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

Ecology of a Pure Order Driven Market Participants meet to establish prices and trade. Ecology of a Pure Order Driven Market Participants meet to establish prices and trade. This requires: Some Participants • Are looking to buy • Are looking to sell • Post limit orders • Submit market orders ©R. Schwartz An ecological balance is required for a market to function Equity Markets: Trading and Structure 2

The Placement of Limit Orders ©R. Schwartz Equity Markets: Trading and Structure 3 The Placement of Limit Orders ©R. Schwartz Equity Markets: Trading and Structure 3

What Drives an Order Driven Market? Limit Orders! • Without sufficient limit orders, the What Drives an Order Driven Market? Limit Orders! • Without sufficient limit orders, the order driven market would fail • What motivates their placement? ©R. Schwartz Equity Markets: Trading and Structure 4

What Motivates/Deters the Placement of Limit Orders? Compensation For Limit Order Traders Results From What Motivates/Deters the Placement of Limit Orders? Compensation For Limit Order Traders Results From the Pricing Dynamics of the Continuous Order-driven Market* How does this work? *Source: Handa & Schwartz, “Limit Order Trading, ” Journal of Finance, December 1996, pp. 1835 - 1861. ©R. Schwartz Equity Markets: Trading and Structure 5

Information Change Assume I have an open, unexecuted buy limit order on the book. 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 ©R. Schwartz Equity Markets: Trading and Structure 6

2 Costs of Trading By Limit Order Cost of being Bagged • Heads You 2 Costs of Trading By Limit Order 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? ©R. Schwartz Equity Markets: Trading and Structure 7

A Liquidity Event Occurs • A liquidity event that results in a price decline 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 Compensates The Limit Order Trader ©R. Schwartz Equity Markets: Trading and Structure 8

Mean Reversion and Accentuated Intra-Day Volatility • Accentuated intra-day volatility implies negative serial correlation Mean Reversion and Accentuated Intra-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 ©R. Schwartz Equity Markets: Trading and Structure 9

What Accentuates Volatility? Of these three different types of events that can trigger executions What Accentuates Volatility? Of these three different types of events that can trigger executions and price changes, which does it? No • Informational events Yes • Liquidity events • Technical trading (momentum) Yes ©R. Schwartz Equity Markets: Trading and Structure 10

All Three Occur in Trader. Ex • Information events • Liquidity events • Momentum All Three Occur in Trader. Ex • Information events • Liquidity events • Momentum trading How sensitive to them were you? ©R. Schwartz Equity Markets: Trading and Structure 11

Conclusion: Accentuated Volatility Is a Natural Property of the Continuous Market Regardless of • 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 ©R. Schwartz Equity Markets: Trading and Structure 12

Intra-Day Volatility Is Accentuated in Trader. Ex Liquidity trading creates volatility and momentum players Intra-Day Volatility Is Accentuated in Trader. Ex Liquidity trading creates volatility and momentum players reinforce it P* Ask Bid ©R. Schwartz Equity Markets: Trading and Structure 13

Optimal Order Placement ©R. Schwartz Equity Markets: Trading and Structure 14 Optimal Order Placement ©R. Schwartz Equity Markets: Trading and Structure 14

Order Placement in an Order Driven Market Should I: • Submit a market order? Order Placement in an Order 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 ©R. Schwartz Equity Markets: Trading and Structure 15

The Gains From Trading and the Concept of a Reservation Price • For a The Gains From Trading and the Concept of a 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 at Gains from trading • For a buyer: reservation price – purchase price • For a seller: Sale price – reservation price ©R. Schwartz Equity Markets: Trading and Structure 16

Gains From Buying 1000 Shares Your Reservation Price= $12. 00 Market Order • Market Gains From Buying 1000 Shares Your 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 ©R. Schwartz Equity Markets: Trading and Structure 17

Breakeven Probability (PBE) Reservation Price = $12. 00 • Market Order Gain ($12. 00 Breakeven Probability (PBE) Reservation Price = $12. 00 • Market Order Gain ($12. 00 – $11. 10) x 1000 = $900 ($12. 00 – $10. 80) x 1000 = $1200 • Limit Order Gain • $900 = PBE x $1200 • PBE = 75% • If actual Prob of Exec > 75%, place Limit Order ©R. Schwartz Equity Markets: Trading and Structure 18

Pricing a 1000 Share Buy Limit: Reservation Price = $12. 00 Trade Price $ Pricing a 1000 Share Buy Limit: Reservation Price = $12. 00 Trade Price $ 11. 10 $ 11. 00 $ 10. 90 $ 10. 80 $ 10. 70 $ 10. 60 Prob of Exec 1. 00* 0. 90 0. 85 0. 80 0. 70 0. 53 * Market order ©R. Schwartz Gain per share Expected Gain 0. 90 1. 00 1. 10 1. 20* 1. 30 1. 40 $ 900. 00 $ 935. 00 $ 960. 00** $ 910. 00 $ 742. 00 ** Best order to place Equity Markets: Trading and Structure 19

Buyer’s Surplus ©R. Schwartz Equity Markets: Trading and Structure 20 Buyer’s Surplus ©R. Schwartz Equity Markets: Trading and Structure 20

Probability of Executing ©R. Schwartz Equity Markets: Trading and Structure 21 Probability of Executing ©R. Schwartz Equity Markets: Trading and Structure 21

Buyer’s Expected Surplus ©R. Schwartz Equity Markets: Trading and Structure 22 Buyer’s Expected Surplus ©R. Schwartz Equity Markets: Trading and Structure 22

Back to Trader. Ex • When you play Trader. Ex, can you quickly make Back to Trader. Ex • When you play Trader. Ex, 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 ©R. Schwartz Equity Markets: Trading and Structure 23

Existence of the Bid-Ask Spread ©R. Schwartz Equity Markets: Trading and Structure 24 Existence of the Bid-Ask Spread ©R. Schwartz Equity Markets: Trading and Structure 24

Why Do Bid-Ask Spreads Exist in Order Driven Markets? • In a quote driven 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? ©R. Schwartz Equity Markets: Trading and Structure 25

Meaningful vs Trivial Spreads • Meaningful spread: economic forces explain its existence • Trivial 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 noninfinitesimal spread when the tick size is infinitesimal (i. e. , price is a continuous variable) ©R. Schwartz Equity Markets: Trading and Structure 26

Bid – Ask Spread Reservation Price = $12. 00 • Market order for 1000 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? ©R. Schwartz Equity Markets: Trading and Structure 27

Should You Ever Place a Limit Buy Infinitesimally Close to an Already Posted Offer? 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? N o! ©R. Schwartz Equity Markets: Trading and Structure 28

Bid-Ask Spread If you are a limit order trader, the bid-ask spread must give Bid-Ask Spread If you are a limit order trader, the bid-ask spread must give you a positive expected return Compensation for • Risk of adverse informational change • Risk of limit order not executing Gravitational Pull Effect ©R. Schwartz Equity Markets: Trading and Structure 29

Gravitational Pull Market Ask Potential Buy Order 2 Potential Buy Order 1 Market Bid Gravitational Pull Market Ask Potential Buy Order 2 Potential Buy Order 1 Market Bid ©R. Schwartz Equity Markets: Trading and Structure 30

Why Do Non-Trivial Spreads Exist in Trader. Ex? Price (5¢ Tick Size) The probability Why Do Non-Trivial Spreads Exist in Trader. Ex? Price (5¢ Tick Size) The probability distribution use to get liquidity driven sell orders 26. 60 26. 50 Limit sell orders 26. 40 26. 30 26. 20 Offer 26. 10 Bid 26. 00 25. 90 Executable sell orders 25. 80 0% 2% 4% 6% 8% 10% 12% 14% Probability ©R. Schwartz Equity Markets: Trading and Structure 31

Two Other Topics ©R. Schwartz Equity Markets: Trading and Structure 32 Two Other Topics ©R. Schwartz Equity Markets: Trading and Structure 32

An Option Trader’s View of Limit Orders • The option extended • The option An Option Trader’s View of Limit Orders • The option extended • The option received ©R. Schwartz Equity Markets: Trading and Structure 33

Working a Large Order • More tools are needed • Slicing and dicing ©R. Working a Large Order • More tools are needed • Slicing and dicing ©R. Schwartz Equity Markets: Trading and Structure 34