In our paper “Do Limits Improve Algo Performance?”, we explored how setting a limit affects execution performance and whether it was possible to optimize limit placement. The focus of the paper was on algo trades executed in less than 24 hours and for G10 currency pairs, which avoided data issues without sacrificing significant statistical power. The bulk of the research concentrated on algos with only one limit, where limit placement is a more straightforward matter than dynamic limit optimisation.
BestX® Expected Risk Transfer Cost1 was used as the primary benchmark to evaluate algo performance with and without limits. This takes into account market conditions at the time of execution to arrive at a fair price estimate of the trade when algo execution begins and can be compared with the achieved average price across algo fills.
Our research focused on five algo styles2:
- Get Done: aggressive algos, where the priority is on getting a specific amount of risk executed as quickly and efficiently as possible and less on minimising market impact.
- Opportunistic: algos that do not have a strict benchmark-dictated schedule, so have the flexibility to execute aggressively or passively according to market conditions.
- Pegged: algos that aim to execute orders at levels within the prevailing best bid/offer. Passive by nature, since they follow the market and usually trade at no worse than mid-price.
- Interval: interval-based algos, such as TWAP, which aim to minimise slippage to a benchmark where the algo slices the parent notional according to an interval- or time-based schedule.
- Volume: volume-based algos, such VWAP, which aim to execute in line with a specified percentage of volume traded within the market.
Preliminary analysis
As a robustness check, we used the performance of a TWAP algo without a limit during the execution period as a secondary benchmark, which more strongly favours having a limit than the primary analysis. However, this out-performance of limits may be quasi-mechanical, because a TWAP with a limit will on average outperform by avoiding prices when the limit is engaged and the algo is stopped. On the downside, the principal ways a TWAP with a limit can underperform are by being unable to execute the intended trade amount fully or by completing it too late.
This TWAP under/over performance is important in the context of finding an optimal limit value, because having a very tight limit may produce the illusion of out-performance purely by executing only part of the intended amount and only under very favourable market conditions. To control for this, we created a smaller data set composed of mostly clean intended execution amount data to double-check the results inferred from our larger data set, while only including fully executed trades.
Figure 1 (below) compares the Risk Transfer Performance distributions of trades with and without a limit. The limit is clearly already improving the median performance3 in both data sets.
Price limit placement is just a binary decision, so we also needed to evaluate where the limit should be set to assess its utility. We concentrated on trades with only one limit in their lifetimes, partly for simplicity and also because these constituted the vast majority of trades in our data set.
Figure 2 (below) shows how different limit distances affect algo performance. We can see a major difference between the datasets: the large dataset has numerous outperforming trades, while there are far fewer trades with negative distance in the smaller dataset.
Figure 3 (below) shows trade performance by limit engagement, with negative limit distance cases combined under Limit Started Engaged, while the positive limit distance cannot engage during the algo execution period (Limit Not Engaged) or engage after the start (Limit Engaged). Much of the limit performance derives from trades with an engaged limit at start, while trades with limit engaged later mostly underperform those where the limit never engages or limitless trades.
Figures 4 and 5 show the other side of the trade-off: order completion, over limit distance from market arrival mid-price.
Statistical Analysis
Our starting point for statistical analysis of limits was a regression model for the effectiveness of using only single limits with a positive distance. We then extended this model to accommodate dynamic limits by adding variables for trades with multiple limits during their lifespan.
We found that for both the large and small data sets a single limit:
- Degraded the performance of Opportunistic algos for almost any positive limit distance.
- Improved Interval and Pegged algos with statistical significance
- Had a directly diverging effect for each data set for GetDone algos
- Improved Volume algo performance for the larger data set, but had no statistically significance for the smaller data set.
The results for one limit do not change qualitatively when indicator variables for multiple limits are added. Overall, having multiple limits over the lifetime of a trade is associated with statistically significant performance deterioration across all algos, except for Interval algos.
Figures 6 and 7 display the estimation results for the large and small data sets together for limit distance. The dashed 95% confidence line indicates whether the solid limit performance line is statistically significantly different from the zero line representing the performance without an algo limit.
Examination of Figures 6 and 7 reveals that:
- The conflicting results for GetDone algos between the two data sets also applied when performance was broken down by limit distances. While the limit performance line is below the zero-line for the large data set, in the small data set tighter limits are statistically significant above the line when up to 5% of the daily volatility away from the limit. Any limit farther away than this fails to improve the performance.
- Also in line with the previous results, the limit performance line is below the zero-line for almost any positive limit distance for Opportunistic algos. The one exception, proving the rule, is the very tight 1% of daily volatility away from the arrival market mid, which comes with order completion issues.
- A tight limit can boost the performance of Pegged algos with a limit placed up to 15% of daily volatility away from the market mid-price still improving the results.
- A number of limit distances enabled performance improvements for Interval algos. The limit performance estimates are almost always above the zero-line, but mostly not statistically significantly above. A relatively tight distance of 2.5%-5% as well as having a limit >50% of daily volatility away (up to 4 times the daily volatility) can improve the limit.
- Volume algos exhibit a similar, but weaker structure to Interval algos, with out-performance from a limit 10%-15% and 1.5-2 times daily volatility away from market mid. Both these algos aim to follow the market movements without too many attached smart features, so these relatively distant limits may be exploiting mean reversion in the market to avoid trading in transitorily bad market conditions.
Conclusion
Our original paper analysed whether setting a limit aids algo performance and where to set a limit to optimize any beneficial effect. We explored the performance/completion trade-off, where a tighter limit causes better performance at the expense of only partial execution of the intended trade amount.
We found that setting limits improved Interval and Volume algo performance, particularly when distant from the market mid, thereby avoiding extreme unfavourable market moves. The evidence for GetDone algos was mixed, but tight limits were favoured, while taking the partial completion risks into consideration. It was challenging to improve Opportunistic algos, which lie on the smarter end of the spectrum investigated, by using limits.
1. https://www.bestx.co.uk/glossary
2. Fixing algos, where the aim is to match the relevant fix price around the official fixing window and outperforming a fair value price is less relevant, were excluded.
3. Risk Transfer Performance is defined as the performance of the algo relative to the BestX® Expected Risk Transfer Cost.
