The Effects of Market-Making on Price
Dynamics
Presented by:
Mehmet Bicer
The Graduate Center/CUNY
mbicer@gc.cuny.edu
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.
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 MarketMaker
• 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
887-894, 2008, http://www.cs.rpi.edu/~sanmay/papers/mm-pricediscovery.pdf
[2] S. M. Kakade, M. Kearns, Y. Mansour, and L. Ortiz, Competitive algorithms for VWAP and limitorder trading. In Proceedings of the ACM Conference on Electronic Commerce, pages 189-198,
2004. http://ttic.uchicago.edu/~sham/papers/gt/vwap.pdf
[3] S. Das. A learning market-maker in the Glosten-Milgrom model. Quantitative Finance, 5(2):169180, April 2005.
[4]http://www.thaindian.com/newsportal/world-news/google-posts-surprise-earnings-despite-weakus-economy_10039198.html
Q &A