# Transaction Cost Analysis to Optimize Trading Strategies

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1 W W W. I I J O T. C O M OT F A L L V O L U M E 5 N U M B E R 4 Transaction Cost Analysis to Optimize Trading Strategies CARLA GOMES AND HENRI WAELBROECK Sponsored by: Goldman Sachs Morgan Stanley UBS The Voices of Influence iijournals.com

5 Determining the Optimal Speed The decomposition of implementation shortfall can be extended to include the relative performance of the selected speed (R) as compared to a benchmark speed level. For example, for a % participation rate benchmark, the alpha loss and market impact can be expressed as the combination of their respective values at the benchmark and the marginal effect of the elected speed. The example in Exhibit 2 illustrates the case of considering a 20%, rather than %, participation rate in the presence of significant short-term alpha. The market impact at 20% is equal to the market impact at % plus the additional impact from uting at 20%. Alpha loss over a 20% participation window is the alpha loss over a % window net of the alpha capture from completing the order earlier. In the example shown in Exhibit 2, due to the significant short-term alpha loss, the increase in market impact is more than compensated by the gains in alpha capture, so 20% would be the better choice of ution speed. A P/(L) decomposition that accommodates a speed benchmark can be written as a lower speed level given that moderate adverse price movements throughout a longer ution can be more than compensated by lower market impact costs. Alpha capture and speed impact can be calculated for any speed level r. The optimal participation rate R* is such that the net cost of the speed choice is minimized as follows: PWP R* ln MI( S ) MIS ( ) MI PWPR * PWP PWP + + ( S, r = R* ) MI( S, %) PWP r = Min 0,ln PWP MI( S ) + MIS ( ) PWPr PWP + MI( S,) r MIS (, %) (3) PWP ln Parrival MI( S PWP ) ln PWP ( ) + MI S MI S PWP PWP PWP P 1 ln Short-term AlphaLoss Speed AlphaCapture/Loss = P arrival AlphaLoss atselected Speed MI at Selected Speed ( ) MI ( S, r = % ) MI( S, r = R) + MI( S, r = %) ( AS SO ) MI ( %) Speed Impact (2) Speed Impact is the net market impact cost of the selected speed, measured as the difference between the market impact at the corresponding participation rate and the market impact at %. Speed Alpha Capture/Loss is the effect of the selected speed on the timeliness of the trading with respect to the alpha loss. This is measured by the tracking performance of the PWP at the chosen participation rate as compared to the PWP at the % benchmark, adjusted for the differential market impact in the two PWP evaluation windows. The combined result of alpha capture and speed impact provides an assessment of the adequacy of the speed choice. As a rule, a less significant alpha loss is associated with higher potential gains from uting at DeTermInIng The OpTImAl limit price In the case of limit orders, the P/(L) decomposition adjusts for the price limit in the following manner: P 1 ln = 1 ( Short-term AlphaLoss P arrival + Speed AlphaCapture/Loss + MI( %) + Speed Impact) 1 P ln ( e PWP _lim ( MI S ) ( )) xec MI S PWP AS OS + PWP ln PWP _lim LimitSavings (4) 32 TransacTion cost analysis To optimize Trading strategies fall 20

6 E x h i b i t 2 The Trade-off between Market Impact and Alpha Capture for Two Speeds The algorithm s performance in terms of AS/OS is isolated from the effect of the limit price by comparing the average ution price against the PWP within the range of the limit (PWP_lim). The difference between PWP_lim and PWP reflects the savings from imposing the limit price, which need to be weighed against the cost of uting any unfilled shares due to the limit in order to properly evaluate the adequacy of the limit price strategy. We assume the order completion (cleanup) occurs after the reversion period at an ution price that accounts for the market impact of the ution of this residual. The resulting overall ution price for the order size is P S S = P + S W S S ( 1 W ) P (1 + MI( S post rev S P d )) (5) The overall P/(L) associated with this average ution price is: P P 1 ln = ln P P arrival arrival P cl ln W + ( 1 W ) P Opportunity Costs (6) The net savings of the limit order over a market order are measured as ln(pwp/p ). When the alpha loss is not significant, the limit price generates savings that are likely to outweigh the opportunity costs. Otherwise, the cost associated with the cleanup of the unfilled shares due to the lower tape volume within the limit will overcompensate for the limit savings. The example in Exhibit 3 illustrates this case. Although the loss associated with the ution of the limit order is, in general, lower than that of the market order, the limit price in this example prevents completion of the ution early on, causes delays, and forces a cleanup at much less favorable prices. Exhibit 4 shows an example of the P/(L) decomposition for a set of limit orders placed by an institutional client. Market impact is the largest component of implementation shortfall. In this particular case, because the alpha loss is weak, the impact cost of an average speed higher than % does not outweigh the gains from alpha capture. The opportunistic savings generated by the Algorithm Switching Engine outweigh the adverse selection costs. The opportunity costs from imposing a limit price outweigh the limit savings, suggesting that more aggressive limit prices will produce better performance, on average. fall 20 The Journal of Trading 33

7 E x h i b i t 3 The Trade-off between Limit Price Savings and Opportunity Costs E x h i b i t 4 Value-Weighted P/(L) Decomposition for Limit Orders (in bps) 34 TransacTion cost analysis To optimize Trading strategies Fall 20

9 e x H i b i t 6 Order flow Analysis urgency and 2) a more tactical strategy for low-urgency orders. Exhibit 7, Panels A and B, show the P/(L) decomposition for the two types of strategies. On the one hand, the results show that low-urgency orders were uted with an average speed below % without significant alpha loss. On the other hand, although high-urgency orders are inevitably associated with higher trading implementation losses due to the significant short-term alpha, the additional market impact cost of a speed level over % was compensated by the benefit of alpha capture. Exhibit 8 displays the market impact cost net of the alpha capture benefit of each benchmark speed level, suggesting 5% for low-urgency orders and 20% or 40% for high-urgency orders as the optimal speed levels. e x H i b i t 7 profit/(loss) Decomposition of low-urgency and high-urgency Orders 36 TransacTion cost analysis To optimize Trading strategies fall 20

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