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Fine-Tuning Participation Rate Constraints for Portfolio Construction in Futures Trading: An Empirical Approach

September 19, 2023

Portfolio managers often employ participation rate heuristics to determine the maximum size of a trade. Generally, these constraints, such as participating at 5% or 10% of interval volume, are arbitrary. These constraints are also used to estimate how much money portfolio managers can invest in a particular product based on turnover and participation rate ceiling. This article delves into the possibility of fine-tuning these constraints using empirical trade data for various products and different durations. 

Portfolio managers predominantly limit trade sizes to prevent round-trip transaction costs from overshadowing the expected returns from the trades and, more commonly, as a sanity check to avoid trading in sizes that are atypical. This practice stems from the fear that the marketplace might not absorb an atypical demand on liquidity, potentially causing price dislocation and excessive impact.  

In most cases, market impact functions are concave, implying a decreasing incremental market impact with each subsequent trade. However, that may not be true if the liquidity demand surpasses the product’s typical liquidity demand, at which point liquidity providers might be forced to withdraw, as evidenced by events like flash crashes.

So the question for portfolio managers to consider is this: what constitutes “typical” liquidity demand for a product over a specific trading interval? And with that information in mind, can portfolio managers improve their strategies beyond using arbitrary numbers like 5% of volume or 10% of volume? As demonstrated by the largest flash crash in US market history, a 5% daily volume participation rate was excessively high for E-mini.

We propose that typical levels should be determined through empirical analysis of market data, rather than arbitrary decision-making. Our study examined trade imbalances in various futures contracts over various trading intervals to gauge the total liquidity demand a futures product faces in aggregate. We calculated the trade imbalance (TI) as the absolute difference between buyer-initiated (trades at or above the offer) and seller-initiated (trades at or below the bid) trading volume over specified trading intervals.  

Our goal was to identify "extreme" inventory positions and establish appropriate participation rates by analyzing trade imbalances in relation to the total interval volume–the TI%. We characterized the average TI% as the “typical” liquidity demand and the 90th percentile of TI% as the level of “extreme” liquidity demand that liquidity providers can absorb for a given product. We analyzed a year of quote and trade data for various futures products, considering only “active” trading intervals and excluding typically very illiquid overnight hours.

Let us focus on our findings for Energy futures products first, shown in the table below. The comprehensive data for other products is detailed in the Appendix.

Our investigation revealed two crucial insights.

1. Typical participation rates are smaller for more liquid products and larger for less liquid ones.

For instance, for very liquid products like Crude Oil futures, a daily trade imbalance of 2.8% would be deemed extreme, whereas for a less liquid product like RBOB Gasoline, the extreme value would be 17.5%. It is essential to note that we are discussing participation rates, not order sizes. This insight suggests that "sanity check" participation rate constraints should be adapted downwards for liquid products and could be increased for less liquid products, benefiting strategies like those used by quantitative managers, risk parity strategies, and CTAs.

2. Typical participation rates are larger for shorter durations.

Many managers use uniform participation rate ceilings irrespective of the trade interval. However, empirical data suggests that while the market can sustain higher participation rates over shorter periods, it cannot do so over longer durations. Therefore, adjusting the participation rate constraint based on the trading period length could be beneficial. To illustrate, in the case of Crude Oil, a 17% participation rate would be extreme over a 5-minute trading interval, which adjusts to 9% over a 30-minute interval and further reduces to 2.7% for a full day.

In conclusion, while heuristic constraints serve as a sensible starting point, our study advocates for a more empirical, flexible approach to setting participation rate boundaries in futures trading for both trading and estimating fund capacity. By understanding the nuances of varying products and time frames, portfolio managers can craft strategies that are better aligned with each product and trading interval. 

At BestEx Research, we offer algorithmic trading products designed to minimize transaction costs, along with complimentary consulting services on transaction costs and market structure on an ongoing basis. In addition, our clients can receive quarterly estimates of the analytics provided here and more.

Contact us for more information about how you can apply this to your trading or to learn more about our products and services for institutional investors.

This material is intended solely for institutional investors, is for illustration purposes only, should not be viewed as a solicitation or recommendation, and does not constitute a promise of future performance. Individual client performance is dependent upon a variety of factors including but not limited to the investment strategy of the client and products traded.

Appendix: Typical & Extreme Imbalances Across Products

Energy Products


Equity Indices

Agricultural Products


More information about our sample data:

  • Data for typical and extreme events are obtained from active trading hours on each day
  • An active hour is an hour when trading volume is greater than the average volume per hour for that day