Podcast: Muhle-Karbe on the maths behind broker selection

Imperial College’s mathematical finance head introduces new tool to measure slippage and trade quality

For investors that run high-frequency strategies, trade execution is as important as security selection or market timing. The problem is that this is often out of their hands. Most investors lack the internal resources to optimise their execution strategies, and rely on brokers to manage their trades. And while researchers have produced a vast amount of academic literature on minimising market impact, few have tackled the practical challenge of assessing broker performance.

Johannes Muhle-Karbe, head of mathematical finance at Imperial College London, and one of the best-known and prolific academics in the field of market impact, has turned his attention to just this problem. In this episode of Quantcast, he discusses a quantitative tool he developed with systematic trading professional Zoltán Eisler to help investment firms select the right brokers for their strategies.

Quantcast – a Risk.net Cutting Edge podcast · Johannes Muhle-Karbe – 24/07/25

 

To assess broker performance, researchers must first estimate the slippage inherent in their trading activity. This estimate consists of two components: linear cost, which is a fraction of the bid-ask spread; and impact cost, which increases quadratically with the size of a position. The standard approach is to examine total slippage, represented by the execution cost relative to arrival price. After standardising by order size, researchers can determine whether the slippage resulted from linear or impact costs.

Muhle-Karbe and Eisler acknowledge the merits of this approach. However, they argue the signal-to-noise ratio is low, making it less efficient. “The problem is that when you execute the orders, you’re exposed to all the market noise, the price changes that happen during the duration of your order that are not coming from you,” says Muhle-Karbe. “And so that’s why there really is a lot of noise and a pretty weak signal.”

The researchers propose an alternative approach that uses mid-prices instead of arrival prices, coupled with a time-weighting scheme that prioritises the efficiency of execution at the beginning of the trade over subsequent phases. This improves the signal-to-noise ratio and allows for a more accurate assessment of trade quality.

Related

Optimising broker evaluation through intraday modelling of execution cost 

A method to assess brokers’ performance via their market impact is presented

If that sounds surprisingly straightforward, it’s because it is. “I think the basic ideas are very simple and intuitive,” says Muhle-Karbe. “And I would be very surprised if this isn’t in production somewhere. I think the contribution of the paper really is to formalise this.”

That simplicity also adds to the method’s utility. While the tool was originally developed to assess broker performance, Muhle-Karbe says it could also be used by investors to assess their own execution efficiency. The approach is also applicable to almost any market, as long as intraday execution data is available and trading is sufficiently liquid, with equities and foreign exchange being the obvious candidates.

The conversation also veers into related topics. While minimising impact cost is the common objective of researchers working on trade execution, Muhle-Karbe notes there are times when the ability to recognise market impact could be an advantage. Examples include some forms of predatory trading, where a firm has knowledge of a directional trade and seeks to exploit it. The case of Jérôme Kerviel at Societe Generale, which resulted in outsized trades having to be unwound, is one such scenario.

Another involves trading around FX fixing, a topic that Muhle-Karbe delved into with Roel Oomen of Deutsche Bank in a separate study. That paper describes how trading during the fixing window can influence the price in a beneficial way, suggesting that minimising market impact is not always the best outcome.

Another relevant case relates to the flow of fund assets. Muhle-Karbe recalls a recent study by quants at Capital Fund Management on Ponzi funds. “They look at this feedback loop that if you buy, you push up the price, and you see very good performance,” he says. “Then investors put even more money into the fund, and then you can buy even more. The price goes up even more. And this can continue for a while, until at some point, like any Ponzi scheme, it comes crashing down.” In such cases – at least, in the short term – market impact is a positive outcome.

The conversation also touches on the recent charges made by the Indian market regulator against trading firm Jane Street. Muhle-Karbe’s view: it’s complicated!

Index

00:00 Introduction and brokers’ performance

04:13 Linear and impact costs

06:52 Novel elements of the new method

10:25 Applicability

20:33 Existing uses of similar solutions

21:53 Minimisation of impact cost and the Jane Street case

32:07 Future research projects

To hear the full interview, listen in the player above or download. Future podcasts in our Quantcast series will be uploaded to Risk.net. You can also visit the main page here to access all tracks, or go to Spotify, Amazon Music or Apple Podcasts to listen and subscribe.