Transcript Prices

Lecture 3
Secondary Equity Markets - I
Trading motives
• Is it a zero-sum game?
• Building portfolio for a long run.
• Trading on information.
• Short-term speculation.
• Liquidity provision.
Secondary Market Types
• Immediacy Provision:
– Dealers – all receive immediacy; all pay the
spread;
– Call auction – none receive immediacy – all wait.
– Limit order book – patient supply, impatient
demand immediacy. The importance of choice.
• Electronic vs. Trading Floor.
• Multilateral vs. Bilateral.
• Price priority and time priority.
Orders
• Market order – specifies the quantity, but not the
price. Demands immediacy.
• Limit order – specifies the quantity as well as the
price. Usually supplies immediacy.
• Marketable (executable) limit order – demands
immediacy, but not at any price.
• Orders with conditions.
Limit Order Book (Quotations)
PRICES
19
19.25 19.5 19.75 20
200 1,000 300
250
750 1,200
20.25 20.5 20.75 21
21.25 2
200 1,600 3,000 300
QUANTITIES
Market Buy Order for 500 Shares
PRICES
19
19.25 19.5 19.75 20
20.25 20.5 20.75 21
21.25 2
200 1,000 300
250
750 1,200
200 1,600 3,000 300
200 1,000 300
250
750 1,200
1,300 3,000 300
QUANTITIES
Limit Buy Orders: 1,000 at 20 and 500 at 20.25
PRICES
19
19.25 19.5 19.75 20
200 1,000 300
250
200 1,000 300
250
20.25 20.5 20.75 21
21.25 2
750 1,200
1,300 3,000 300
750 2,200 500
1,300 3,000 300
QUANTITIES
Market Sell Order for 3,000
PRICES
19
19.25 19.5 19.75 20
200 1,000 300
250
200 1,000 300
250
20.25 20.5 20.75 21
750 2,200 500
450
21.25 2
1,300 3,000 300
1,300 3,000 300
QUANTITIES
Limit Buy Order: 1,500 at 20.75
PRICES
19
19.25 19.5 19.75 20
200 1,000 300
250
200 1,000 300
250
20.25 20.5 20.75 21
21.25 2
450
1,300 3,000 300
450
200 3,000 300
QUANTITIES
Dealer markets
• Previous example – could it have been a
dealer market?
• Some changes:
– Quotes instead of limit orders;
– Standard size of a quote;
– Quotes are updated: one is removed another
appears
– Other than that – it would look very similar…
INET
• An example of a limit order book.
• Formerly Island, owned by Instinet.
• Recently purchased by NASDAQ.
• Pure Limit Order Book without
intermediaries..
• http://www.inetats.com/prodserv/bookviewer/htmlversion
.asp
Dealer markets - Overview
• Inventory model – risk averse dealer
provides immediacy to all, but bears the
risk.
• Asymmetric information model – riskneutral dealer faces better informed traders.
• Other aspects of competition.
• Examples.
Inventory model
• Dealer stands ready to provide immediacy
to all clients by quoting prices and
supplying the stocks from his inventory:
• The dealer takes into account:
– His risk tolerance (define);
– His inventory;
– Trade size;
– Competition.
Let’s play another game
You are a dealer in a particular security. Write down the
last 4 digits of your phone number. Your inventory is:
Last 4 digits of your phone
number
Even and > 5,00
Inventory
Long 1,000 shares
Even and < 5,000; > 0
Odd and < 5,000; > 0
Odd and > 5,000
Long 250 shares
Short 250 shares
Short 1,000 shares
After the round of trading each share will pay either
$80 or $120 with equal probabilities.
Rules (cont.)
In a few seconds a market order will arrive;
it could be a buy or a sell order for 500 shares.
You have to quote a Bid and an Ask price at
which you are willing to make these trades.
You compete with your classmates for these
trades. All of you must set your quotes
independently. Go ahead, and quote!
Formal Model
• Risk averse dealer with inventory Y.
• Perfectly competitive market (simplification) –
derive break-even prices.
• The value of security, V, is a random variable
with Mean m and Variance s2.
• Mean - variance preferences (W – wealth):
E(W) – 0.5zVar(W)
• Trade size is X.
Dealer choice:
• Perfect competition ensures that the dealer is
indifferent between buying (selling) and not trading.
• The action determines the risk.
• We derive the Bid and the Ask price separately,
then compute the Dealer Spread.
• Discussion.
Bid Price
• No action:
Ym - 0.5zY2s2.
• Buy at the Bid, B, to increase the inventory by X:
Ym + (m - B)X - 0.5z(Y + X)2s2
• If indifferent, then the maximal bid price must be:
Bmax = m - zs2Y - 0.5zs2X.
Ask Price and Spread
• No action:
Ym - 0.5zY2s2.
• Sell at the Ask, A, to increase the inventory by X:
Ym + (A - m)X - 0.5z(Y - X)2s2
• If indifferent, then the bid price must be:
Amin = m - zs2Y + 0.5zs2X.
Dealer Spread
• The same dealer quotes two different prices:
Amin = m - zs2Y + 0.5zs2 X;
Bmax = m - zs2Y - 0.5zs2 X.
• The dealer’s spread is:
Amin - Bmax = zs2X.
Dealer Spread
Zero inventory
Bmax
m
Amin.
Positive inventory
Bmax
m
Amin.
Negative inventory
Bmax m
Ami
Is this possible?
Very large positive inventory
Bmax
Amin
m
Very large negative inventory
m
Bmax
Amin
Market spread
Dealer 1 - Positive inventory
Dealer 2 - Negative inventory
B2max
B1max
A2min
m
Market Spread
A1min
Discussion
• Why isn’t the spread symmetric around the mean value?
• When will we ever observe it as a Market Spread?
• What if the volume depends on the spread?
• Alternative competition models.
• The basic intuition remains: if traders demand liquidity,
they impose costs on the dealer, and have to pay a
premium to cover these costs.
Asymmetric Information
Risk neutral dealer is willing to provide liquidity
from his inventory: what are his considerations?
– Risk aversion? - No
– Competition? - Yes.
– Inventory size? - No
– Trade size? - No
– Information? - Yes
Refresher
• When somebody has private information, they
will use it to choose actions.
• While the others cannot observe the information,
they can observe the action, thus should infer the
information from the action.
• This assumes rationality on the part of the
informed party.
Formal Model
• Risk neutral dealer, who has to quote Bid and Ask
prices.
• Perfectly competitive market (simplification).
• The value of security, V, is a random variable,
which can be either VH with probability a or VL,
with probability (1- a): VA = VH*a + VL*(1- a).
• The trader that submits a market order knows the
realized value of V with probability l.
Dealer choice:
• A trade may signal information, in which
case the dealer will lose money on it.
• Otherwise the trade is profitable.
• If he is willing to quote prices to all, he
must on average break even, thus he has
to charge informationless traders for the
losses caused by the informed.
Prices
• Amin = VA + (VH - VA) l > VA
• Bmax = VA - (VA - VL) l < VA
• These prices take into account the information
imbedded in the trades.
• They yield zero profits to the dealer.
• The spread S = (VH - VL) l
is not symmetric around the VA. Why?
Conclusions
• Inventory models – spread exists to cover the cost
of risk imposed on the dealer by the demanders of
immediacy.
• Information models – the mainstream – the spread
protects the dealer from the better informed traders.
The spread covers dealer’s “cost of ignorance”.
• In both cases the spread may impede trading.
• Insider trading prohibition.