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c behind this is that a stock which is slow to incorporate market information is less efficient than a stock which responds quickly to market movements.

S&P 500 index is employed in delay test to examine the sensitivity of stock returns to market information. For each stock and decile index, both restricted and unrestricted models are estimated from January 2000 to December 2005. The unrestricted model is given by:

(4) where is the log-return on stock i at time t; is the market log-return (return for S&P 500 index) at time t; is the lagged market return; is the coefficient on the lagged market return; and is the lag which is 1, 2, 3, 4 for the daily data and 1, 2, 3 for the monthly data. The restricted model is as follows which sets all to be zero:

(5) Delay is then calculated based on adjusted R-squares from above regressions as follows:

(6) An alternative scaled measure of delay is given by:

(7) Both measures are reported in a way that the larger the calculated delay value, the more return variation is explained by lagged market returns and thus the more delayed response to the market information.

III.描述统计学-III. Descriptive Statistics

A. Daily frequencies

Table I shows the summary statistic of daily returns for the three stocks and two decile indices. The highest mean return is for FARO (0.0012), whereas the lowest mean return is for NAN D10 (0.0000). In terms of median return, NAN D1 (0.0015) outperforms all the other stocks. Both the highest maximum return and the lowest minimum return (0.2998 and -0.2184, respectively) are for FARO, corresponding to its highest standard deviation (0.0485) among all, indicating that FARO is the most volatile in returns. On the other hand, both the lowest maximum return and highest minimum return (0.0543 and -0.0675, respectively) are for NAN D10. However NAN D10 is only the second least volatile, while the lowest standard deviation is for NAN D1 (0.0108). Figure 1 and 2 presents the price level of the most and least volatile index (stock). All the above observations remain true if we change from log-return basis to a simple return basis.

In terms of the degree of asymmetry of the return distributions, all stocks and indices are positively skewed, with the only exception of NAN D1. The positive skewness implies that more extreme values are in the right tail of the distribution, i.e. stocks are more likely to have times when performance is extremely good. On the other hand, NAN D1 is slightly negatively skewed, which means that returns are more likely to be lower that what is expected by normal distribution. In measuring the 'peakedness' of return distributions, positive excess kurtosis is observed in all stocks and indices, also known as a leptokurtic distribution, which means that returns either cluster around the mean or disperse in the two ends of the distribution. All the above observations can be used to conclusively reject the null hypothesis that daily returns are normally distributed. What' more, results from Jarque-Bera test provide supportive evidence for rejection of the normality hypothesis at all significant levels for all stocks and indices.

B. Monthly frequencies

Descriptive statistics of monthly returns are likewise presented in Table II. Most of the above conclusions reached for daily returns are