We first estimate a standard regression equation on total trading cost based on the regression approach used in Keim and Madhavan (1997) and Jones and Lipson (1999).28 From the de- terminants of trading costs in these studies we include as explanatory variables: a variable for order size, reflecting the fact that large orders are more expensive than small orders, a variable for liquidity, reflecting a negative relationship between execution costs and stock liquidity, a
27In fact this strategy was described to us at a conference after we presented our paper, how one could “ping” a
crossing network by sending a small order, and use the lack of success in the cross as a buy signal. (The term “ping” is presumably from the UNIX program used to test communication lines, and is actually a very apt name for such a strategy. The program ping sends a short message to another machine on a communication network and asks for a response. The receipt of the response is a confirmation that there is a way to get to the other machine through the communication network.)
28Keim and Madhavan (1997) examine the magnitude and determinants of transaction costs for a sample of insti-
tutional traders with different investment styles. Jones and Lipson (1999) compare transaction costs across NYSE, NASDAQ and AMEX using a sample of institutional equity orders in firms that switch exchanges.
variable for total market activity, reflecting the potential greater ease of trading when market ac- tivity is high, a variable for “adverse momentum,” reflecting the greater difficulty of executing a buy order when prices are rising, a variable for intraday volatility, reflecting the fact that it is more difficult to trade when markets are volatile, and the inverse of the stock price, reflecting the effects of general price movements on proportional costs.29
We estimate two regression equations. In the first we use the total trading costs of all orders as the dependent variable, and include dummies for the externally crossed orders and the market orders. Since our cost estimates for the internally crossed orders are the most robust, we run a second regression where we only consider these orders.
Table 2.5: Regression analysis of total trading costs for all orders
The table reports the results from estimation of the regression model
TCi = β+ βIPi+ βln(MCapi) + βln(Ordi) + βln(MktV lmi,t−) +βRi,t−,t−+ βHLi,t−+ βDiEC+ βDMi + βDPi+ εi
where, for trade i, IPiis the inverse of the price per share of the stock traded, MCapiis the market capitalization of the stock traded, Ordiis the order size measured as number of stocks, MktV lmi,t−is the number of stocks traded on the NYSE on the day before the transaction, Rt−,t−is total returns over the two days preceding the transaction, HLi,t−is the difference between the highest and lowest mid quote on the day before the transaction. DEC
i is a dummy variable equal to one for stocks that were externally crossed, D M i is a dummy variable equal to one for stocks that were bought in the market and DP
i is a dummy variable equal to one if the order is partially filled. ln() is the natural logarithm. The model is estimated using all orders in the data sample for which we can extract returns data and data on market capitalization from Datastream. In the table the first column lists the variable, the second the coefficient estimate, the third the estimated standard deviation, the fourth the probability value of the coefficient being nonzero, and the last column the mean of the explanatory variable.
Dependent variable: TC
coeff (stdev) pvalue mean Constant -0.0010 (0.0039) 0.79 IPi,t -0.1693 (0.0259) 0.00 0.0248 ln(MCapi) -0.0035 (0.0006) 0.00 9.0354 ln(Ordi) 0.0028 (0.0004) 0.00 8.2910 ln(Voli,t−) 0.0012 (0.0004) 0.00 13.1239 Ri,t−,t− 0.0003 (0.0001) 0.04 0.2684 HLi,t− 0.0000 (0.0002) 0.96 1.2350 DEC -0.0061 (0.0011) 0.00 0.0987 DM 0.0014 (0.0009) 0.12 0.1704 n 3516 R 0.03 Average (TC) 0.0012
Table 2.5 presents the estimated coefficients of the regression model on all orders. The first thing to note is that the part of the total variation in trading costs explained by the independent variables is very small. This is natural since most of the explanatory variables measures trade difficulties in the primary market which by construction should be less important in a crossing network. The coefficients of stock liquidity and order size are both significant and have the
expected signs. A positive coefficient of trading volume the day before the transaction is also significant, indicating higher costs the more popular the stock has been lately in the primary market. The size of the dummies are supposed to capture any “order form” effects on trading costs that are unrelated to the explanatory variables.30 The dummy variables for externally
crossed orders is negative and significant, indicating lower costs for these orders after controlling for the trade difficulty variables. As mentioned before, however, the cost estimates of both externally crossed orders and market trades should be interpreted with great caution due to the few dates on which they were traded in our sample.
Table 2.6: Regression analysis of total trading costs for internally crossed orders only
The table reports results from estimation of the regression
TCi = β+ βIPi+ βln(MCapi) + βln(Ordi) + βln(MktV lmi,t−) +βRi,t−,t−+ βHLi,t−+ εi,
where, for trade i, IPiis the inverse of the price per share of the stock traded, MCapiis the market capitalization of the stock, Ordiis the order size measured as number of stocks, MktV lmi,t−is the number of stocks traded on the NYSE/NASDAQ on the day before the transaction, Ri,t−,t−is total returns over the two days preceding the transaction, and HLi,t−is the difference between the highest and lowest mid quote on the day before the transaction. ln() is the natural logarithm. The model is estimated using all internally crossed orders in the data sample for which we can extract returns data and data on market capitalization from Datastream. In the table the first column lists the variable, the second the coefficient estimate, the third the estimated standard deviation, the fourth the probability value of the coefficient being nonzero, and the last column the mean of the explanatory variable.
Dependent variable: TC
coeff (stdev) pvalue mean Constant 0.0012 (0.0044) 0.79 IPi,t -0.2125 (0.0293) 0.00 0.0246 ln(MCapi) -0.0042 (0.0006) 0.00 9.0890 ln(Ordi) 0.0035 (0.0005) 0.00 8.3099 ln(Voli,t−) 0.0010 (0.0004) 0.02 13.2048 Ri,t−,t− 0.0003 (0.0001) 0.01 0.4685 HLi,t− -0.0000 (0.0002) 0.86 1.2513 n 2917 R 0.03 Average (TC) 0.0009
Table 2.6 presents the estimated coefficients of the regression model on the total costs of in- ternal crosses. The only difference from the results of the estimation of the regression model on all orders is that the positive coefficient for adverse momentum becomes significant, indicating that stocks that did well recently are more costly to buy in the crossing network.
One problem with the regression analysis above is that the result whether a stock was crossed or not is given as an exogenous variable. In section 5.3 below we estimate a limited dependent variable model where we treat the cross dummy as the dependent variable. This is more correct in that we assume that the probability of success in the crossing network is endogenous.
30In the cost estimation in section 4.1, the comparison of costs across trading venues does not control for differences
in trade difficulty between venues. If e.g. the market orders were all large orders, and large orders are more difficult to fill, this could cause the results.