The Paradox of the Pre-Trade Cost Model

As financial markets get more efficient and alpha signals get more fleeting, transaction costs are often one of the largest determinants of investment success. But proper interpretation of pre-trade cost models often is not so simple. Quantitative Brokers explains the nuances that must be understood before applying a pre-trade cost model, including the fact that distinguishing market impact from alpha can be impossible.

QB’s clients are very interested in pre-trade transaction cost estimates, with good reason: As financial markets get more efficient and alpha signals get more fleeting, transaction costs are often one of the largest determinants of investment success. A good understanding of likely costs for a proposed trade can be an important ingredient in making and adjusting trade decisions. Questions such as, “How large a trade can we do?” or “What time horizon should we set?” or even “Does this trade have a strong enough alpha to overcome the transaction costs?” all can be systematically evaluated using a good pre-trade cost model.

We have a cost model that is calibrated on a large sample of historical trades. Although this model does an excellent job of capturing the features of the data on which it is calibrated, there are some nuances that should be understood before applying it to contemplated future trades.

The first fact is that by far the largest determinant of slippage on any individual trade is the direction that the market moves during the trade execution: If the market comes toward us, the slippage will be negative, while if it moves away, the slippage will be positive. Although on one level this statement is trivial and obvious, nonetheless it has some rather profound consequences.

The most important consequence is the impossibility of distinguishing market impact from alpha. The trader sends a buy order because he or she anticipates that the market will rise; if it rises during execution of the buy order, was that because the execution pushed the market, or because the trader correctly anticipated the move? It is impossible to distinguish these two effects. Our model simply reports the combination of the two, assuming that whatever combination of alpha and impact prevailed in the past will continue to hold during future executions.

Furthermore, the degree to which alpha contributes to observed slippage depends very strongly on the nature of the investment strategy: A short-term alpha strategy will necessarily induce much higher observed slippage than a long-term strategy. The degree to which alpha has a short enough horizon to affect slippage varies very strongly from one client to another, and between different strategies executed by the same fund.

Since QB, as an execution agent, is not privy to the underlying alpha information of the investment model, and in order to get a reasonable degree of statistical significance, we necessarily lump together a very heterogeneous collection of different strategies. The resulting model is accurate on average but may be very inaccurate as applied to any particular strategy. Thus, the forecast slippages given by the transaction cost model should be interpreted only as very approximate estimates. The only way to know what slippage will be incurred for a particular strategy is to calibrate it on trades for that strategy specifically, if enough data is available, which is not always the case.

The second aspect of pre-trade cost models, closely related to the first, is the role of volatility. That is the uncertainty in how much, and in which direction, the market will move during execution. Because volatility is generally much larger than market impact costs, the best model is able to predict only a very small component of the cost on any particular order. To use statistics jargon: The t-stat may be very good if enough data is available (the model coefficients can be determined accurately) but the R-squared is always very small (there is a lot of unexplained noise). Fortunately, what matters for investment success is the mean slippage across a large number of executions, which the model is able to realistically forecast. It does mean that the model should not be accepted or rejected based on a small number of executions.

The third aspect of cost models, also a consequence of volatility, is the large amount of data needed to calibrate a model. Not only is it hard to predict the outcome of any individual trade, but also the low ratio of signal to noise means that a very large number of trade observations is needed to build an adequate model for the mean slippage. Even for active instruments, we generally need to combine all our data to achieve statistical significance for the model parameters. It is often not possible to determine accurate models if the data is subdivided into individual clients or strategies.

Finally, the fourth aspect of cost models that is often misunderstood is the role of the time horizon of execution. It is reasonable to suppose that faster execution will incur higher slippage costs, as larger demands are made on available market liquidity. In fact, a conspicuous feature of the data is that faster execution is generally associated with “lower” impact costs. The reason for this is that for arrival price benchmarked orders, when the market moves towards the trader, the order executes quickly with low cost, while when it moves away, the order executes slowly with high cost. This is true unless the execution interval is constrained to be very short, which usually leads to poor performance on average. Thus, execution duration should be thought of as an “output” variable rather than an “input” variable. Sometimes it is possible to tease out the effects of a requested high participation rate, but the effects are subtle and secondary to the primary effect of trade size.

In summary, a pre-trade transaction cost model gives a seemingly simple forecast for execution slippage as a function primarily of order size, but depending also on other market parameters such as volume and volatility. But proper interpretation of such models is often not so simple. The numerical results given by the model cannot be compared directly with execution results obtained through our algorithms or through other channels, without a detailed comparison of the conditions of execution. The only model that is truly able to give a meaningful prediction for any particular strategy is a model that is calibrated on trades for that strategy specifically. And by the time you break down a firm’s trading activity into individual alpha strategies, there is often insufficient data in each one to draw a statistically significant conclusion. Therein lies the paradox of the pre-trade cost model.

Dr. Robert Almgren is the Co-founder and Head of Research at Quantitative Brokers. This article originally was published on the Quantitative Brokers Blog.

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