Cost Models can be a BEAST

Chandan Jha and Chris Sparrow

Understanding the expected market impact of an institutional order is important when considering investment possibilities. A cost model can provide Portfolio Managers with an estimate that can be used not only to determine the suitability of getting into a position, but also to provide traders with a way to assess the difficulty of implementing the order.

Trader’s Dilemma

Traders are faced with decisions about how to execute orders that are generated by portfolio managers. Do they execute quickly and have a large but certain impact on the price, or do they execute slowly to minimize their impact but have less certainty about the final price? This is the so-called “trader’s dilemma”. Traders need to also consider any instructions from the PM as well as the reason behind the order to make optimal decisions.

We can incorporate the trader’s dilemma into a pre-trade framework by providing scenario analysis. We do this by varying different trading strategies and then computing the impact and the range of outcomes for the expected price of implementing the various strategies. Traders can then use this information along with instructions to choose the strategy that best meets their needs.

Where do costs come from?

Costs arise from three main components: spreads, order books and price discovery. Costs are typically measured relative to the mid-point of the bid and ask prices at the time the order starts trading. Spread costs arise when crossing the spread and removing shares booked passively at the far touch of the order book. The cost of these aggressive orders is half the spread if they execute against the far-touch but can be less when interacting with dark liquidity which may be available at better prices than the far touch. Liquidity costs arise from removing all visible liquidity priced at the far touch from the order book which changes the mid-price and therefore moves the stock price (up for buy orders and down for sell orders). Price discovery costs, also known as permanent impact, come from market participants updating their view of the equilibrium price for the stock given that there was a large order.

We can think of spread and liquidity costs as coming from the physics of the market, i.e., how the various order books that trade the security and are supplied with passive liquidity, while the permanent impact comes from the collective views of all market participants and can be thought as being derived from game theory. This is the market price discovery mechanism at work.

Relationship of Post-Trade TCA and Cost models – Calibration

Cost models can be used in both a pre-trade mode where input liquidity analytics are predicted and the trading strategy is specified but is not certain (i.e., is subject to change when interacting with the market) and in a post-trade mode where the strategy and liquidity analytics are both known and can be measured directly by observing the level one market data and the fills obtained by the order.

When supporting a cost model, we need to know if it is producing good estimates. To check, we use the post-trade results from many orders. We can directly measure the performance of each order relative to the mid-point at the start of the order. We can also generate an estimate from the cost model which consists of both an expected impact and a range of expected outcomes. From these numbers, we then compute a z-score which measures the difference in the actual result and the predicted impact relative to the expected range of outcomes. We can then use the distribution of z-scores to assess how well the model is making predictions. We can also look at the performance of different groups and strategy types. For example, is the model working as well for small caps as it is for large cap stocks? How well does the model work for different participation rates and durations?

By having an on-going calibration process we keep tabs on the model and can adjust it as necessary to ensure the model is making good predictions.

Use cases of cost model

Cost models are used for scenario analysis where traders can compare the expected costs and related uncertainties associated with various trading strategies as part of a pre-trade analysis. They can also be used in the portfolio optimization process to estimate returns as alpha minus expected costs. Another use case is to provide an estimate for orders that were already executed to compare with the pre-trade estimate where we predicted the strategy and liquidity analytics. We can provide the estimate directly into a trading blotter allowing the trader to assess the difficulty of each order. We can also make the cost estimates available to automated trading processes like algo wheels.

Because the models are calibrated using post-trade TCA measurements, we can mitigate things like liquidity fade and dark liquidity by looking at stock specific responses for a given set of liquidity parameters. This means we look at the totality of volume, volatility, book depth and lit spreads.

Applications of ML to Cost Model Function and Calibration

Historically the approach has been to come with some kind of cost model function like linear, power law, log model etc… and try to fit this model for various groups of orders based on market cap, order duration, volatility, order size relative to historical orders etc... A different approach will to be use a data-driven methodology where it’s not compulsory to assume any specific cost model function. Machine Learning algorithms follow a data-driven approach where the models are fed with more features, including ones which may not affect market impact. This approach needs a large amount of data to train the model. With deep neural network and support vector regression approach we can come up with grouping based on the data rather than some assumption and then can calibrate the models accordingly.

BEAST Cost Model

The BEAST cost model uses liquidity analytics at a five-minute granularity as inputs. The output is also at a five-minute granularity, which provides an expected evolution of cost throughout the life of the order. The BEAST cost model computes the component costs for spread, liquidity and signaling costs.

In addition, the model follows the generative model approach whereby there is an instantaneous impact and a decay term. The model takes a time-series of inputs (i.e., uses predicted intra-day liquidity profiles) and instead of instantaneous impact, we estimate the impact and related costs at a five-minute granularity.

The model also uses a cap to introduce concavity of costs – as the number of shares increases, the cost versus shares has a concave shape. The concavity is seen empirically in the post-trade TCA data and is also supported by academic research.

There are various ways to consume the estimates from api access to full views that show the details of the contributing factors to the overall cost.

The BEAST cost model calculates the cost for a given strategy at five-minute granularity. The estimated cost data can be streamed back to running live orders in the market for near real time cost guidance and can be used in automated trading decisions, alerting traders, and suggesting different strategies.

The workflow to calibrate the model involves a series of steps. First, orders are run through the TCA post-trade calculation engine where benchmarks and performance metrics are applied to each order. Next, the cost model can be called where the executed strategy and the liquidity analytics that were prevailing during the order are provided to the model and an estimate is obtained. The next step is to compute the z-score for each order. Finally, we investigate the distribution of z-scores to assess model quality and if necessary, tune the model to ensure it is providing good estimates. This is an important process because as the market evolves, the factors driving market impact can also change.

Best Execution is a process that involves pre-trade, in-trade, and post-trade analysis. A cost model is an important component of each part of the process and provides a way of assessing how an order is expected to cost and how difficult it is to execute. By employ methods to constantly assess model quality we can be confident of our predictions and address our Best Execution requirements. It involves a lot of work but is an important process for the portfolio lifecycle that leverages the valuable information generated from a post-trade TCA process.