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Market Making and Mean Reversion University of Pennsylvania ScholarlyCommons Departmental Papers (CIS) Department of Computer & Information Science 6-2011 Market Making and Mean Reversion Tanmoy Chakraborty University of Pennsylvania Michael J. Kearns University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/cis_papers Part of the Computer Sciences Commons Recommended Citation Tanmoy Chakraborty and Michael J. Kearns, "Market Making and Mean Reversion", . June 2011. Chakraborty, T. & Kearns, M., Market Making and Mean Reversion, 12th ACM Conference on Electronic Commerce, June 2011, doi: 10.1145/1993574.1993622 ACM COPYRIGHT NOTICE. Copyright © 2011 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a ee.f Request permissions from Publications Dept., ACM, Inc., fax +1 (212) 869-0481, or [email protected]. This paper is posted at ScholarlyCommons. https://repository.upenn.edu/cis_papers/643 For more information, please contact [email protected]. Market Making and Mean Reversion Abstract Market making refers broadly to trading strategies that seek to profit yb providing liquidity to other traders, while avoiding accumulating a large net position in a stock. In this paper, we study the profitability of market making strategies in a variety of time series models for the evolution of a stock’s price. We first provide a precise theoretical characterization of the profitability of a simple and natural market making algorithm in the absence of any stochastic assumptions on price evolution. This characterization exhibits a trade-off between the positive effect of local price fluctuations and the negative effect of net price change. We then use this general characterization to prove that market making is generally profitable on mean reverting time series — time series with a tendency to revert to a long-term average. Mean reversion has been empirically observed in many markets, especially foreign exchange and commodities. We show that the slightest mean reversion yields positive expected profit, and also obtain stronger profit guarantees for a canonical stochastic mean reverting process, known as the Ornstein-Uhlenbeck (OU) process, as well as other stochastic mean reverting series studied in the finance literature. We also show that market making remains profitable in expectation for the OU process even if some realistic restrictions on trading frequency are placed on the market maker. Disciplines Computer Sciences Comments Chakraborty, T. & Kearns, M., Market Making and Mean Reversion, 12th ACM Conference on Electronic Commerce, June 2011, doi: 10.1145/1993574.1993622 ACM COPYRIGHT NOTICE. Copyright © 2011 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Publications Dept., ACM, Inc., fax +1 (212) 869-0481, or [email protected]. This conference paper is available at ScholarlyCommons: https://repository.upenn.edu/cis_papers/643 Market Making and Mean Reversion Tanmoy Chakraborty Michael Kearns University of Pennsylvania University of Pennsylvania [email protected] [email protected] ABSTRACT 1. INTRODUCTION Market making refers broadly to trading strategies that seek A market maker is a firm, individual or trading strategy to profit by providing liquidity to other traders, while avoid- that always or often quotes both a buy and a sell price for a ing accumulating a large net position in a stock. In this financial instrument or commodity, hoping to make a profit paper, we study the profitability of market making strate- by exploiting the difference between the two prices, known as gies in a variety of time series models for the evolution of a the spread. Intuitively, a market maker wishes to buy and stock’s price. We first provide a precise theoretical charac- sell equal volumes of the instrument (or commodity), and terization of the profitability of a simple and natural market thus rarely or never accumulate a large net position, and making algorithm in the absence of any stochastic assump- profit from the difference between the selling and buying tions on price evolution. This characterization exhibits a prices. trade-off between the positive effect of local price fluctua- Historically, the chief purpose of market makers has been tions and the negative effect of net price change. We then to provide liquidity to the market — the financial instru- use this general characterization to prove that market mak- ment can always be bought from, or sold to, the market ing is generally profitable on mean reverting time series — maker at the quoted prices. Market makers are common time series with a tendency to revert to a long-term aver- in foreign exchange trading, where most trading firms offer age. Mean reversion has been empirically observed in many both buying and selling rates for a currency. They also play markets, especially foreign exchange and commodities. We a major role in stock exchanges, and historically exchanges show that the slightest mean reversion yields positive ex- have often appointed trading firms to act as official market pected profit, and also obtain stronger profit guarantees for makers for specific equities. NYSE designates a single mar- a canonical stochastic mean reverting process, known as the ket maker for each stock, known as the specialist for that Ornstein-Uhlenbeck (OU) process, as well as other stochastic stock. In contrast, NASDAQ allows several market makers mean reverting series studied in the finance literature. We for each stock. More recently, fast electronic trading systems also show that market making remains profitable in expec- have led trading firms to behave like market makers without tation for the OU process even if some realistic restrictions formally being designated so. In other words, many trading on trading frequency are placed on the market maker. firms attempt to buy and sell a stock simultaneously, and profit from the difference between buying and selling prices. Categories and Subject Descriptors We shall refer to such trading algorithms generally as market making algorithms. F.2.2 [Theory of Computation]: Analysis of Algorithms In this paper, we analyze the profitability of market mak- and Problem Complexity; J.4 [Social and Behavioral Sci- ing algorithms. Market making has existed as a trading ences]: Economics practice for a long time, and it has also inspired significant amount of empirical as well as theoretical research [9, 5, 10, General Terms 1, 2, 3]. Most of the theoretical models [5, 9, 2, 3] view mar- ket makers as dealers who single-handedly create the market Theory, Economics, Algorithms by offering buying and selling prices, and there is no trading in their absence (that is, all trades must have the market Keywords marker as one of the parties). On the other hand, much of Computational Finance, Algorithmic Trading, Market Mak- the empirical work has focused on analyzing the behavior of ing, Mean Reversion specialist market makers in NYSE, using historical trading data from NYSE [10, 1]. In contrast, our theoretical and empirical work studies the behavior of market making algo- rithms in both very general and certain specific price time Permission to make digital or hard copies of all or part of this work for series models, where trading occurs at varying prices even personal or classroom use is granted without fee provided that copies are in the absence of the market maker. This view seems ap- not made or distributed for profit or commercial advantage and that copies propriate in modern electronic markets, where any trading bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific party whatsoever is free to quote on both sides of the mar- permission and/or a fee. ket, and officially designated market makers and specialists EC'11, June 5–9, 2011, San Jose, California, USA. are of diminishing importance. Copyright 2011 ACM 978-1-4503-0261-6/11/06 ...$10.00. Market Making vs. Statistical Arbitrage. can place buy and sell limit orders with some quoted limit Before describing our models and results, we first offer order prices at any time, and may also cancel these orders some clarifying comments on the technical and historical dif- at any future time. For simplicity, we assume that each or- ferences between market making and statistical arbitrage, der requests only one share of the stock (a trader may place the latter referring to the activity of using computation- multiple orders at the same price). If at any time after plac- intensive quantitative modeling to design profitable auto- ing the order and before its cancellation, the asset price of mated trading strategies. Such clarification is especially the stock equals or exceeds (respectively, falls below) the called for in light of the blurred distinction between tra- quoted price on a sell order (respectively, buy order), then ditional market-makers and other kinds of trading activity the order gets executed at the quoted price, i.e.
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