Transaction Cost Analysis A-Z

Transaction Cost Analysis A-Z — November 2008

VI. A New Framework: the EBEX Indicators

still depend on market conditions as well as price volatility. If the price range was less than 40bp yesterday, a value of 30bp indicates that the order got one of the least favourable prices of the day. Furthermore, if the price range today is much larger than it was yesterday, a value of 40bp implies better trading performance, even if the deviation from the VWAP is higher. So, benchmarks do not make comparison easy at all. By contrast, if the absolute EBEX is 0.65 today and was 0.45 yesterday, we can conclude that the quality of execution is better today. The second advantage of the absolute EBEX is that it makes possible evaluation of intermediary trading performance consistence. This evaluation can be done easily by using a sufficiently large sample of trades executed by the intermediary and analysing the distribution of absolute EBEX. Traders who exhibit little deviation in performance measures are consistent while traders who often get extreme scores are gambling or taking risks. Moreover, comparative analysis across several intermediaries may easily be conducted based on absolute EBEX distributions wherein the score of each intermediary is defined as a risk-adjusted trading performance computed as the mean value of EBEX divided by its standard deviation. We illustrate this approach with the following example. Suppose two brokers who executed approximately the same number of orders on similar stocks. According to their respective absolute EBEX distribution, broker A exhibits an average absolute EBEX of 0.65 for a standard deviation of 0.45 while broker B provides an average EBEX score of 0.55 for a standard deviation of 0.33. These figures

Figure 14: Interpretation of the Absolute EBEX indicator

The closer to 0 EBEX

abs is, the worse the execution!

Among all the "similar" trades of the interval, most got a price better than the trade price of the broker. A terrible performance!

0

1

The closer to 1 EBEX

abs is, the better the execution! Among all the "similar" trades of the interval, few got a price better than the trade price of the broker. An excellent performance!

The absolute EBEX indicator is superior to any other performance measure based on benchmark comparison because it provides a meaningful metric that is consistent over time and across securities. Two simple examples illustrate this advantage. Example 1: Suppose two orders for which the benchmark comparison to the VWAP is 15bp in stock A and 40bp in stock B. Both executions are less favourable than the VWAP but one could be tempted to believe that the execution quality is higher in stock A, since 15bp is lower than 40bp. In fact, this way of thinking is misleading, as the difference may be caused by differences in market conditions, trading patterns, or stock prices. So, even if order size is comparable, the values themselves are not. By contrast, if we observe an absolute EBEX of 0.2 in stock A and 0.75 in stock B, we can conclude that the trader did a bad job in stock A but an excellent job in stock B. This means that the trading performance was better in stock B than in stock A, although the trader has a better benchmark score in stock A. Example 2: Suppose a single stock for which the benchmark comparison to the VWAP is 40bp today but was 30bp yesterday. Although the stock is identical, the values

71 An EDHEC Risk and Asset Management Research Centre Publication