quant research
As part of our commitment to transparency, Proof publishes all of the research findings that inform our trading algorithm design.
October / 2021
Rejecting the Black Box
An inside look at the design of Proof Trading's new algorithm.
The notion of an "algorithm" sits both atop this hierarchy and outside it. If you consult a computer science textbook, the definition of algorithm will likely use words like "procedure" or "recipe" that are not intrinsically tied to the realm of computers.
April / 2024
Close Prediction
A new methodology for estimating closing auction size.
The closing auction can provide a fair amount of cover for large trades that might otherwise move the market. But misjudging the amount of cover on any particular day can lead a trader to expose too much interest and move the market against themselves, or to expose too little and miss an opportunity to complete more of their order while staying under the radar. In either direction, mis-estimation can be costly. There are many reasons to suspect, though, that decent predictions of closing auction size are possible. In this paper, we present our initial work on developing and evaluating models that attempt to predict closing auction sizes as a function of historical data from previous days as well as measurements that can be made earlier in the same trading day.
June / 2023
Information Leakage
A new framework for measuring and controlling information leakage.
We present a new framework for defining information leakage in the setting of US equities trading, and construct methods for deriving trading schedules that stay within specified information leakage bounds. Our approach treats the stock market as an interactive protocol performed in the presence of an adversary, and draws inspiration from the related disciplines of differential privacy as well as quantitative information flow. We apply a linear programming solver using examples from historical trade and quote (TAQ) data for US equities and describe how this framework can inform actual algorithmic trading strategies.
December / 2024
TCA: Public Analyses
Proof's design for public-facing TCA.
Here we develop and apply Proof’s framework for evaluating our trading performance. We have designed strong robustness and client privacy checks that enable us to make any stable results public. For latest results, please see the latest report below.
December / 2020
VWAP
An initial approach to incorporating real time data into a VWAP algo.
Very few things about stock market prices are straightforward. Most people know they can vary quite quickly as a function of time. But this is just the first of many complications. You can't just ask: "What is the price for Apple right now?"
December / 2019
Simulation
A framework for historical simulation of trading behavior.
"Back-testing" of trading strategies in US equities often comes with the caveat that "transaction costs" are not considered. This may appear to be a fundamental limitation of working with historical data: how can we know what would have happened in an interactive system if some party had behaved differently?
July / 2021
Distilled Impact
An approach for reducing market noise in transaction cost analyses.
For trading in US equities, measuring slippage is important and also hard. There is little agreement among market practitioners on how best to do so, and the most common approaches have serious limitations.
October / 2020
Pretrade Analysis
A method for modeling the price impact of a proposed trading activity as a probability distribution, based on historical data.
Pretrade analysis addresses the following scenario: we are considering trading a large amount of stock, and we want to predict what might happen if try to trade it over various timescales. Within a day? Within 3 days? How much more should we expect to pay in total implicit and explicit costs if proceed very aggressively versus very passively?
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