Recently, we shared a deep-dive on the importance of modeling transaction costs correctly, an exercise that inevitably forces us to confront the non-linear nature of market frictions.
If you have ever worked on quant-trading desks, or been involved in advisory work, you already know that portfolio managers and institutional clients are always keen to know whether a signal can support a certain amount of capital in production and real-world trading settings.
With this new follow-up piece, we would like to present some additional insights on how fees and market impact can be used to estimate the capacity of a trading strategy. Using an intraday mean-reversion signal as a case study, we hope to offer a useful framework for how, as quants, we can try to tackle the “capacity dilemma”.
Dissecting Capacity
In our experience, capacity is best understood as a three-way problem. More specifically, we believe it can be broken down into three sub-questions:
How much capital can we run a signal on?
How much capital should we run a signal on?
What minimum capital does the signal require to run?
The first question relates to an upper-bound problem, where we want to determine the maximum amount of capital a signal can sustain before being eaten away by costs. Given what we already discussed at length in our previous article, we expect market impact to be the predominant cost driver in this case.
The second question poses a classic optimization problem, where we seek the ideal amount of capital that minimizes the total impact of frictions (comprised of fees and slippage), allowing us to capture the highest possible (net-of-fee) risk-adjusted returns.
Last but not least, the third question constitutes a lower-bound problem. As unusual as it might sound, there is such a thing as trading a signal with too little capital: knowing that fees are often priced with hard minimum-commission thresholds, committing very limited capital to a given strategy means many trades could hit that commission floor, disproportionately eroding realized P&L.
Crucially, none of these questions matters more than the others: they are all relevant, as market participants can face widely different constraints and limitations.
A Valid Framework
Now that we have established that the capacity problem is more multi-faceted than it might appear at first glance, we can lay out a framework to answer all three key questions (one we have adopted many times in our practice) summarized in the following steps:
Define a set of reference AUMs, which act as discrete anchor points at which the signal must be evaluated, spanning the range of possibile capital allocations we wish to study,
Simulate how the signal responds (net-of-fee) across those reference AUMs, through a continuous cost-normalization procedure,
Keep track of how risk-adjust metrics (i.e. Sharpe ratios) vary as the reference AUM progressively increases.
While the first step is trivial and rather arbitrary, we think the second one deserves more attention, namely for its cost-normalization procedure.
From our previous article, we learned that transaction costs do not scale linearly with traded notional, which makes cost figures highly AUM-dependent. The problem arises when, in historical simulations, the underlying AUM used to size positions fluctuates as profits and losses accrue, drifting substantially over time.
If we want to study the net-of-fee feasibility of a signal at a precise reference AUM, yet the capital we actually deploy varies over time, the very premise of tying our estimates to a specific amount of capital falls apart.
To correct for this effect, in a 2025 paper titled The Tranching Dilemma, we introduced a cost-normalization procedure designed to keep cost figures comparable across drifting AUMs.
Specifically, transaction costs are always computed relative to a fixed reference AUM, and then rescaled so that their impact on the current (effective) AUM matches what it would be under the reference AUM.
This ensures that the effect of transaction costs (including both fees and market impact) remains consistent and comparable over time, independent of portfolio growth.
Our Case Study
To illustrate the above, we take as our case study an intraday mean-reversion signal that trades across a basket of liquid single-name equities, entering positions via Market-If-Touched (MIT) orders.
Often, these signals are simulated using canonical limit orders, which guarantee an execution price at or below our chosen level but do not guarantee that the full intended quantity gets filled. MIT orders exhibit the opposite behavior: they guarantee full execution once triggered but not price, so we should expect some slippage as the cost of transacting the entire intended size.
As always, the details of how the signal is constructed and how stocks are selected are provided at the end of the article.
To run our capacity simulation, we assume the following cost structure and apply the daily normalization procedure outlined above, across reference AUMs of $10K, $20K, $50K, $100K, $500K, and $1M:
For transaction costs, we assume the standard Interactive Brokers tier of $0.0035 per share, with a minimum commission of $0.35 per trade (both values are doubled for sell transactions to conservatively account for SEC and FINRA regulatory fees).
Market impact is estimated via I-Star model, with parameters a1 = 708, a2 = 0.55, a3 = 0.71 (in our implementation, σ and ADV are computed using rolling windows that include the entire day of trade execution).
We allow fractional-share trading, and the MOC orders sent to liquidate positions end-of-day are assumed to incur no slippage.
What becomes clear is that the erosion in risk-adjusted performance, much like the transaction costs driving it, scales non-linearly with traded size.
From a theoretical Sharpe ratio just above 1, introducing a realistically modeled impact of fees and slippage generates different erosion for different reference AUMs, suggesting that for this specific signal:
The lower-bound solution of our capacity problem sits around a $20K reference AUM: below that level, the impact of fees becomes disproportionately large and erodes Sharpe too heavily.
The ideal AUM is $50K, where net-of-fee Sharpe reaches its peak value.
As the reference AUM grows, market impact becomes increasingly punishing: $100K appears to mark the upper bound of our capacity, beyond which trading would require more sophisticated execution algorithms to contain slippage.
What Can We Do?
Now that we have understood the outlines of the problem, we should ask ourselves whether there is anything we can do to “lift” the decay curve and improve risk-adjusted performance as our baseline AUM moves above or below the ideal value we identified.
On the left side of the erosion curve, the only way to ease the minimum-commission problem is to either find a broker that does not price fees with hard dollar minimums, or commit more capital to the strategy; otherwise, there is little room for intervention.
At the upper bound of the capacity issue, however, there is genuine room for improvement: as a matter of fact, our simulation assumes no sophisticated execution policy, and it sticks to plain-vanilla (“one-shot”) MIT orders.
What well-capitalized institutions and trading desks typically do is leverage their technological stack to build up desired exposures in ways that minimize market impact. In other words, participants who must execute sizeable quantities can ease into their positions through more numerous, smaller orders, usually within a maximum signal-to-execution time window.
Seen this way, execution becomes operationally more delicate as a function of how much we need to transact (Q) relative to the typical liquidity of the traded security (ADV) and the maximum allowable time (T) between signal generation and full execution.
Ideally, each “sliced” order remains large enough to avoid brokers’ hard commission minimums, yet small enough to keep slippage (i.e. market impact) in check, effectively lifting the right side of the Sharpe erosion curve.
The chart above illustrates what would happen if we could hypothetically slice each order into several (smaller) sub-orders while still securing the same execution price across them all. This order-slicing practice (destructive for smaller accounts) can meaningfully extend the signal’s estimated capacity at larger AUM levels.
For reference, through 4 sub-orders, the capital that maximizes net-of-fee Sharpe ratio climbs to $500,000: ten times the ideal AUM identified under one-shot execution.
Conclusion
All things considered, we hope to have made clear that the capacity dilemma is better framed as a three-way optimization problem, spanning how much capital a signal can, should, and must run on, and we hope the framework we’ve proposed can prove useful in your own work as a quantitative researcher or systematic trader.
Since we’re currently planning a follow-up piece exploring more advanced intraday order execution techniques, we would recommend subscribing to ensure you are notified upon its release.
If you found this article useful, feel free to leave a comment and reach out via direct message or email at info@concretumgroup.com for any questions.
Strategy Rules & Methodology
The full set of trading rules used in the case study is summarized below, covering signal construction, the stock-selection universe, and the entry and exit logic implemented through MIT and MOC orders.