The Effects of Market-Making on Price Dynamics Presented by: Mehmet Bicer The Graduate Center/CUNY May 5, 2009

Topics Introduction Background The Model Simulation Results Summary

Introduction This paper is about market-makers and their role in price discovery and market quality. Information shock  Reflected new price is orderly or a sudden increase? Fund manager example (VWAP) Google example. Some Terms

VWAP (Volume Weighted Average Price) A fund manager example. She wants to reduce a security holding from 3% to 2%. How will she do it?

Google example for information shock Google posts surprise earnings despite weak US economy New York, April 18 (DPA) Google Inc reported a 30-percent jump in first-quarter earnings Thursday to $1.31 billion, allaying fears that the internet search engine leader was struggling with the effects of a US economic slowdown. Revenue also climbed 42 percent to $5.19 billion, with more than half its sales coming from outside the US, the company said after market close. Google’s shares shot up more than 11 percent in after-hours trading as the earnings report beat analysts’ estimates. “People said ‘Google can’t keep defying the laws of gravity,’ but it looks like Google is flying high again,” Jerome Dodson of Parnassus Investments told Bloomberg News.

Some Terms Efficient Market Hypothesis Prediction markets Specialist Market Maker

Terms Efficient markets hypothesis: “prices reflect all available information”. Yet we need to know how this new price gets formed. Prediction Markets:”Prediction markets (also known as predictive markets, information markets, decision markets, idea futures, event derivatives, or virtual markets) are speculative markets created for the purpose of making predictions.”

Specialist “ A member of an exchange who acts as the market maker to facilitate the trading of a given stock. The specialist holds an inventory of the stock, posts the bid and ask prices, manages limit orders and executes trades. Specialists are also responsible for managing large movements by trading out of their own inventory. If there is a large shift in demand on the buy or sell side, the specialist will step in and sell out of their inventory to meet the demand until the gap has been narrowed. There is usually one specialist per stock who stands ready to step in and buy or sell as many shares as needed to ensure a fair and orderly market in that security.”

Market Maker (MM) “ A broker-dealer firm that accepts the risk of holding a certain number of shares of a particular security in order to facilitate trading in that security. Each market maker competes for customer order flow by displaying buy and sell quotations for a guaranteed number of shares. Once an order is received, the market maker immediately sells from its own inventory or seeks an offsetting order. This process takes place in mere seconds. The Nasdaq is the prime example of an operation of market makers. There are more than 500 member firms that act as Nasdaq market makers, keeping the financial markets running efficiently because they are willing to quote both bid and offer prices for an asset.” “Major firms making markets in global stock exchanges as well as software agents (electronic markets, prediction markets)”.

Background Market Microstructure Limit Orders and Market Orders Limit order Limit order book Highest buy/lowest sell limit order Market order Guaranteed Typical market order Spread

Liquidity and Market-Making Different exchanges have one or more MMs Main responsibility of MM is liquidity and keeping trading interest in a security Liquidity is also about the depth of the limit order book In absence of MMs there is no guarantee that even a market order will get executed.

Microstructure Theory Process of price adjustment to new information Market quality and liquidity Entire limit order book Bid ask spread How market maker gets compensated transaction costs (cost of doing business) inventory holding costs (risk) adverse selection costs (focus of this paper: traders who have better information.)

The Model Structure Trader Model Market-maker Model

Structure Episode (day) is divided into n units of time (rounds) A single stock A true value V of a stock V is sampled from normal distribution with mean μv and standard deviation σv Informational shock, reflected time 0 True value stays the same during rest of the day MM is buyer for all sellers and seller for all buyers. She is the one against the whole trading crowd. The Trader model The Market-maker model

Trader Model A trader is selected beginning of each round. This trader values the stock at W^I with some variance. If the value of stock is greater than the asked price, he buys a unit of stock, if the value is less, then, he sells. If neither of these holds, then two things can happen: 1) The trader doesn't trade (b/c he is not allowed to submit limit orders) 2) Allowed to submit limit orders, so submits them in between ask and bid prices and depending the assumed true value of the stock.

Market-Maker model MM has no information about the true value of the stock--except she knows the value at time 0 of each day. Afterwards, she estimates this based on the orders and probability density. They are risk-neutral or risk-averse. The set the bid and ask prices. All transactions occur trader against MM. If there are multiple MMs, then, max bid is bid, min ask is ask price. Two types of traders: Informed (subscribed to services, insiders) who know the true value. Uninformed. They buy or sell with equal probability.

Expected Profit Calculation s

A zero profit market maker In a perfectly competitive environment, MM's strategy is to set prices so that there is zero profit. In this environment bid price is equal to expected value of sell price.

A Myopically Optimizing Market- Maker There is only one market maker She sets the bid and ask prices to maximize her expected profits The trading crowd are not allowed to put limit orders. Yet, the overall profit maximization is not guaranteed to be the best. See Table1. When traders are allowed to place limit orders, then, unless the market maker improve its bid and ask price no trade will take place therefore there will be no profit.

Simulation Results Experimental Design μv = 75, σv=1, σw = 0.2 Each episode (day) consist of n = 100 periods (rounds). Delta = 0.10

Interpreting the Results A price jump High spread Low volume Heterogeneous information (once it becomes homogeneous then the other issues will be resolved) Price discovery and efficient markets regimes The average trader incur higher costs when the spread is high. (if they have liquidity problem or other immediate reasons, they will incur loss.) Stock exchanges prefer lower spreads and higher volume Myopic MMs would want to optimize their profit.

A Price-Setting Market-Maker First simulations (Table 1) MM is monopolistic Zero-profit +- delta is better than myopic MM in terms all of the criteria: profit, lower spread and more liquidity (I.e. more # of trades) Zero profit provides most liquidity. Myopic algorithm doesn't optimize over a sequential game. Prices give information about the true value of stock. MM's narrower spreads will allow her make more trades and potentially more profits in the future.

Competition in the Limit Order Book Faster price discovery Table 2 shows that market quality is significantly improved. See average spread and number of trades.

The Absence of a Market-Maker See figure 6.

Summary Market-makers speed up the process of finding the true price of a stock which is reflected as low spread. Even having a less regulated, myopic MM is better than not having one at all because they increase the quality of the markets.

Open problems "What is the optimal market-making algorithm for a monopolistic, price-setting market maker in the sequential context?" "The market maker's exploration-exploitation trade of can be thought of as a tradeoff between price discovery and profit taking. The optimal strategy for a market maker in this setting is uncharacterized."

References [1] Sanmay Das, The effects of market-making on price dynamics, Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2, Pages , 2008, [2] S. M. Kakade, M. Kearns, Y. Mansour, and L. Ortiz, Competitive algorithms for VWAP and limit- order trading. In Proceedings of the ACM Conference on Electronic Commerce, pages , [3] S. Das. A learning market-maker in the Glosten-Milgrom model. Quantitative Finance, 5(2): , April [4] us-economy_ html

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