At Concretum Group, a relevant part of our research effort goes into developing strategies for external clients, each arriving with different requirements about what market behavior to model and, just as importantly, about how much capital a given strategy is meant to run on.
This brings us to a very delicate part of our work, which might not seem exciting at first, but becomes crucial before entering production stage: modeling transaction costs.
Today, we would like to present some considerations around this matter that might be helpful to aspiring quants and systematic traders.
Our Starting Point
If one wanted to render an accurate estimate of transaction costs, a valid starting point would be the following:
Fees are the dollar amount we owe our broker for routing and executing an order, typically quoted as dollars per share, with a minimum commission that applies below certain order sizes.
For reference, when trading US stocks and ETFs, Interactive Brokers charges $0.0035 per share subject to a $0.35 minimum, where additional exchange, regulatory, clearing, and pass-through fees can apply.
Instead, market impact (also referred to as slippage) represents the delta that can arise between a theoretical execution price and the actual one. Every time we buy or sell securities via liquidity-taking orders (such as market orders), we push the price in the direction of our trade: given that the liquidity resting in an order book is finite, if we transact a meaningful quantity we risk consuming all the size available at the first bid or ask and must then reach into levels that are progressively higher (when buying) or lower (when selling).
A simulation that assumes fills at one clean price essentially ignores this dynamic: a large order in a thin stock might fill fifty percent at best-bid or best-ask, thirty percent one level away, and the remaining twenty percent a level beyond that, so that the realized execution price is worse than the theoretical level the backtest recorded. Such deterioration, which forces us buy higher and sell lower than we originally intended, effectively behaves as a cost component.
In options trading, another relevant cost factor is tied to bid-ask spreads, something Andrea Barbon (CEO of Concretum Group) has outlined in detail in a recent piece that you can find here.
Technically, the most rigorous way to estimate market impact is to leverage depth-of-book (i.e. Level 2) data, using snapshots of the liquidity resting across multiple bid and ask levels at the time of execution: knowing how many shares we must transact, we can then compute how many levels of the book we would have to “cut through”, and from that we can derive what a more realistic execution price might be.
It is, in principle, the most faithful estimate possibile, and yet there are two reasons we rarely reach for it.
First of all, observing the book still abstracts from the reality that other market participants may be faster than us in taking the very liquidity we were observing, or may withdraw their resting orders instants before we execute, thereby thinning the book.
The second reason is more straightforward: depth-of-book data is heavy. Carrying full L2-data snapshots into a dataset introduces a meaningful computational burden, making it harder to keep the research pipeline nimble and scalable to a multitude of securities to be traded on a daily basis.
A more practical approach, and one we have relied on in much of our public work, is to introduce a market-impact model that estimates slippage without having to rely on additional datasets. The framework we have often presented is known as the I-Star Model, originally developed by Robert Kissell and Roberto Malamut, which can be used to estimate slippage (expressed in basis points) through its instantaneous-impact component:
The coefficients presented in the formula above (a1, a2, a3) are empirically calibrated and vary by stock universe, market-cap segment and geography: the values shown are those indicated by the authors for the broad US equity market, and will be used as reference for all simulations going forward.
Understanding Non Linearities
The crucial point for our analysis is that, when appropriately modeled, neither fees nor market impact scale linearly with traded notional.
Put in other words, a $100 order, a $10,000 order, and a $1M order in the same security generate different costs not just in absolute dollar terms (as we would expect), but also relative to their own size: in a sense, the cost per-dollar-traded is itself a function of how many dollars we trade.
Let us make this concrete with an illustrative example. Suppose that at the close of every trading day we buy a fixed quantity of AMD shares, in three parallel experiments of 10, 100, and 1,000 shares, and that each day we record the drag coming from fees and market impact, both expressed in basis points relative the traded notional.
Now, if trading costs were to scale in a linear fashion with transacted notional, we would see the same exact impact of fees and slippage going from 10 to 100 and 1,000 shares, but as the table below highlights, this is far from what the numbers suggest.
Notably, trading 10 shares of AMD (~$5,000 of notional at early-June closing prices) and trading 1,000 shares (~$500,000) generate a rather similar cost impact; yet in the first case ~90% of that impact comes from fees, while in the second case ~90% stems from slippage.
Starting with fees, 10-share orders accrue roughly 10 times the cost impact observed for 100- and 1,000 share orders. This is due to the minimum commission threshold of $0.35: below a certain size, fees are no longer proportional to the number of shares traded. As a result, under IBKR’s rates, a 10-share order is charged the same minimum commission as a 100-share order, making its fee burden 10 times as large when measured relative to transacted notional.
In our experience, this issue becomes particularly relevant when simulating realistic rebalancing trades across large baskets of equities: changes in signal strength or volatility estimates can trigger small adjustments, some of which require buying or selling fewer than 100 shares of a given stock, thereby hitting minimum commission thresholds and generating disproportionately large costs. In practice, fees start to behave linearly only once a minimum “efficient” trade size is reached: in our simulation period, the 100- and 1,000-share orders experienced the same fee impact.
Market impact follows a different but equally important non-linear progression. As order size increases, slippage does not remain constant relative to traded notional; instead, its effect becomes larger. This is particularly relevant in historical simulations that assume large underlying AUMs and rebalancing policies that favor infrequent, larger orders. Executing through “chunkier” orders does not just increase market impact in absolute dollar terms, as we would expect: the real pain-point is that deterioration in execution quality becomes more severe on a relative basis too.
This behavior is consistent with a well documented stylized fact of market microstructure literature: market impact scales approximately with the square root of the participation rate; that is, with how much we trade relative to the average liquidity of a given security.
For instance, in Anomalous Price Impact and the Critical Nature of Liquidity in Financial Markets (Tóth, Lempérière, Deremble, de Lataillade, Kockelkoren, and Bouchaud, 2011) the authors analyze nearly 500,000 trades executed by Capital Fund Management and find that the average relative price change ∆ between the first and the last trade of a metaorder of size Q is well described by the so-called “square-root” law:
The authors define as metaorder a bundle of orders corresponding to a single trading decision, with each metaorder typically traded incrementally through several child orders.
A consistent behavior is captured by the I-Star model through the a2 exponent (equal to 0.55 in our chosen specification), which governs how trading costs increase as order size rises relative to the average traded volume of the stock.
Conclusion
Modeling transaction costs rigorously inevitably brings us to the challenge of dealing with non-linear behaviors in how fees and market impact can affect results in real production settings.
The key point we would like to emphasize is that a correct and precise estimate of trading costs cannot be separated from the amount of capital a strategy is assumed to run on. Since both commissions and slippage can change in relative impact as traded size changes, the same strategy can look materially different when simulated across different AUM levels.
In a follow-up article, we will show why this becomes especially relevant in long-term, multi-year backtests, where AUM growth itself introduces effects that are easy to overlook, yet have a meaningful impact on estimating the true capacity of a trading strategy.
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If you found this piece useful, feel free to leave a comment and reach out via direct message or email at info@concretumgroup.com for any questions.
Disclaimer
This publication is provided by Concretum Group for informational, educational, and research purposes only. It does not constitute investment, financial, legal, or tax advice, nor a recommendation to buy or sell any security, instrument, strategy, or investment product. All investments involve risk, including possible loss of principal. Past performance, backtested performance, and historical analysis are not reliable indicators of future results. Readers should conduct their own research and consult qualified professionals before making investment decisions.
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