The aim of this project is the cross-sectional analysis of data collected from different exchange venues for different stocks, obtained from the Trades and Quotes (TAQ) Database.
The data set includes information for trades, BBO and quotes of 10 stocks (BAC, CCU, DE, EXXI, KLAC, KO, MIPS, MS, NCR, SSCC) gathered from 10 venues (NYSE Amex, Boston, Cincinnati, NASD ADF and TRF, Chicago, NYSE, Pacific (NYSE Arca), NASD, X Philadelphia, CBOE), and reported to the Consolidated Quote System.
The original TAQ data set can be found here:
http://www.2shared.com/file/o4aX2Wvn/20110201_MS_trades.html
http://www.2shared.com/file/E3RILlc5/bbo.html
http://www.2shared.com/file/h8ON3AJT/quotes.html
http://www.2shared.com/file/nUridLRq/trades.html
http://www.2shared.com/file/o4aX2Wvn/20110201_MS_trades.html
http://www.2shared.com/file/E3RILlc5/bbo.html
http://www.2shared.com/file/h8ON3AJT/quotes.html
http://www.2shared.com/file/nUridLRq/trades.html
The code is self-sufficient, in the sense that you can just run it and you will obtain all the results presented, as long as you save the 20110201_MS_trades.csv file in the same folder as all the other trades files and change the paths for the data files in the code file accordingly.
(a)
First, the Market Share (MS) of each stock is computed as the share of the Market Cap of one stock on the Total Market Cap. Denoting price with P and size with S, the Market Share for stock i is given by
where N = 10. The following table and figure reproduce the results for each stock.
Table 1 - Market Share for the ten stocks
Stock | MS (%) |
BAC | 61.45% |
CCU | 0.04% |
DE | 11.58% |
EXXI | 0.80% |
KLAC | 2.73% |
KO | 10.30% |
MIPS | 0.87% |
MS | 7.09% |
NCR | 0.52% |
SSCC | 4.60% |
Figure 1 - Market Share for the ten stocks
From the results, it is possible to conclude that BAC plays the major role as for the share of the total Market Cap among the considered stocks. Also, DE and KO withhold a Market Share of about 10%.
(b)
Second, the percentages of sub-penny transactions occurring for each stock are reported in the table below.
Table 2 - Percentage of sub-penny transactions for the ten stocks
Stock | PSPE (%) |
BAC | 7.56% |
CCU | 4.58% |
DE | 4.33% |
EXXI | 2.31% |
KLAC | 2.87% |
KO | 3.91% |
MIPS | 6.72% |
MS | 3.06% |
NCR | 3.93% |
SSCC | 1.08% |
Figure 2 - Percentage of sub-penny transactions for the ten stocks
(c)
In order to assess how the share of D transactions (occurring on the NASD ADF and TRF markets) (SD) depends on (i) average bid-ask spread (BAS), (ii) realized mid-quote volatility (MQV), (iii) average price (AP), (iv) market cap (MC), and (v) trading volume (TV), the following regression was carried out
and the results are provided in the following tables.
Table 3 - OLS estimation results for the single coefficients
OLS | t | p-value | |
Constant | 4.77E-01 | 1.54E+01 | 5.24E-05 |
BAS | -1.41E+00 | -2.10E+00 | 5.18E-02 |
MQV | 3.45E-04 | 1.24E+00 | 1.41E-01 |
AP | -2.74E-03 | -3.15E+00 | 1.72E-02 |
MC | -6.69E-11 | -1.63E+00 | 8.97E-02 |
TV | 1.47E-09 | 2.42E+00 | 3.62E-02 |
Table 4 - OLS estimation results for the regression
adj R2 | F | p-value |
2.45E-01 | 1.58E+00 | 3.38E-01 |
From the analysis of the results, it is possible to conclude that, at a 5% significance level, average price, market cap and trading volume (together with the constant term) significantly affect the share of D transactions, whereas average bid-ask spread would pass the 10% significance test; instead, realized mid-quote volatility do not significantly explain the variations occurring in SD. Nevertheless, the adjusted coefficient of determination, which accounts for the few degrees of freedom of the model (we have but 10 data points, and we are using 5 explanatory variables), implies that the variations in the regressors explain roughly 25% of the variations in the dependent variable. Finally, through the F-test, it follows that the regression as a whole is not statistically significant at the 5% significant value.
(d)
Now, we want to assess how the percentage of sub-penny executions (PSPE) is affected by the same independent variables as in part (c); thus, the following regression was carried out:
and the results are provided in the following tables.
Table 5 - OLS estimation results for the single coefficients
OLS | t | p-value | |
Constant | 3.19E-02 | 4.70E+00 | 4.66E-03 |
BAS | 8.70E-02 | 5.94E-01 | 2.92E-01 |
MQV | 3.16E-05 | 5.19E-01 | 3.16E-01 |
AP | 2.42E-04 | 1.28E+00 | 1.35E-01 |
MC | -6.97E-11 | -7.75E+00 | 7.48E-04 |
TV | 1.25E-09 | 9.43E+00 | 3.52E-04 |
Table 6 - OLS estimation results for the regression
adj R2 | F | p-value |
-2.14E-01 | 6.83E-01 | 6.62E-01 |
From the analysis of the results, it is possible to conclude that, at a 5% significance level, only market cap and trading volume (together with the constant term) significantly affect the share of D transactions, whereas average bid-ask spread, realized mid-quote volatility and average price do not significantly explain the variations occurring in SD. Moreover, the adjusted coefficient of determination now assumes a negative value: it is telltale indeed as for the low (almost nil) explanatory power of the regression. Finally, through the F-test, it follows that the regression as a whole is not statistically significant at the 5% significant value (in particular, it is even less significant than the regression in part (c)).
