Size Matters: A Better than Average Fill Metric

With the current focus in equity markets on transparency, brokers are being measured by many different metrics to assess their performance including spread capture and their ability to interact effectively with both lit and dark order books. One of the metrics being used to assess how brokers interact with the market is the average trade size achieved by the broker. This metric is used to proxy for liquidity capture and is simple to calculate. The problem is that is also a simplistic measure.

When it comes to liquidity capture, there are three dimensions to consider. What can be captured by removing liquidity from an order book, what can be captured from sitting passively in a lit order book and what can be sourced in dark pools.

Let’s first consider how to measure the ability of a broker to successfully capture passive liquidity that is sitting in a lit order book. The average trade size will depend on two things: the size of the active order sent by the broker to access the passive liquidity and the structure of the orders that are sitting passively in the order book.

An example can help: consider a broker that would like to immediately execute 1,000 shares. The broker sends a marketable order for 1,000 shares to an order book displaying 1,000 shares. At one extreme, the order book could consist of a single passive order for 1,000 shares while at the other extreme, the order book could consist of 10 passive orders of 100 shares each. In the first case, the broker will execute one trade of 1,000 shares and have an average trade size of 1,000 shares. In the second case, the broker will execute 10 trades for 100 shares each resulting in an average trade size of 100 shares. In both cases the broker captured 1,000 shares of liquidity at the once but the resulting average size depends on the structure of the order book at the time the broker sends their order. The broker has no control over the order book, yet if we use average fill size as our proxy for performance, we would come to very different conclusions about how the broker did. If we had an effective metric, we should see no difference between these two outcomes – in both cases the broker got us our 1,000 shares.

We can easily fix this problem by simply aggregating the executions that are done at the same time, and then averaging. When a broker removes 10 orders of 100 shares at the same time, it should be equivalent as the broker getting an average fill size of 1,000 shares, not 100 shares. It is very easy to make this adjustment and is much fairer to the broker being measured.

Figure 1 On the left, we show a chart that stacks individual fills of various sizes for each time. The average size is shown in the title and is a result of averaging all the individual fills without aggregating by time. On the right, we aggregate all the volume that is stacked and then compute the average. If there is more than one fill in a time window, the average on the right will be larger than the average on the left. This method can be used to compute the average fill size of active volume to measure a broker’s ability to capture passive liquidity.

We can also extend this concept by aggregating fills across multiple order books. Maybe a broker got the 1,000 shares by simultaneously removing 200 shares from 5 venues. The average fill size would be 200 shares (or less depending on the structure of the order books). But the broker captured 1,000 shares of liquidity and should get credit for that, possibly even more credit than when executing versus a single order book because the it is more difficult to capture liquidity distributed across different venues than it is from single venue. Again, it is easy to measure this and reward the broker with a larger liquidity capture metric, i.e. 1,000 shares in this example.

Next, we can consider the case where a broker posts 1,000 shares passively in either a lit order book or a dark pool. The broker has no control over when liquidity is removed by incoming marketable orders. The broker’s passive order could be filled all at once, be filled over time, be partially filled or go unfilled. Again, the broker has no control over when incoming orders arrive, so why would we think that measuring the average fill size would be a good measure of broker performance? The broker does have control over which venue they choose to post on, and in some cases, they may choose to post simultaneously on several venues.

A much better performance metric would be the time that it takes to get filled. We could transform to volume time to allow comparisons between stocks that have different liquidity characteristics. This would measure the opportunity cost of getting filled passively rather than crossing the spread and getting an immediate fill. We could also measure how much volume traded at the same price (or better if we are in a dark pool) on both the venue the broker has booked their order and on other venues where the broker may not have placed a passive order.

To rectify the situation, we would first consider the active fills and aggregate them by time (down to the millisecond or better) to get an effective liquidity capture that recognizes all fills that occur at the same time whether it is 10 fills of 100 or 1 fill of 1,000. We could also specify a time window, for example all fills within 3 milliseconds. We would then measure the passive fills differently, looking at the opportunity cost of booking passive orders on a venue or group of venue.

It is a complex market structure and applying simplistic metrics such as average trade size does not adequately measure what it purports to measure, i.e. a broker’s ability to capture liquidity. Luckily there are alternatives that are straightforward to compute and that provide deeper insights into a broker’s performance.

?2018, LiquidMetrix