# The (implicit) cost of equity trading at the Oslo Stock Exchange. What does the data tell us?

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7 Figure 1 Time series evolution of bid/ask Spread Average Median The figures show the average (top) and median (bottom) time series of the (kroner) bid/ask spread. For each stock we calculate the quarterly average bid/ask spread using all dates in a quarter. We then average these quarterly averages across stocks each quarter. The average on the top is trimmed by removing the most extreme observations on each side. 7

8 Figure 2 Time series evolution of relative bid/ask spread Average Median The figures show the average (top) and median (bottom) time series of the relative bid/ask spread. For each stock we calculate the quarterly average relative bid/ask spread using all trade dates in a quarter. We then average these quarterly averages across stocks. The average on the top is trimmed by removing the most extreme observations on each side at each date. 8

9 Figure 3 Time series evolution of Roll measure Average Median The figures show the average (top) and median (bottom) time series of the Roll measure of transaction. For each stock we calculate the annual estimate of the Roll measure using all trade dates in the year. We then average these annual averages across stocks. The average on the top is trimmed by removing the most extreme observations on each side at each date. 9

10 costs that can be calculated using lower frequency data, such as daily returns. The idea of the model is to estimate a threshold where transaction costs are higher than the cost of not updating the price (by trading). To understand the LOT measure, let us start by assuming there are, and suppose returns are generated according the usual market model R jt = a j + b j Rmt + ε jt where R jt is the return on stock j at time t, Rmt is the corresponding return on the market portfolio, a j and b j are (stock specific) constants, and ε jt an error term. For any change in the market return R mt we should expect a corresponding change in the return R jt of stock j. If we now posit a (constant) transaction cost we would only expect a change in R jt when the change in R mt is large enough to outweigh the transaction cost. Lesmond et al. (1999) propose a limited dependent variable model where observed returns R jt are related to the true returns R jt as follows where R jt = β j R mt + ε jt R jt = R jt α 1j if R jt < α 1j R jt = 0 if α 2j R jt α 1j R jt = R jt α 2j if R jt > α 2j The transaction costs are represented by the constants α 1j and α 2j for each stock j. The LOT measure of trading costs are found by estimating the thresholds α 1j and α 2j. These are found by a maximum likelihood formulation by assuming Gaussian errors. From this one gets estimates α 1j and α 2j. The difference LOT j = α 2j α 1j is the estimate of the round trip transaction cost for this stock. In Panel C of table 1 we show averages of estimated LOT measures. We see that the implicit transaction costs are much higher than both the relative bid/ask spreads and the Roll estimates. But, the most interesting observation is a comparison of the time series of this cost measure with the other two. Although they have been calculated using very different methods, and even different base data (spreads and returns), they very much agree on the time periods in which costs are low and when they are high. The same pattern of low costs in the late eighties and nineties and the current time, and high costs in the early eighties, nineties and just after

11 Figure 4 Time series evolution of the LOT measure Average Median The figures show the average (top) and median (bottom) time series of the Lesmond et al. (1999) measure of transaction costs. For each stock we calculate the annual estimate of the Roll measure using all trade dates in the year. We then average these annual averages across stocks. The average on the top is trimmed by removing the most extreme observations on each side at each date. 11

13 Figure 5 Time series evolution of cost measures size sorted portfolios BA spread (small firms) (large firms) LOT (small firms) (large firms) Roll (small firms) (large firms) Medians for four size sorted portfolios for each of the three cost measures: Relative B/A spread, 13

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