Multi-dimensional TCA Benchmarks

Are your Transaction Cost Analysis (TCA) benchmarks telling you what you need to know?

Measuring price performance is at the core of TCA. This involves comparing the average price obtained in the market for a given order and comparing that price with a reference price or benchmark. The difference between the price of the order and the benchmark can then be used to compute the performance relative to the benchmark.

A common TCA benchmark is the arrival price. This benchmark is the price of the security being traded at the time the order arrives on the buy-side trader’s screen. Often, we use the mid-point of the prevailing bid and ask when the order starts trading. While this benchmark serves multiple purposes, it also has some limitations.

The arrival price can be compared with the decision price to measure how much the stock price changed between the time a portfolio manager created the order and the price at the time that the order started trading. Additionally, the arrival price can be used to measure the market impact of executing the order in the open market. These are both useful numbers when assessing trading performance but there are also limitations. In particular, the arrival price does not consider the size of the order. Part of the issue here is that we are dealing with a single number, i.e., the prevailing price (whether the last traded price or a mid-point from the quoted bid/ask) is used as the benchmark. We are not considering the available liquidity when we compute performance versus arrival price. There can be situations where the market changes appreciably on little volume which has the effect of skewing our performance. While we can mitigate this by adjusting the performance based on how much the market moved and our pre-trade estimated price impact, we can also consider other benchmarks that provide additional perspectives on performance.

One benchmark that is often used is the Price Weighted Participation (PWP) benchmark. This benchmark uses the order size to determine the time horizon over which to compute the average price of traded market volume. For example, a 20% PWP for an order of 100,000 shares will compute the average price of the first 500,000 shares that traded since we started our order. The PWP uses what’s called ‘volume-time’ to determine the time horizon over which to compute the benchmark. Instead of using traditional clock ticks, this benchmark uses volume reported to the market data ‘tape’ to measure time. We can compute various ‘tenors’ of PWP such as 5%, 20%, 30% PWP etc… These tenors can often map to instructions that a trader may send to a broker. For example, a trader may instruct their broker to try and be 10% of the volume when working their order.

But we are not done with the PWP. While the procedure described above provides a benchmark: i.e., the average price of the volume executed within the volume-time specified by the tenor of the PWP, we can go a step further. The first thing is to note that the volume between the start of our order and the end determined by the tenor represents the opportunity set that a trader had when interacting with the market.

The PWP itself is a number, just like the arrival price. But we can provide additional context by computing the range of possible outcomes we could have achieved when interacting with this opportunity set. We start with the volume profile over the trading horizon. Assuming as before that our order is 100,000 shares, the volume profile we are interested in is the volume from the time we start trading our order until we observe 500,000 shares traded by all market participants (we can exclude certain types of volume like odd-lots or block trades if we want). We then take this set of market trades that add up to 500,000 shares and compute the average price of the lowest-priced 100,000 shares. That would give us the lowest possible price we could have achieved in this same time-period and completed our order. We do the same for the highest priced 100,000 shares. Now we have the PWP which is the average price of the 500,000 shares which is a one-dimensional (single number) benchmark and put this into context by providing the range of prices that we could have achieved for our order size. This range is defined by the lowest and highest prices described above. This gives a two-dimensional benchmark.

In the top right of Figure 1, we show an example where immediately following the start of the order, the price of the stock increased and stayed well above the arrival price up to a point where 5 times the order volume traded in the market. There is very little volume at the arrival price resulting in a large difference between the average price of the order and the arrival benchmark. While we get some information for the arrival price benchmark, we can get a different perspective on performance by considering how much volume was available at various prices while we were interacting with the market to complete our order.

In the bottom right chart of Figure 1, we show the volume profile for a period defined by a PWP20% benchmark. We can use the combination of the prices and volumes of trades that hit the ‘tape’ to compute the average price for the PWP20 benchmark. We can go an extra step and compute the lowest and highest average prices an order the same size as our order could have achieved given the transacted volume that is used to compute the PWP. We show the benchmark and the range of possibilities in Figure 1, top right. The minimum and maximum of the gauge represents the lowest and highest prices for volume equal to our order volume. The white needle indicates the average price of the order, and the thick grey needle represents the PWP benchmark price.

This approach also allows us to plot the time-dependence of the lowest and highest priced volume. Figure 1 lower left shows the complete volume profile available to the PWP 20% benchmark along with the highest and lowest priced volume. The red vertical lines represent the lowest and highest average prices achievable for an order of our size.

Now we have a two-dimensional benchmark that provides not a single number but two numbers, the benchmark price and the range around the benchmark price that represents the set of possible prices we could have obtained for an order the same size as the order we are working.

The PWP range allows us to compare where in the distribution of possible outcomes we obtained our fill. This allows us to ask deeper questions about performance. Not only can we ask what the absolute price performance was in terms of either currency units or basis points, but we can also ask whether that is a ‘good’ or ‘bad’ execution by comparing our price with the range of possible outcomes we described above.

These advanced analytics allow us to provide deeper insights into performance. While traditional benchmarks such as arrival price are useful, more advanced benchmarks that can consider the available liquidity and how well we executed relative to the available opportunity take us to the next level of analysis.