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)

200 1,000 300 750 1,200 200 1,600 3,000 300 250

19 19.25 19.5 19.75 20 20.25 20.5 20.75 21 21.25 21.5

PRICES

QUANTITIES

Market Buy Order for 500 Shares

200 1,000 300 750 1,200 200 1,600 3,000 300 250

19 19.25 19.5 19.75 20 20.25 20.5 20.75 21 21.25 21.5

PRICES

QUANTITIES

200 1,000 300 750 1,200 1,300 3,000 300 250

Limit Buy Orders: 1,000 at 20 and 500 at 20.25

200 1,000 300 750 1,200 1,300 3,000 300 250

19 19.25 19.5 19.75 20 20.25 20.5 20.75 21 21.25 21.5

PRICES

QUANTITIES

200 1,000 300 750 2,200 500 1,300 3,000 300 250

Market Sell Order for 3,000

19 19.25 19.5 19.75 20 20.25 20.5 20.75 21 21.25 21.5

PRICES

QUANTITIES

200 1,000 300 750 2,200 500 1,300 3,000 300 250 200 1,000 300 450 1,300 3,000 300 250

Limit Buy Order: 1,500 at 20.75

19 19.25 19.5 19.75 20 20.25 20.5 20.75 21 21.25 21.5

PRICES

QUANTITIES

200 1,000 300 450 1,300 3,000 300 250 200 1,000 300 450 200 3,000 300 250

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 – risk-neutral 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 gameYou are a dealer in a particular security. Write down

the last 4 digits of your phone number. Your inventory is:

After the round of trading each share will pay either $80 or $120 with equal probabilities.

Last 4 digits of your phone number

Inventory

Even and > 5,00 Long 1,000 shares

Even and < 5,000; > 0 Long 250 shares

Odd and < 5,000; > 0 Short 250 shares

Odd and > 5,000 Short 1,000 shares

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 and Variance .• 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:

Y0.5zY22.

• Buy at the Bid, B, to increase the inventory by X:

Y + (- B)X0.5z(Y + X)22

• If indifferent, then the maximal bid price must be:

Bmaxz2Y 0.5z2X.

Ask Price and Spread

• No action:

Y0.5zY22.• Sell at the Ask, A, to increase the inventory by X:

Y + (A - )X0.5z(Y - X)22

• If indifferent, then the bid price must be:

Amin = z2Y 0.5z2X.

Dealer Spread

• The same dealer quotes two different prices:

Amin = z2Y 0.5z2 X;

Bmaxz2Y 0.5z2 X.

• The dealer’s spread is:

Amin - Bmax = z2X.

Dealer Spread

Bmax Amin.

Bmax Amin.

Zero inventory

Negative inventory

Positive inventory

Bmax Amin.

Is this possible?

Bmax Amin

Very large negative inventory

Very large positive inventory

Bmax Amin

Market spread

B1max A1

min

Dealer 1 - Positive inventory

Dealer 2 - Negative inventory

B2max A2

min

Market Spread

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 or VL,

with probability (1- ): VA = VH* + VL*(1- ).

• The trader that submits a market order knows the realized value of V with probability

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) VA

• Bmax = VA - (VA - VL) VA

• These prices take into account the information imbedded in the trades.

• They yield zero profits to the dealer.

• The spread S = (VH - VL) is

notsymmetric 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.