©R. Schwartz Equity Markets: Trading and Structure Slide 1 Topic 5.

©R. Schwartz Equity Markets: Trading and Structure

Topic 5


Ecology of a Pure Order Driven Market

Some Participants

• Are looking to buy

• Are looking to sell

• Post limit orders

• Submit market orders

Participants meet to establish prices and trade. This requires:

An ecological balanceis required for a

market to function


The Placement of Limit Orders


What Drives an Order Driven Market?

• Without sufficient limit orders, the order driven market would fail

• What motivates their placement?

Limit Orders!


What Motivates/Detersthe Placement of Limit Orders?

How does this work?

Compensation For Limit Order TradersResults From the Pricing Dynamics of the

Continuous Order-driven Market*

*Source: Handa & Schwartz, “Limit Order Trading,” Journal of Finance, December 1996, pp. 1835 - 1861.


Information Change

Assume I have an open, unexecuted buy limit order on the book. If a news event occurs, it’s …

"Heads You Win, Tails I Lose”

• Heads You Win: Bearish news has caused the price of the stock to fall and my limit order executes

• Tails I Lose: Bullish news has caused the price of the stock to rise and my limit order doesn’t execute


Cost of being Bagged

• Heads You Win: Bearish news has caused the price of the stock to fall and my limit order executes

Non-execution Cost

• Tails I Lose: Bullish news has caused the price of the stock to rise and my limit order does not execute

• Or no news, and still my limit order does not execute

So Why Did I Place That Limit Order?So Why Did I Place That Limit Order?

2 Costs of Trading By Limit Order


A Liquidity Event Occurs

• A liquidity event that results in a price decline could cause my buy limit order to execute

• After being driven down, price would revert back up

• I profit as price mean reverts after my order has executed

• Sufficient mean reversion can offset the costs that result from informational change

Mean Reversion CompensatesThe Limit Order Trader


Mean Reversion and AccentuatedIntra-Day Volatility

• Accentuated intra-day volatility implies negative serial correlation

• Negative serial correlation implies mean reversion

Mean Reversion = Accentuated Volatility

They are the same thing


Of these three different types of events that can trigger executions and price changes,

which does it?

• Informational events• Liquidity events• Technical trading (momentum)

What Accentuates Volatility?

NoYes

What Accentuates Volatility?

Yes


All Three Occur inTraderEx

• Information events

• Liquidity events

• Momentum trading

How sensitive to them were you?


Conclusion:Accentuated Volatility Is a Natural Property of the Continuous Market

Regardless of

• Size of customer orders

• Sophistication of computer technology

• Speed with which orders can be submitted, withdrawn, or turned into trades


Intra-Day Volatility Is Accentuatedin TraderEx

Liquidity trading creates volatility and momentum players reinforce it

$21.00

$22.00

$23.00

$24.00

$25.00

$26.00

$27.00

$28.00

Ask

Bid

P*


Optimal Order Placement


Order Placement in anOrder Driven Market

Should I:

• Submit a market order?

• A limit order?

• If a limit order, how should I price it?The decision is made with respect to:

• Gains from trading

• Probability of a limit order executing


The Gains From Trading and the Concept of a Reservation Price

Reservation Price

• For a buyer: the highest price you are willing to pay for shares

• For a seller: the lowest price you are willing to sell shares atGains from trading

• For a buyer: reservation price – purchase price

• For a seller: Sale price – reservation price


Gains From Buying 1000 SharesYour Reservation Price = $12.00

Market Order

• Market ask = $11.10

• Buy 1000 by Market Order @ $11.10

• Gain ($12.00 – $11.10) x 1000 = $900

Limit Order

• Attempt to buy 1000 by Limit Order @ $10.80

• Gain ($12.00 – $10.80) x 1000 = $1200


Breakeven Probability (PBE) Reservation Price = $12.00

• Market Order Gain

($12.00 – $11.10) x 1000 = $900

• Limit Order Gain

($12.00 – $10.80) x 1000 = $1200

• $900 = PBE x $1200

• PBE = 75%

• If actual Prob of Exec > 75%, place Limit Order


Trade PriceProb of Exec

Gain per share Expected Gain

$ 11.10 1.00* 0.90 $ 900.00

$ 11.00 0.90 1.00 $ 900.00

$ 10.90 0.85 1.10 $ 935.00

$ 10.80 0.80 1.20* $ 960.00**$ 960.00**

$ 10.70 0.70 1.30 $ 910.00

$ 10.60 0.53 1.40 $ 742.00

* Market order ** Best order to place

Pricing a 1000 Share Buy Limit: Reservation Price = $12.00


Buyer’s Surplus


Probability of Executing


Buyer’s Expected Surplus


Back to TraderEx

• When you play TraderEx, can you quickly make decisions like this?

• Of course not

• But you might nevertheless feel your way instinctively

• Our discussion has hopefully formalized your instincts

• And, of course, you could always write an algo


Existence of the Bid-Ask Spread


Why Do Bid-Ask Spreads Exist in Order Driven Markets?

• In a quote driven market: the spread is the source of market maker profits

• In an order driven market? In a pure order driven market, there is no market maker intermediary

– Why isn’t the spread eliminated as the book fills in the neighborhood of equilibrium?


Meaningful vs Trivial Spreads

• Meaningful spread: economic forces explain its existence

• Trivial spread: minimum tick size explains its existence

• We can demonstrate existence of a meaningful spread by showing the existence of a non-infinitesimal spread when the tick size is infinitesimal (i.e., price is a continuous variable)


Bid – Ask Spread Reservation Price = $12.00

• Market order for 1000 shares (ask = $11.10)

Gain: ($12.00 – $11.10) x 1000 = $900

• Limit order infinitesimally close to $11.10

Gain: infinitesimally close to = $900

PBE: infinitesimally close to 100%

• Should you ever place a limit order to buy this close to an already posted limit order to sell?


Should You Ever Place a Limit Buy Infinitesimally Close to an Already

Posted Offer?

• PBE would be infinitesimally close to 100%

• With discrete order arrival, the probability of order execution at any price below the offer will never be infinitesimally close to 1

• So, should you ever place a limit order so close to an already posted contra-side quote?

No!


Bid-Ask Spread

Compensation for

• Risk of adverse informational change

• Risk of limit order not executing

Gravitational Pull Effect

If you are a limit order trader, the bid-ask spread must give you a positive expected return


Market Ask

Market Bid

Gravitational Pull

Potential Buy Order 2

Potential Buy Order 1


Why Do Non-Trivial SpreadsExist in TraderEx?

0% 2% 4% 6% 8% 10% 12% 14%

25.80

25.90

26.00

26.10

26.20

26.30

26.40

26.50

26.60

Price (5¢ Tick Size)

Probability

Limit sell orders

Offer

Bid

Executable sell orders

The probability distribution use to get liquidity driven sell orders


Two Other Topics


An Option Trader’s View of Limit Orders

• The option extended

• The option received


Working a Large Order

• More tools are needed

• Slicing and dicing

©R. Schwartz Equity Markets: Trading and Structure Slide 1 Topic 5.

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