Economics of Market Making

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Topic 4
Liquidity
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The Frictionless Environment
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A Perfect, Frictionless World

• No transaction costs
• CAPM
• Stocks have intrinsic values
• What does this mean?

Infinite elasticity implies infinite liquidity
what explains it?
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Stocks and Portfolios have Replicating
Portfolios in a CAPM World

• The covariance of a stocks returns with the
  market portfolios returns can be replicated
• Cov (A,M) gt Cov (B,M) gt Cov (C,M)
• With proper weights on A and C,
• Cov (A C,M) Cov (B,M)

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A Stock and its Replicating Portfolio

• Stocks (portfolios) with the same covariance
  should be priced to yield the same expected
  return, E(ri)
• If E(ri) is too high, Pi is too low vis-à-vis the
  replicating portfolio
• If E(ri) is too low, Pi is too high vis-à-vis the
  replicating portfolio
• Any price divergence between a stock and its
  replicating portfolio will be arbitraged away
• Arbs are the source of infinite liquidity in a
  CAPM world

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Information Needed in the Frictionless World

• Stock Returns
• Means
• Variances
• Covariances (cross-sectional)

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The Efficient Market Hypothesis (EMH)

• Existing information cannot be exploited to
  realize above normal (risk adjusted) trading
  profits
• Weak form
• information historical market information
• Semi-strong form
• information weak form publicly available
  info
• Strong form
• Information semi-strong form private info
• the complete information set

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Random Walk
If the EMH holds Security price changes
(returns) are not serially correlated
Ri,t ? f(Ri,t-1)
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What is Risk?

• Stock Returns
• Variances
• Covariances (cross-sectional)

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Illiquidity, Information Expectations
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Risk vs (IL)Liquidity
Against the Gods The Remarkable Story of Risk,
Peter L. Bernstein Against the Devil The
Remarkable Story of Liquidity (Just a
title) Lets start at the beginning (it has to do
with information)
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Information

• Classification 1
• Market info
• Fundamental info
• Classification 2
• Public info
• Inside info
• Private info

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Information isVast, Complex and Imprecise
Yet, we can trivialize it. Here is
O, The Information Set
O
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6 Blind Men An Elephant
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ExpectationsBased on Information

• Three possible situations
• Investors have homogeneous expectations
• There is asymmetric information
• Investors have divergent expectations based on
  information that they all possess

Question Under which scenario will liquidity be
greatest?
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Liquidity What is it?

• Difficult to define measure but
• You know when its not there
• Ability to trade in reasonable size, at a
  reasonable price, in a reasonable amount of time

• A quick operational definition
• Lots of orders on the book
• Lots of order flow

Without sufficient liquidity, a market will not
function
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Some Better Definitions

• Depth and breadth
• Resiliency
• Market cap and trading volume
• Bid-ask spread
• Accentuated intra-day volatility

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Intra-Day Volatility
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INTRADAY VOLATILITY NYSE
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INTRADAY VOLATILITY NASDAQ
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INTRADAY VOLATILITY LONDON STOCK EXCHANGE
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INTRADAY VOLATILITY EURONEXT PARIS
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INTRADAY VOLATILITY DEUTSCHE BÖRSE
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U-Shaped Intra-Day One-Minute Volatility
60 bps Feb 2004 (Pre-Calls)
w
Market Structure and Intra-day Price Behavior
An Event Study on Nasdaqs Crosses, Pagano, Peng
and Schwartz, 2008, working paper
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U-Shaped Intra-Day10-Second Volatility
40 bps Feb 2004 (Pre-Calls)
5 Min After Opening
5 Min Before Close
Market Structure and Intra-day Price Behavior
An Event Study on Nasdaqs Crosses, Pagano, Peng
and Schwartz, 2008, working paper
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What Explains This Volatility?

• Transaction costs
• Explicit costs
• Execution costs (See pages 64 69)
• Price discovery
• Quantity discovery

In a Word Illiquidity
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Other Issues
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Origins of Liquidity

• Continuous order-driven market
• Periodic call auctions
• Quote driven markets
• Negotiated trades
• Hybrid markets

A Bottom Line Market Structure Effects Liquidity
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Illiquiditys Footprints inTransaction Records

• Relevant Concepts
• Intertemporal correlation
• Autocorrelation
• Serial correlation
• First order autocorrelation
• Higher order autocorrelation
• Serial cross-correlation

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Autocorrelation and Market Factors
Market Factor
Correlation what kind?

• Sequential information arrival
• Limit order book
• Market maker intervention
• Inaccurate price discovery
• Bid-ask spread
• Market impact
• Non-synchronous price adjustment across stocks

• ,-, or what?
• ,-, or what?
• ,-, or what?
• ,-, or what?
• ,-, or what?
• ,-, or what?
• ,-, or what?

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How Do The Following Affect How Frequently You
Trade?

• High explicit trading costs (commissions and
  fees)
• High implicit costs (bid-ask spreads and market
  impact)
• Accentuated intra-day volatility
• Capital gains taxes
• A feeling that our markets are not fair, that
  others participants will benefit at your expense
• A feeling that prices adjust so quickly to news
  that you will never be able to buy profitably
  when there is good news, or will be unable to cut
  your losses by selling before the market has
  fully responded to bad news

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Liquidity and Network Externalities

• Network examples
• Fax machines
• Microsoft Word
• An equities market
• Network externalities
• Order flow attracts order flow
• Network externalities, market size, and liquidity
• The most important determinant of the quality of
  a market is its size

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What Do the Following Have in Common?
Without Gas, Neither Will Run