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A.3. Tests for the Absolute Values of Log-Returns

Table V provides autocorrelation results for the absolute value of log-returns in similar manner. However, as will be discussed below, the results are even more contrasting than that in Table IV.

In Panel A, all the stocks and indices have significant positive serial correlation while insignificant PAC estimates are only displayed in lag 5 for both FARO and LION. Supporting above result, Q values provide evidence against the null hypothesis of no autocorrelation. Therefore, absolute value of daily log-returns exhibit stronger serial dependence than in Table III and IV, and autocorrelations are strictly positive for all stocks and indices. Coming to the absolute value of monthly log-returns, only FEIC displays significant individual and joint serial correlation. NAN D1 also displays a significant Q value in lag 2 at 5% level, but it is insignificant at 1% level.

Based on the above evidence, two consistent conclusions can be made at this point. First of all, by changing ingredients in our test from log-returns to squared log-returns and absolute value of log-returns, more positive serial correlation can be observed, especially in daily data. Therefore, return variances are more correlated. Secondly, monthly returns tend to follow a random walk model better than daily returns.

A.4. Correlation Matrix of Stocks and Indices

Table VI presents the correlation matrix for all stocks and indices. As is shown in Panel A for daily result, all of the correlations are positive, ranging from 0.0551 (LION-FARO) to 0.5299 (NAN D10-FEIC). Within individual stocks, correlation coefficients do not differ a lot. The highest correlation is between FEIC and FARO with only 0.1214, indicating a fairly weak relationship between individual stocks returns. However, in terms of stock-index relationships, they differ drastically from 0.0638 (NAN D10-FARO) to 0.5299 (NAN D10-FEIC). While the positive correlation implies that the three stocks follow the indices in the same direction, the extent to which they will move with the indices is quite different, indicating different levels of risk with regard to different stock. Finally, we find that the correlation between NAN D10 and NAN D1 is the second highest at 0.5052.

Panel B provides the correlation matrix for monthly data. Similar to results for daily data, negative correlation is not observed. The highest correlation attributes to that between NAN D10 and FEIC (0.7109) once again, but the lowest is between LION and FEIC (0.1146) this time. Compared with results in Panel A, correlation within individual stocks is slightly higher on average. The improvement in correlation is even more obvious between stocks and indices. It implies that stock prices can change dramatically from day to day, but they tend to follow the movement of indices in a longer horizon. Finally, the correlation between two indices is once again the second highest at 0.5116, following that between NAN D10 and FEIC. It is also found that the correlation between indices improves only marginally when daily data are replaced by monthly data, indicating a relatively stable relationship between indices.

B. Variance Ratio Tests

The results of variance ratio tests are presented in Table VII for each of the three stocks and two decile indices. The test is designed to te