Transaction Cost Analysis A-Z

Transaction Cost Analysis A-Z — November 2008

VI. A New Framework: the EBEX Indicators

When intermediaries are given explicit price constraints, they have a specific target to beat but they still have discretion over how they will work the order to reach their objective. Since they do not have any restrictive timing constraints within the trading horizon, EBEX indicators based on all market activity traded in that horizon reflect their ability to time orders and seize the best available trading opportunities. By contrast, when intermediaries are given implicit price constraints or volume constraints, they have limited discretion over how they can work the order to reach the investor’s objective. In fact, both implicit price constraints and volume constraints impose indirect timing constraints on intermediaries, who are then forced to schedule in a predetermined way the trade by the historical average volume profile of the security. In such situations, we need to avoid noise and distinguish the trading performance of the intermediary and the instructions given by the investor. For this purpose, EBEX indicators may be adjusted on both the specified strategy and the expected market conditions over the trading horizon as follows: EBEX abs ,i = x i , j X i EBEX abs ,ij j = 1 T ∑ where j is the time interval, T is the total number of intervals within the entire trading horizon, x i,j is the quantity to execute in interval j according to the specified strategy for order i , X i is the total size of order i and EBEX abs,ij is the absolute EBEX indicator of the lot x i,j computed over interval j . EBEX abs ,i is then the weighted absolute EBEX for order i that attempts to measure the global quality of execution achieved for this order while accounting for the times that trades are requested of the intermediary.

The example shown in figure 18, a VWAP strategy for an order of 120,000 shares, illustrates this approach. If eight intervals are considered over the trading horizon, the schedule of execution is predetermined to participate proportionally in the total volume over the horizon. The order is broken up into eight lots that depend on expected market conditions. Once the entire order is executed, the absolute EBEX indicator for each lot can be computed by comparing its average execution price and the actual market activity within the corresponding trading period. Next, the quality of execution for the entire trade is obtained by computing the weighted average of all the absolute EBEX scores. Figure 18: Illustration of the weighted absolute EBEX for a VWAP strategy Trading period Expected volume VWAP strategy

Executed shares

EBEX score

Buy

Sell

1

200,000 200,000 24,000

0.52

2

150,000 150,000 18,000

0.63

3

100,000 100,000 12,000

0.71

4

50,000 50,000

6,000

0.44

5

50,000 50,000

6,000

0.54

6

100,000 100,000 12,000

0.52

7

150,000 150,000 18,000

0.72

8

200,000 200,000 24,000

0.27 Weighted EBEX 0.53

3. Illustration of the Framework To illustrate both the use and the interpretation of our framework, we present hereafter the findings that we obtained for a relevant sample of orders provided by a European investment firm. Before presenting and interpreting the results, we will describe the data that we used as well as the assumptions that we made to calculate our indicators.

77 An EDHEC Risk and Asset Management Research Centre Publication