1. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 1 Bob Schwartz Zicklin School of Business Baruch College, CUNY

2. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 2 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 balance is required for a market to function

3. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 3 Placement of Limit Orders

4. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 4 What Drives an Order Driven Market? Without sufficient limit orders, the order driven market would fail What motivates their placement? Limit Orders!

5. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 5 What Motivates/Deters the Placement of Limit Orders? How does this work? Compensation For Limit Order Traders Results From the Pricing Dynamics of the Continuous Order-driven Market* *Source: Handa & Schwartz, “ Limit Order Trading,” Journal of Finance, December 1996, pp. 1835 - 1861.

6. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 6 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

7. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 7 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? 2 Costs of Trading By Limit Order

8. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 8 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

9. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 9 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

10. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 10 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? No Yes What Accentuates Volatility? Yes

11. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 11 All Three Occur in TraderEx Information events Liquidity events Momentum trading How sensitive were you to them?

12. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 12 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

13. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 13 Intra-Day Volatility Is Accentuated in TraderEx Liquidity trading creates volatility and momentum players reinforce it Ask Bid P*

14. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 14 Order Placement

15. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 15 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

16. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 16 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 at Gains from trading For a buyer: reservation price – purchase price For a seller: Sale price – reservation price

17. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 17 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

18. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 18 Breakeven Probability (P BE ) 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 = P BE x $1200 P BE = 75% If actual Prob of Exec > 75%, place Limit Order

19. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 19 Trade Price Prob of Exec Gain per shareExpected Gain $ 11.101.00* 0.90$ 900.00 $ 11.00 0.901.00$ 900.00 $ 10.90 0.851.10$ 935.00 $ 10.80 0.80 1.20* $ 960.00** $ 10.70 0.701.30$ 910.00 $ 10.60 0.531.40$ 742.00 * Market order ** Best order to place Pricing a 1000 Share Buy Limit: Reservation Price = $12.00

20. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 20 Buyer ’ s Surplus

21. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 21 Probability of Executing

22. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 22 Buyer ’ s Expected Surplus

23. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 23 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

24. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 24 The Bid-Ask Spread

25. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 25 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?

26. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 26 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)

27. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 27 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 P BE : infinitesimally close to 100% Should you ever place a limit order to buy this close to an already posted limit order to sell?

28. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 28 Should You Ever Place a Limit Buy Infinitesimally Close to an Already Posted Offer? P BE 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!

29. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 29 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

30. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 30 Market Ask Market Bid Gravitational Pull Potential Buy Order 2 Potential Buy Order 1

31. ©R. Schwartz, B Steil, & B. Weber June 2008 Slide 31 Why Do Non-Trivial Spreads Exist 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