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.
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
II. DATA AND TESTS
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
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)
m = q (nq - q + 1)(1 - q/nq)
[[sigma].sup.2](1) = 1/(nq - 1)[nq.summation over (t=1)]
[([I.sub.t] - [I.sub.t-1] - [??]).sup.2] (3)
[??] = 1/nq ([I.sub.nq] - [I.sub.0])
[I.sub.0] and [I.sub.nq] are the first and last observations of the
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
z(q) = VR (q) - 1/[[phi](q)].sup.0.5] ~ N (0,1) (4)
[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)
[[phi].sup.*](q) = [q-1.summation over (j=1)][[2(q - j)/q].sup.2]
[??](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] -
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)
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)
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] =
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)
[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
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
[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]
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.
I thank the reviewer, Robert Everett, Nader Asgary, Christopher
Annala and Mary Ellen Zuckerman for helpful comments.
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.
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,
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,
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.
(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
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
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
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) ***
(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) ***
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