Topic 8
©R. Schwartz
Equity Markets: Trading and Structure
Slide 1
Introductory Remarks
©R. Schwartz
Equity Markets: Trading and Structure
Slide 2
The Dynamic Behavior of Prices
The Effect of Trading Costs
• In a frictionless environment, prices would follow
random walks
• Do they?
• If so, how valuable would technical analysis and
algorithmic trading be?
• If not, would shares have unique fundamental values?
©R. Schwartz
Equity Markets: Trading and Structure
Slide 3
Do Shares Have Unique Values?
Belief
• Equilibrium values exist
• Complex information translates into a single price
• Shares have fundamental values
But
 This is not as simple as elementary economics
©R. Schwartz
Equity Markets: Trading and Structure
Slide 4
Remember This One?
PRICE
SELL
The perfectly liquid,
frictionless market
solution
P is
Discovered
BUY
0
©R. Schwartz
Q is
Discovered
QUANTITY
Equity Markets: Trading and Structure
Slide 5
Life Really is Not So Simple
©R. Schwartz
Equity Markets: Trading and Structure
The Standard Microstructure Model
• Information traders
• Liquidity traders
• Noise traders
©R. Schwartz
Equity Markets: Trading and Structure
Slide 7
TraderEx Orders Come From
3 Types of Participants
Information
traders
P*
Is p*>offer
or p*<bid?
Liquidity
Traders
Quotes,
Prices,
Volume
Noise
Traders
Is there a
trend/
pattern?
Trading Mechanism
©R. Schwartz
Equity Markets: Trading and Structure
Slide 8
Thoughts of a Efficient Market
©R. Schwartz
Equity Markets: Trading and Structure
Slide 9
What is Behind
Standard Finance Models?
• Markets are informationally efficient (EMH)
• Shares have unique fundamental values
• Informed investors form identical expectations
 Homogeneous expectations
©R. Schwartz
Equity Markets: Trading and Structure
Slide 10
With Homogeneous Expectations
• Information maps uniquely into security values
(fundamental values)
• If trades are triggered for liquidity reasons only, shares will
trade at bid & ask quotes that are appropriate given the
fundamentals
• Aside from bid-ask bounce, prices will follow random walks
Hmmm…
What economic function is left for an exchange?
©R. Schwartz
Equity Markets: Trading and Structure
Slide 11
Traditional Support for
Random Walk
Burton Malkiel, A Random Walk Down Wall Street, 1973
“Technical analysis is anathema to the academic
world. We love to pick on it. Our bullying tactics are
prompted by two considerations: (1) the method is
patently false; and (2) it's easy to pick on."
©R. Schwartz
Equity Markets: Trading and Structure
Slide 12
Of Course, We All Know That…
• Investors are rational and prices reflect
fundamental information
• Systematic patterns can be arbitraged away
• But… hmmm…wait a minute…
©R. Schwartz
Equity Markets: Trading and Structure
Slide 13
©R. Schwartz
Equity Markets: Trading and Structure
Slide 14
A Second Opinion
“The efficient market
hypothesis is the most
remarkable error in the history
of economic theory”
Lawrence Summers
Subsequently U.S. Treasury Secretary
The Wall Street Journal, 1987
©R. Schwartz
Equity Markets: Trading and Structure
Slide 15
An Earlier Opinion
Bernard M. Baruch, My Own Story,
Henry Holt & Company, 1957, p. 84
The prices of stocks – and commodities and bonds as well – are affected
by literally anything and everything that happens in our world, from new
inventions and the changing value of the dollar to vagaries of the weather
and the threat of war or the prospect of peace.
• But these happenings do not make themselves felt in Wall Street in an
impersonal way, like so many jigglings on a seismograph.
• What registers in the stock market’s fluctuations are not the events
themselves but the human reactions to these events, how millions of
individual men and women feel these happenings may affect the future.
©R. Schwartz
Equity Markets: Trading and Structure
Slide 16
With Whom Do You Agree?
1. Burton Malkiel
2. Lawrence Summers
3. Bernard Baruch
???
©R. Schwartz
Equity Markets: Trading and Structure
Slide 17
Another Perspective
©R. Schwartz
Equity Markets: Trading and Structure
Slide 18
A Deceptively Simple Question:
What motivates individuals to trade?
Accepted academic answer
• Informed traders
• Liquidity traders
• Noise traders
Perhaps we should add a fourth
• Divergent expectations (people disagree…)
©R. Schwartz
Equity Markets: Trading and Structure
Slide 19
Divergent Expectations
Has Implications For
•
•
•
•
Understanding market structure & operations
Assessing market quality
Government regulatory policy
Understanding volatlity
©R. Schwartz
Equity Markets: Trading and Structure
Slide 20
Edward M. Miller
“Risk, Uncertainty, & Divergence of Opinion”
Journal of Finance, Sept. 1977
“…it is implausible to assume that although the future is
very uncertain, and the forecasts are very difficult to
make, that somehow everyone makes identical estimates
of the return and risk from every security. In practice,
the very concept of uncertainty implies that reasonable
men may differ in their forecasts.”
©R. Schwartz
Equity Markets: Trading and Structure
Slide 21
Complexity of Information
•
•
•
•
Information sets are typically huge,
complex, & imprecise
Crudeness of our analytic tools
Price & quantity discovery may be more
complicated than academicians previously
thought
Technical analysis and algo trading may be
valid Wow, did an academician say this?
©R. Schwartz
Equity Markets: Trading and Structure
Slide 22
Difficulty of Assessing Share
Valuations With Precision
Can a stock analyst or portfolio manager
say with precision that the expected
growth rate for XYZ is:
 7.000%, not
 7.545%?
©R. Schwartz
Equity Markets: Trading and Structure
Slide 23
Analyst Evaluation of XYZ
Dividend one year from now
= $1.35
Appropriate cost of eq. cap.
= 10%
(1) Growth rate (g)
= 7.000%
(2) Growth rate (g)
= 7.545%
Share price if g =7.000%
Share price if g =7.545%
= $45.00
= $55.00
©R. Schwartz
Equity Markets: Trading and Structure
Slide 24
Evidence of Divergent Expectations
• Private information
• Analyst recommendations commonly differ
• Prevalence of short selling
• Two large institutions trading with each other on an ATS
(e.g., Posit, Pipeline or Liquidnet)
– Neither is likely to be a liquidity or noise trader
– Neither may presume to have an informational edge
– They are simply “agreeing to disagree”
©R. Schwartz
Equity Markets: Trading and Structure
Slide 25
Representing Divergent
Expectations in TraderEx
Informed
Traders
Liquidity
Traders
P*
Is p*>offer
or p*<bid?
Do the informed
Traders agree with
each other? maybe not!
©R. Schwartz
Quotes,
Prices,
Volume
Noise
Traders
Is there a
trend/
pattern?
P* + 10% = VH (the bulls)
P* - 10% = VL (the bears)
Equity Markets: Trading and Structure
Slide 26
Price Discovery
©R. Schwartz
Equity Markets: Trading and Structure
Slide 27
The Inside Scoop on
Price Discovery
• A complex, protracted process
• Contributes to intra-day volatility
• Equilibrium depends on the sequence of order arrivals &
on how orders are handled
→ A coordination problem
• The quality of price discovery depends on trader behavior
& market structure
• Divergent expectations underlie the complexity of price
discovery
©R. Schwartz
Equity Markets: Trading and Structure
Slide 28
Divergent Expectations:
A Simple Setting
•
•
•
A company is facing a jury trial – its share value will be affected
appreciably by the outcome
Investors can have 1 of 2 expectations
 Some believe pr(acquittal) = .80
 Some believe pr(acquittal) = .35
Shares are valued at
 $55 by those who expect acquittal
 $45 by those who expect conviction
©R. Schwartz
Equity Markets: Trading and Structure
Slide 29
Lets Be More Generic
• Bi-variate outcome: a decision will soon be made that
will appreciably affect the value of a company
 Legal case: Acquit or convict
 Loan application: Grant or deny
 Takeover campaign: Win or loose shareholder votes
• Investors disagree about probability of positive outcome
• For bulls: positive expectation – stock is worth VH
• For bears: negative expectation – stock is worth VL
• The truth will soon be revealed
©R. Schwartz
Equity Markets: Trading and Structure
Slide 30
Price Determination in the
Bi-variate Context
VH = $55 (k percent of participants are bulls)
– A*
– B*
Bid-Ask Spread for k = 0.6
VL = $45 (1-k percent of participants are bears)
“Quote Setting and Price Formation
in an Order Driven Market”
Puneet Handa, Robert Schwartz, & Ashish Tiwari (HST)
Journal of Financial Markets, August 2003
©R. Schwartz
Equity Markets: Trading and Structure
Slide 31
From Divergent Expectations to…
•
•
•
We have not heard much about this
It implies endogeneity of the trading decision
A “Wisdom of the Crowds” reality
 A crowd is more likely to reach a correct decision
than any single member of the crowd assuming
independence
©R. Schwartz
Equity Markets: Trading and Structure
Slide 32
Picture It This Way
• 800 observes are guessing the number of beans
in a jar (the jar holds a lot, say 2500)
• Each observer looks at the jar individually and forms
an estimate
• The observers come up one at a time and disclose their
expectations
• Each observer’s expectation depends on his initial
estimate and on what he observes others guessing
• As more observers arrive, each places less weight on
his initial estimate
©R. Schwartz
Equity Markets: Trading and Structure
Slide 33
Adaptive Valuations (AV) Imply
•
•
Random (multiple) equilibria
Path dependency
With random equilibria, shares do not have
unique values
©R. Schwartz
Equity Markets: Trading and Structure
Slide 34
Our Starting Point:
The Handa, Schwartz, Tiwari Model
•
•
•
•
Risk neutral participants
Participants arrive in random sequence
Order driven, limit order book market
There are just two valuations: VH & VL
•
Orders are placed w.r.t. VH, VL, and k
→ k percent are bulls (VH)
→ (1-k percent are bears (VL)
©R. Schwartz
Equity Markets: Trading and Structure
Slide 35
HST Model Cont.
•
•
Market bid and offer prices for XYZ can be solved for
if we know
→ VH, VL, & k
If we know VH & VL only,
→ Price discovery is equivalent to k discovery
→ Remember…
VH = $55 (k percent are bulls)
– A*
– B*
Bid-Ask Spread for k = 0.6
VL = $45 (1-k percent are bears)
©R. Schwartz
Equity Markets: Trading and Structure
Slide 36

1 k
1 k  k 2
HST’s Optimal Bid (B*) and Offer (A*)
B* = γ VL + (1-γ) VH
A* =  VH + (1- ) VL
where
1 k
 
2
1 k  k
k

1 k  k 2
©R. Schwartz
Equity Markets: Trading and Structure
Slide 37
What if k is Not Known?
Orders are Based On
• Each participant’s own assessment of information
• Others’ assessments [ADAPTIVE VALUATIONS]
• Others’ opinions are reflected in k, the % who are bulls
©R. Schwartz
Equity Markets: Trading and Structure
Slide 38
How Does Price Evolve When
Everyone Uses This Basic Algorithm
“The Dynamic Process of Price
Discovery in an Equity Market,”
J. Paroush, R. Schwartz & A. Wolf
Working paper, 2008
©R. Schwartz
Equity Markets: Trading and Structure
Slide 39
Representative Price Paths
Alternative Equilibrium Prices
55
54
53
Price
52
51
50
49
48
47
46
45
0
5
10
15
20
25
30
No. Arrival
©R. Schwartz
Equity Markets: Trading and Structure
Slide 40
Volatility Consequences
• RC(t) = PC(t)/PC(t-1)
• Multiply and divide the RHS by VL(t)/ VL(t-1)
• Rearranging gives:
• RC(t) = [VL(t)/ VL(t-1)][PC(t) / VL(t)] ÷ [PC(t-1) / VL(t-1) ]
News
Price Discovery
• Volatility of RC(t)
= Vol [VL(t)/ VL(t-1)] + Vol [PC(t) / VL(t) ÷ PC(t-1) / VL(t-1)]
Efficient Vol
©R. Schwartz
Price Discovery Vol
Equity Markets: Trading and Structure
Slide 41
Information Complexities:
Consequences
Investor Expectations
• Divergent
• Can change independently at any time
• Adaptive
Simulation Results
55
54
53
Price Discovery
• Random (multiple) equilibria
• Path dependency
• Accentuated intra-day volatility
52
Price
51
50
49
48
47
46
45
1
©R. Schwartz
9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161 169 177 185 193 201 209 217 225 233 241 249
Equity Markets: Trading and Structure
Events
Slide 42
Implications
• Volatility
→ Intra-day & longer run bubbles and crashes
• Technical analysis
→Validation of a price
• Profitability of momentum and algorithmic trading
→Path dependency
• Importance of market structure
→ The quality of a network
• Algorithmic trading
©R. Schwartz
Equity Markets: Trading and Structure
Slide 43
Algorithmic Trading
©R. Schwartz
Equity Markets: Trading and Structure
Slide 44
Question
How Does Algo Trading Impact
Price Discovery?
©R. Schwartz
Equity Markets: Trading and Structure
Slide 45
Remember
Fragmentation Has a Temporal Dimension
• An order
can be fragmented
→ Slicing, dicing, & shredding
→ A breading ground for algo trading
→ Goal: make an elephant look like an ant
→ Warning: there can be negative consequences
©R. Schwartz
Equity Markets: Trading and Structure
Slide 46
From Elephants to Ants
©R. Schwartz
Equity Markets: Trading and Structure
Slide 47
If Algo Trading Helps Traders
Individually, Does it Benefit Them
Collectively?
• Yes, in an electronic world, algos are essential
• But some can lead to undesirable results
• Lets look at one that might
 Slice & dice algos?
 VWAP algos?
 Momentum algos?
 Contrarian algos?
 An algo for an ant…
©R. Schwartz
Equity Markets: Trading and Structure
Slide 48
An Algo for an Ant
That ant is a
momentum player…
©R. Schwartz
Equity Markets: Trading and Structure
Slide 49
An Algo for an Ant
???
©R. Schwartz
Equity Markets: Trading and Structure
Slide 50
The Ants Are Now in a “Circular Mill”
???
©R. Schwartz
Equity Markets: Trading and Structure
Slide 51
The Wisdom of the Crowds
James Surowiecki, 2005
• Who wants to be individually responsible for price
discovery?
•A consensus evaluation is likely to be more accurate than
participants’ individual valuations
• A “Wisdom of the Crowd” reality
• But how wise is the crowd if everyone is keying off of
what everyone else is doing?
• There is no wisdom in a circular mill
©R. Schwartz
Equity Markets: Trading and Structure
Slide 52
Further Discussion
©R. Schwartz
Equity Markets: Trading and Structure
Slide 53
Question
We have been focusing on trading, market
structure, and price discovery:
How well does anyone understand the markets?
©R. Schwartz
Equity Markets: Trading and Structure
Slide 54
… Both Sides of the Atlantic Have
Experienced Major Change in
• Technology
• Regulation
• Organizational Structure
• Competitive Environment
• Global Environment
How Far Have We Come?
©R. Schwartz
Equity Markets: Trading and Structure
Slide 55
How Far Have We Come?
• Commissions have shrunk
• Trading volumes have soared
• Implicit costs of trading have gone
down (in the opinion of many)
• A new, technologically savvy breed of
traders are on the scene
• Markets around the world are linked
Have we arrived in the
Promised Land?
©R. Schwartz
Equity Markets: Trading and Structure
Slide 56
Have We Arrived?
Not quite
Old issues are still with us
• Small orders for large caps: no problem
• Large orders for large caps: problems
• All orders for mid & small caps: problems
©R. Schwartz
Equity Markets: Trading and Structure
Slide 57
More Old Issues
• Transparency
• Best Execution
• Sub-Second Transaction Response Times
• Elevated intra-day volatility
• Spatial Consolidation/Fragmentation
• Temporal Consolidation/Fragmentation
– Slicing and dicing
©R. Schwartz
Equity Markets: Trading and Structure
Slide 58
Slicing & Dicing
•
Quantity discovery gets surprisingly little
Fact
Slicing and dicing are
prevalent
Average Trade Size at NYSE
• 1988:
2,303 shares
• June 2007:
297 shares
Block Trading Volume at NYSE
• 1988:
52 percent
• June 2007:
20 percent
©R. Schwartz
Equity Markets: Trading and Structure
Slide 59
Decreasing Trade Size
Average Daily Shares (Mils)
Average Shares/Trades
1,600
5,000
1,400
4,000
1,200
1,000
3,000
800
2,000
600
400
1,000
200
NYSE Shares (right axis)
NYSE Shares / Trade (left axis)
©R. Schwartz
6
Ja
n0
5
Ja
n0
4
Ja
n0
3
Ja
n0
2
Ja
n0
1
Ja
n0
0
Ja
n0
Ja
n9
Ja
n9
9
0
8
0
Nasdaq Shares (right axis)
NASDAQ Shares / Trade (left axis)
Slide 60
Equity Markets: Trading and StructureSources: NYSE, Nasdaq, TowerGroup
Why Does Market Structure Matter?
• Why does market structure matter?
 Because price & quantity discovery are complex!
• Why are these processes complex?
 Because shares do not have fundamental values!
• Why don’t they?
 Because investors have divergent expectations!
• Why do they?
 Because of the enormous complexity of information!
©R. Schwartz
Equity Markets: Trading and Structure
Slide 61
One More Statement
It is time we recognize that we operate in a
world where expectations are divergent,
evaluations are adaptive,
and analyze it as Such
©R. Schwartz
Equity Markets: Trading and Structure
Slide 62