©R. Schwartz Equity Markets: Trading and StructureSlide 1 Topic 4

Slide 1 ©R. Schwartz Equity Markets: Trading and Structure

Topic 4


The Frictionless Environment


A Perfect, Frictionless World

• No transaction costs• CAPM• Stocks have intrinsic values

What does this mean?

a

No. Shares

Price

Infinitely elastic demand to hold shares

Infinite elasticity implies infinite liquidity – what explains it?


Stocks and Portfolios have Replicating Portfolios in a CAPM World

The covariance of a stock’s returns with the market portfolio’s returns can be replicated

• Cov (A,M) > Cov (B,M) > Cov (C,M)

• With proper weights on A and C,

• Cov ([A+ C],M) = Cov (B,M)


A Stock and it’s Replicating Portfolio

Stocks (portfolios) with the same covariance should be priced to yield the same expected return, E(r i)

• 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


Information Needed in the Frictionless World

Stock Returns:

• Means

• Variances

• Covariances (cross-sectional)


The Efficient Market Hypothesis (EMH)

Existing information cannot be exploited to realize above normal (risk adjusted) trading profits

• Weak forminformation = historical market information

• Semi-strong form information = weak form + publicly available info

• Strong formInformation = semi-strong form + private info

= the complete information set


Random Walk

If the EMH holdsIf the EMH holds

Security price changes (returns) Security price changes (returns) are notare not serially serially correlatedcorrelated

Ri,t ≠ f(Ri,t-1)


What is Risk?

Stock Returns:

• Variances

• Covariances (cross-sectional)


Illiquidity, Information & Expectations


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)


Information

Classification #1• Market info• Fundamental info

Classification #2• Public info• Inside info• Private info


ΩΩ, , The Information SetThe Information Set

Information isVast, Complex and Imprecise

Yet, we can trivialize it. Here is…


6 Blind Men & An Elephant


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

QuestionUnder which scenario will liquidity be greatest?


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

Without sufficient liquidity, a market will not function

A quick operational definition:

• Lots of orders on the book

• Lots of order flow


Some Better Definitions

• Depth and breadth

• Resiliency

• Market cap and trading volume

• Bid-ask spread

• Accentuated intra-day volatility


Intra-Day Volatility


INTRADAY VOLATILITYNYSE

October - December 1999

0.00%

0.40%

0.80%

1.20%

1.60%

Hal

f-Hou

r V

olat

ility

The First 1/2 Hour


INTRADAY VOLATILITYNASDAQ

October - December 2000

0.00%

0.50%

1.00%

1.50%

2.00%

Ha

lf-H

ou

r V

ola

tili

ty

The First 1/2 Hour


January - May 2000

0

0.5

1

1.5

2

2.5

3

8:00

-8:3

0

8:30

-9:0

0

9:00

-9:3

0

9:30

-10:

00

10:0

0-10

:30

10:3

0-11

:00

11:0

0-11

:30

11:3

0-12

:00

12:0

0-12

:30

12:3

0-1:

00

1:00

-1:3

0

1:30

-2:0

0

2:00

-2:3

0

20:3

0-3:

00

3:00

-3:3

0

3:30

-4:0

0

4:00

-4:3

0

Ha

lf-H

ou

r V

ola

tili

ty

INTRADAY VOLATILITYLONDON STOCK EXCHANGE

The First 1/2 Hour


INTRADAY VOLATILITYEURONEXT PARIS

January - May 2000

0

0.2

0.4

0.6

0.8

1

1.2

1.4

9:00-9

:30

9:30-1

0:00

10:00

-10:30

10:30

-11:00

11:00

-11:30

11:30

-12:00

12:00

-12:30

12:30

-1:00

1:00-1

:30

1:30-2

:00

2:00-2

:30

2:30-3

:00

3:00-3

:30

3:30-4

:00

4:00-4

:30

4:30-5

:00

Clos

ing Call

Ha

lf-H

ou

r V

ola

tili

ty

The First 1/2 Hour


INTRADAY VOLATILITYDEUTSCHE BÖRSE

January - May 2000

0

0.2

0.4

0.6

0.8

1

1.2

Ha

lf-H

ou

r V

ola

tili

ty

The First 1/2 Hour


U-Shaped Intra-Day One-Minute Volatility*

* “Market Structure and Intra-day Price Behavior: An Event Study on Nasdaq’s Crosses,” Pagano, Peng and Schwartz, 2008, working paper

wr ange

0

20

40

60

i nt er val

0 30 60 90 120 150 180 210 240 270 300 330 360 390

60 bps60 bps Feb 2004 (Pre-Calls) Feb 2004 (Pre-Calls)


U-Shaped Intra-Day10-Second Volatility*

* “Market Structure and Intra-day Price Behavior: An Event Study on Nasdaq’s Crosses,” Pagano, Peng and Schwartz, 2008, working paper

r ange

0

10

20

30

40

i nt er val

0 6 12 18 24 30 36 42 48 54 60

40 bps40 bps Feb 2004 (Pre-Calls) Feb 2004 (Pre-Calls)5 Min After

Opening5 Min Before

Close


What Explains This Volatility?

• Transaction costs

Explicit costs

Execution costs (See pages 64 – 69)

• Price discovery

• Quantity discovery

In a Word“Illiquidity”


Other Issues


Origins of Liquidity

• Continuous order-driven market

• Periodic call auctions

• Quote driven markets

• Negotiated trades

• Hybrid markets

A Bottom LineMarket Structure Effects Liquidity


Illiquidity’s Footprints inTransaction Records

Relevant Concepts:

• Intertemporal correlation

• Autocorrelation

• Serial correlation

• First order autocorrelation

• Higher order autocorrelation

• Serial cross-correlation


Autocorrelation and Market Factors

• Sequential information arrival

• Limit order book

• Market maker intervention

• Inaccurate price discovery

• Bid-ask spread

• Market impact

• Non-synchronous price adjustment across stocks

Correlation: what kind?Market Factor• +,-, or what?

• +,-, or what?

• +,-, or what?

• +,-, or what?

• +,-, or what?

• +,-, or what?

• +,-, or what?


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


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


What Do the Following Have in Common?

Documents

©R. Schwartz Equity Markets: Trading and StructureSlide 1 Topic 4