinlay (1988).

(2) This is estimated through Box-Cox transformation.

Anthony Yanxiang Gu, State University of New York, Geneseo

Advances in communication and information technologies are expected to have significant impacts on stock return behavior. As a major aspect of the advances, higher information frequency tends to reduce autocorrelation and volatility, or make the market more efficient and relatively more stable. The generally random arrival of more frequent information and thus more frequently adjusted trading activities at smaller scales may explain the negative connection between autocorrelation and information frequency. Autocorrelation and volatility exhibit a positive, nonlinear relation when stock price fluctuates more than randomly. The relation between autocorrelation and trading volume is negative and nonlinear.

INTRODUCTION

The quantity of information has been growing geometrically for the last few decades and is expected to increase even more rapidly in the future. Information affects stock return behavior through its influence on investors' expectations. If the assumption of random arrivals of information is valid, then ceteris paribus, more frequent information should make their "shocks" more random and less heavy. Thus, one can hypothesize that greater quantity of information would help to increase market efficiency and reduce market volatility.

There are numerous financial or economic studies on whether stock price changes follow a random walk or whether the stock market is efficient by testing autocorrelation between stock returns and the related factors. For example, Fama (1970) raises the efficient market hypothesis and states that if the market is efficient in the weak form, the information on past prices or returns should not be useful in achieving abnormal returns. As one of the earliest studies on market efficiency, Fama (1965) investigates the behavior of the daily closing prices of the 30 Dow Jones Industrials and finds evidence inconsistent with weak form market efficiency. His serial correlation tests reveal that the first-order autocorrelation of daily returns is positive for 23 of the 30 firms, but his runs tests reveal no significant autocorrelation. Lo and MacKinlay (1988) find that weekly returns on portfolios of NYSE stocks show consistent positive autocorrelation and the autocorrelation is stronger for portfolios of small companies. Similarly, Conrad and Kaul (1988) find that daily and Wednesday-to-Wednesday returns are positively autocorrelated, and more so for portfolios of small stocks.

However, all of the previous studies have focused on whether stock price movements are random or whether the markets are efficient. There is no work relating the quantity of information on stock price behavior, though there are some studies on stock reactions to news. Campbell and Hentschel (1992) examine the impact of the size of news on stock price behavior, Ross (1989), Ederington and Lee (1993, 1995) look at the relation between news release and stock price and volatility. McQueen, Pinegar and Thorley (1996) analyze the reaction of stocks to good news and the cross-autocorrelation of portfolio returns.

This study explores the impacts of information frequency or quantity of information, on stock price behavior and examines the relation between volatility, firm size, trading volume, rate of return and autocorrelation. Information frequency or the number of news items about publicly traded banks during a specified period of time is used as an explanatory variable to estimate the impact of greater information quantity on the behavior of stock returns. A further understanding of the behavior of bank stocks and of the related factors can help bank investors develop better investment strategies.

The plan of the paper is as follows. In Section II, we estimate the autocorrelation between daily returns on the bank stocks and present the results. In Section III we analyze the relations between autocorrelation and information frequency, return volatility, bank size and trading volume, and discuss the implications. We provide a conclusion in Section IV.

II. DATA AND TESTS

The Data

In the data set there are 177 bank stocks that traded for at least 250 days in the year of 1998. The list of the banks and their total assets as of the end of 1998 are from Thomson North American Financial Institutions Directory, Thompson Financial Publishing. Daily stock price and volume in the year of 1998 is from Yahoo.

The Variance-Ratio Test

Variance ratio and runs tests are performed to estimate autocorrelation between daily returns on the bank stocks. The use of a short (daily) horizon may reduce the cost of statistical imprecision.

Let [I.sub.t] represent the natural logarithm of a time series with nq + 1 observations. If [I.sub.t] is a pure random walk, the variance of its q-differences grows proportionally with the difference q (we test with q = 2). Hence, a random time series should exhibit a unit variance ratio. (1) A variance ratio that is greater than unity indicates positive auto-correlation and a variance ratio that is smaller than unity indicates negative auto-correlation. The variance-ratio, VR(q) is defined as:

VR (q) = [[sigma].sup.2](q)/[[sigma].sup.2](l) (1)

Where [[sigma].sup.2](q) is 1/q the variance of the q-differences and [[sigma].sup.2](1) is the variance of the first differences. And:

[[sigma].sup.2] (q) = 1/m [nq.summation over (t=q)] [([I.sub.t] - [I.sub.t-q] - q [??]).sup.2] (2)

where

m = q (nq - q + 1)(1 - q/nq)

and

[[sigma].sup.2](1) = 1/(nq - 1)[nq.summation over (t=1)] [([I.sub.t] - [I.sub.t-1] - [??]).sup.2] (3)

where

[??] = 1/nq ([I.sub.nq] - [I.sub.0])

[I.sub.0] and [I.sub.nq] are the first and last observations of the time series.

The asymptotic standard normal test statistics for the variance-ratio is derived by Lo and Mackinlay (1988) and modified by Liu and He (1991). Under the hypothesis of homoskedasticity the test statistic is:

z(q) = VR (q) - 1/[[phi](q)].sup.0.5] ~ N (0,1) (4)

Where,

[phi](q) = 2(2q - 1)(q - 1)/3q(nq)

The asymptotic standard normal test statistic for the heteroskedasticity-consistent estimator is:

[z.sup.*](q) = VR(q) - 1/[[[phi].sup.*](q)].sup.0.5] ~ N (0,1) (5)

where

[[phi].sup.*](q) = [q-1.summation over (j=1)][[2(q - j)/q].sup.2] [??](j)

and

[??](j) = [summation][([I.sub.t] - [I.sub.t-1] - [??]).sup.2][(I.sub.t-j] - [I.sub.t-j-1] - [??]).sup.2]/[summation][[([I.sub.t] - [I.sub.t-1] - [??]).sup.2]).sup.2]

The Runs Tests

The runs test is a non-parametric test used to detect the frequency of changes in the direction of a time series. As it is a non-parametric test, the runs test is not based on any finite-variance assumption and does not require an assumption about the distribution. Runs are defined here as the number of sequences of consecutive positive and non-positive (negative or zero) returns. The runs test tabulates and compares the number of runs in the sample against its sampling distribution under the random walk hypothesis. Suppose that each observation is independently and identically distributed. When the null hypothesis of randomness is true, according to Albright (1987), the mean or expected number of runs can be calculated as

E(R) = N + 2AB/N (6)

Where,

N = total number of positive and non-positive sequences in the sample, A = number of sequences of positive returns in the sample, and B = number of sequences of negative or zero returns in the sample

The standard error of number of runs can be calculated as

SE (R) = [square root of 2 AB (AB - N)/[N.sup.2](N - 1)] (7)

To test whether any apparent non-randomness is the result of chance alone, we use the statistic,

Z = R - E(R)/SE(R) (8)

Where,

R = number of actual runs in the sample.

The null hypothesis, [H.sub.0] (randomness) can be rejected at the a level if [absolute value of z] > [[alpha].z/2]. The test is a two-tailed test since there is evidence of non-randomness when R is too small or when R is too large. For a two-tailed test with [alpha] = 0.10, the tabulated z value we require is [z.sub.0.05] = 1.645, and with [alpha] = 0.05, the tabulated z value we require is [z.sub.0.025] = 1.96.

Negative z-values of the runs test, runs ratios less than unity and variance ratios greater than one indicate positive autocorrelation or that price increases and decreases in streams. Positive z-values or greater-than-unity runs ratios and variance ratios less than one indicate negative autocorrelation or that price movements change directions more frequently than random. The runs ratio is defined as the actual number of runs divided by the expected number of runs.

The tests reveal significant autocorrelation for most of the 177 bank stocks, which is supported by the z-values for the variance ratio and runs tests. Table 1 provides the descriptive statistics of the data and the estimated autocorrelation.

III. THE REGRESSION ANALYSIS AND IMPLICATIONS

Regression analysis is conducted to examine the impact of information frequency on market efficiency and the relations between bank size, return volatility, trading volume, and rate of return and autocorrelation. In the model, the dependent variable is the absolute value of the estimated variance ratio minus 1 and the absolute value of the estimated runs ratio minus 1. Using absolute value of the dependency measurements can measure the extent of deviation from randomness with the same scale, reveal both the direction and the magnitude of the effects of the independent variables on the level of autocorrelation. (Our purpose is to estimate the effects of the independent variables on deviation from efficiency, not on positive or negative autocorrelation. Since both positive and negative values of the dependent variables represent deviation from efficiency, and the independent variables, i.e., standard deviation, variance and volume, except return, all have positive values, using absolute values of the dependent variables can avoid possible distortion of the estimates. We have also used the actual values of the dependent variables but find no significant difference from using absolute values though.) Frequency of information (number of news items), annual average standard deviation and variance of consecutive two-day returns, bank size (total assets), average daily trading volume, and average rate of daily returns are used as explanatory variables. The annual average standard deviation of consecutive two-day returns is calculated as:

[sigma] = [N - 1.summation over (t=1)][square root of [([R.sub.t] - [bar.R]).sup.2]/N - 1 (9)

where,

[R.sub.i] is the rate of return of day i, [bar. R] is the average rate of return of day i and day i+1, and N is the total number of trading days in a year. Three reasons justify the use of standard deviation of consecutive two-day returns. First, it reflects the time-varying characteristic of volatility, hence the time-varying risk faced by investors. This point is stressed by some previous researchers (i.e., LeBaron, 1992, Campbell, et al, 1993, and Chiang, 1998) who use previous period's rates of return to approximate the changing variance in their GARCH models. Second, it is relevant because autocorrelation between returns of two consecutive days is being examined, and third, using it improves the regression, the coefficients of determination (r2) and the t-values are higher compared to that from using annual standard deviation of daily returns. The standard deviation and variance (s 2) are used as volatility measurements, we include both variables in the model to capture any nonlinearity that may exist in the relation between volatility and autocorrelation.

Table 2 presents the results of the regression analyses. Both models show that the number of news items has a significant negative impact on autocorrelation, or a greater number of news items tend to reduce autocorrelation hence increase market efficiency. This phenomenon may be explained by the generally random arrival of more frequent news. A greater number of generally random news items may lead to more frequently adjusted trading activities since investors make their trading decisions in response to news. If trading activities reflect the characteristics of news, i.e., generally random, more frequent, and less shocking, price changes should be more independent and less volatile. Hence, highly advanced communication and information technologies might be an explanation as to why advanced markets are more efficient and less volatile than less developed and emerging markets.

Autocorrelation is positively related to volatility for this data set, and the relation is nonlinear, which is indicated by the significant positive coefficients for standard deviation and the significant negative coefficients for variance. Figure I shows the relation between autocorrelation and volatility. The positive relation between autocorrelation and volatility that found by this study is generally contrary to previous reports while the non-linearity of the relation revealed in this study supports the finding of LeBaron (1992).

[FIGURE I OMITTED]

LeBaron (1992) tests daily and weekly data of the S&P composite index from January 1928 through May 1990, the Dow Jones Index constructed by Schwert (1990), and weekly returns of IBM Stock including dividends. The results of his research indicate that first-order autocorrelation is larger during periods of lower volatility and smaller during periods of higher volatility for both daily and weekly returns. And, the relation between volatility and autocorrelation may not be linear.

Non-trading may be an explanation for the relation between autocorrelation and volatility (Cohen, et al., 1980, 1986, and LeBaron 1992). Some stocks do not trade close to the end of day, which will cause positive correlation in the stock return as information arriving at the end of the day appears in these stocks on the following day. The level of this non-trading should be inversely related to overall trading volume. Since there is a strong positive relation between volatility and volume, non-trading, and therefore autocorrelation, would be higher during periods of lower volatility. Another explanation is the accumulation of news. If news items arrive slowly and in small bits, a trader's optimal behavior may be to "do nothing" until they have received enough information. This optimal non-trading may vary inversely with the level of volatility if this is related to the current rate of information flow.

However, there is no explanation about the positive relation between autocorrelation and volatility has been found from previous studies. A causation-result relation may not exist between volatility and autocorrelation, though several researchers revealed generally negative relations between the two phenomena. Notice that returns show negative autocorrelation when stock return movements change directions more frequently than random, and, returns exhibit negative autocorrelation when volatility is high. Sentana and Wadhwani (1992) examine hourly data around the period of the October 1987 crash, daily data of Dow Jones returns from 1885 to 1928, the S&P composite from 1928 to 1962, and the CRSP value-weighted portfolio from 1962 to 1988. They have reported: "when volatility is low, stock returns at short horizons exhibit positive serial autocorrelation, but when volatility is rather high, returns exhibit negative autocorrelation." Under such situations, the absolute value of autocorrelation and volatility should be positively connected. Examining the estimated autocorrelation provides such evidence. The daily returns on most of the stocks are negatively autocorrelated during the time period. Of the 177 stocks, 145 exhibit negative autocorrelation by runs ratio tests and 140-exhibit negative autocorrelation by variance ratio tests. Moreover, the negative autocorrelation estimates are substantially more significant than that of positive autocorrelation estimates, e.g., the heteroskedasticity-consistent z-values average -2.01 for the negative autocorrelation estimates and 0.86 for the positive autocorrelation estimates. Obviously, there is a difference between the methodologies adopted by previous studies and this one, i.e., time series and cross section, respectively. The difference in methodologies should not contribute to the contrary results.

The negative connection between number of news and autocorrelation and the positive connection between volatility and autocorrelation imply a negative connection between the number of news items and volatility. This confirms my hypothesis that other things being equal, more frequent information should reduce volatility because a greater number of news tends to coexist with small pieces of news, and more frequently informed investors would not take drastic actions. This result is consistent with the findings of Khoo et al. (1993) that increased information reduces the volatility of Equity REIT (real estate investment trust) returns, and partially supports what Campbell and Hentschel (1992) have found.

Bank size generally has negative effects on autocorrelation; the market for big bank stocks tend to be more efficient than that for small ones. The relation between bank size and autocorrelation may not be linear, which is indicated by the fact that the variable assets-2 fits the data better, yielding the greatest coefficients of determination (r2) and t-values. Figure II shows the relation between bank size and autocorrelation. Note that the polynomial trend lines for autocorrelation reach their peaks at the beginning of the third percentile, or around $550 million of total assets. A possible explanation for the non-randomness in price changes of small stocks is that the market for small stocks is very thin. In such a thin market, sophisticated traders may not be able to make price changes independent by profiting from any dependence in successive price changes or in the process of generating new information about a stock.

[FIGURE II OMITTED]

Figure III indicates the relation between bank size and number of news items. Usually, large banks have greater impacts on the economy and have large numbers of shareholders, hence incur more analyst reports and more news. Some very small banks may also have more news reports due to their extraordinary profits or loses. The polynomial trend line for number of news items reaches its minimum at the end of the third percentile, or around $700 million of total assets. Right to this point, the larger the bank, the greater the number of news items. This phenomenon provides further evidence for the negative impact of more frequent news on autocorrelation.

[FIGURE III OMITTED]

Figure IV indicates the negative relation between bank size and their stock price volatility. Small bank stocks tend to be more volatile while large ones are less volatile. This supports the negative relation between bank size and autocorrelation, and the positive relation between stock price volatility and autocorrelation. The chart shows an exception that two stocks of medium size banks are the most volatile, due to their specific events.

[FIGURE IV OMITTED]

Trading volume is significantly negatively connected to autocorrelation and the relation is not linear, or autocorrelation decreases at decreasing rates as trading volume increases. The negative and nonlinear relation is consistent to what Campbell, Grossman and Wang (1993) have found. They test daily returns on a value-weighted index of stocks on the New York Stock Exchange and the American Stock Exchange. The result of their study shows that for large stock indices and individual stock returns, the first order autocorrelation tends to decline as volume increase, i.e., it is lower on high-volume days than on low-volume days. The difference is that their study uses the variables, volume and volume (2), while this study uses volume (-1.5) that results in the greatest coefficients of determination ([r.sup.2]) and t-values (2). Generally, as shown in Figure V, large bank stocks have greater trading volumes. high trading volume can provide a "thick" market, in which sophisticated traders may be able to profit from any dependence in successive price changes or to profit in the process of generating new information about a stock, hence making price changes random.

[FIGURE V OMITTED]

The coefficients for the variable rate of return are not significant though positive, which may imply an unclear relation between rate of return and autocorrelation. If a stock market becomes more efficient, more liquid, and less volatile, the required rate of return should be lower due to lower risk level, which would lead to relatively higher price to earnings level. The record high P/E ratios of US stocks for the last few years may partially reflect the impacts of the technological advances, and the fact that investors' expected rate of growth is higher than their required rate of return.

Figure VI shows the relation between bank size and rates of return. The rates of return for large banks with total assets greater than $3,000 million tend to fluctuate closely around a norm, and the average rate of their returns is the highest. Rates of return for medium size banks with total assets ranging from $500 million to $3,000 million exhibit three patterns. About a third of them fluctuate around a norm but not as close as that of the large banks, a third of them are above normal, and a third of them are below normal. For small banks with total assets less than $500 million, the rates of return tend to be further above or below the norm. The polynomial trend line depicts the relation between bank size and rates of return.

[FIGURE VI OMITTED]

IV. CONCLUSION

This article has provided convincing evidence for the positive impact of information frequency on market efficiency, i. e., first-order autocorrelation is lower for bank stocks with more news items and higher for stocks with less news items. Stated differently, a greater number of news items tend to reduce autocorrelation, hence increase market efficiency. This phenomenon may be explained by the generally random arrival of more frequent news. Greater number of generally random news offers more complete and timely information, which can lead to more frequently adjusted trading activities as investors make their trading decisions in response to the news. If trading activities reflect the generally random characteristics of news, price changes should be more independent with greater number of news.

Contrary to previous reports, autocorrelation and volatility exhibit a positive, nonlinear relation. Volatile price changes usually exhibit negative autocorrelation between returns hence high volatility can coexist with high negative autocorrelation. The negative connection between autocorrelation and volatility implies a negative connection between information frequency and volatility. Investors adjust their trading activities more frequently at smaller scales in response to more frequent, hence less shocking information, which should make the market less volatile. Further tests are required to determine the potential causes for relations between autocorrelation and volatility.

The connection between trading volume and autocorrelation is significantly negative and the relation is nonlinear, or autocorrelation decreases at decreasing rates as trading volume increases. A possible explanation is that large daily trading volume can provide a "thick" market, in which sophisticated traders may be able to profit from any dependence in successive price changes or to profit in the process of generating new information about a stock, hence making price changes more independent. Generally, larger banks have more news reports, their stocks have greater trading volumes, and their price changes tend to be more efficient and less volatile.

Although good theoretical explanations for the phenomena revealed by this study have yet to be obtained, these results add to our knowledge and to our questions about just what affects the behavior of asset prices in the short run, and about the dynamics of information flow, trading activities, and price behavior.

ACKNOWLEDGMENT

I thank the reviewer, Robert Everett, Nader Asgary, Christopher Annala and Mary Ellen Zuckerman for helpful comments.

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ENDNOTES

(1) For the variance-ratio method, see Lo and Mackinlay (1988).

(2) This is estimated through Box-Cox transformation.

Anthony Yanxiang Gu, State University of New York, Geneseo

Table 1 Descriptive Statistics of the Data and Estimated Auto-Correlation This table presents the descriptive statistics of the data and the estimated autocorrelation coefficients using variance-ratio and runs tests. Variance ratio is defined as VR(q) = variance (q)/ variance(1). Where, q represents number of differences or lags, and runs ratio is defined as the actual number of runs divided by the expected number of runs. Mean Stdev. Maximum Minimum Number of News Items 9.33 8.02 65.00 0.00 Total Assets ($Billion) 17.64 52.91 617.68 0.07 Volume (100 shares) 203919 673349 6919476 979 Daily Rate of Return -0.0001 0.0009 0.0021 -0.0051 Return Volatility (s) 0.03 0.01 0.07 0.01 Absolute Value of (RR-1) 0.11 0.07 0.31 0.00 Absolute Value of (VR-1) 0.15 0.12 0.55 0.00 Table 2 Estimation Results This table presents the results of the regression analysis of the effect of information frequency (number of news), return volatility, bank size (assets), trading volume and rate of return on autocorrelation. Dependent Independent Variables Variable intercept no. of news stdev. absolute value of -0.0288 -0.0014 7.0882 (runs ratio--1) (-0.6448) (-2.0997) ** (2.5929) *** absolute value of -0.1550 -0.0040 17.9667 (variance ratio--1) (-2.3027) (-4.0291) *** (4.3573) *** Dependent (b) [(assets). (c) [(volume). Variable (a) variance sup.-2] sup.-1.5] absolute value of -0.6434 -3.8838 2.5446 (runs ratio--1) (-1.6174) * (-1.7030) * (2.4969) *** absolute value of -2.0162 -3.9491 5.9978 (variance ratio--1) (-3.3604) *** (-1.1480) (3.9019) *** Dependent Variable return Adj. [r.sup.2] absolute value of 3.4035 0.1423 (runs ratio--1) (0.5744) absolute value of 7.4646 0.2733 (variance ratio--1) (0.8351) (a) the estimated coefficients are divided by 100 (b) in $10,000,000 (c) in 100 shares t-value in parenthesis. * significant at 0.1 level ** significant at 0.05 level *** significant at 0.01 level

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