The Effects of MarketMaking on Price Dynamics

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The Effects of Market-Making on Price Dynamics
Presented by Mehmet Bicer The Graduate
Center/CUNY mbicer_at_gc.cuny.edu May 5, 2009
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Topics

• Introduction
• Background
• The Model
• Simulation Results
• Summary

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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

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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?

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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. Googles shares shot up more
than 11 percent in after-hours trading as the
earnings report beat analysts estimates. People
said Google cant keep defying the laws of
gravity, but it looks like Google is flying high
again, Jerome Dodson of Parnassus Investments
told Bloomberg News.
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Some Terms

• Efficient Market Hypothesis
• Prediction markets
• Specialist
• Market Maker

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Terms

• Efficient markets hypothesis prices reflect all
  available information. Yet we need to know how
  this new price gets formed.
• Prediction MarketsPrediction 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.

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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.

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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).

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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

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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.

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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.)

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The Model

• Structure
• Trader Model
• Market-maker Model

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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 sv
• 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

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Trader Model

• A trader is selected beginning of each round.
• This trader values the stock at WI 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.

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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.

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Expected Profit Calculation
s
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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.

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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.

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Simulation Results

• Experimental Design
• µv 75, sv1, sw 0.2
• Each episode (day) consist of n 100 periods
  (rounds).
• Delta 0.10

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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.

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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.

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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.

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The Absence of a Market-Maker

• See figure 6.

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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 .

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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."

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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
887-894, 2008, http//www.cs.rpi.edu/sanmay/paper
s/mm-pricediscovery.pdf 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 189-198, 2004. http//ttic.uchicag
o.edu/sham/papers/gt/vwap.pdf 3 S. Das. A
learning market-maker in the Glosten-Milgrom
model. Quantitative Finance, 5(2)169-180, April
2005. 4http//www.thaindian.com/newsportal/world
-news/google-posts-surprise-earnings-despite-weak-
us-economy_10039198.html
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