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1. Insert Presentation Title 1 September 2, 2012

2. Tale of Two Stocks (March 2012, #s are approx) Insert Presentation Title 2 September 2, 2012

3. Annual Price Chart: MSFT Insert Presentation Title 3 September 2, 2012

4. Annual Price Chart: GOOG Insert Presentation Title 4 September 2, 2012

5. Annual Chart Comparison Very hard to tell the difference between the two firms optically Essentially, prices behave similarly on a macro scale Insert Presentation Title 5 September 2, 2012

6. MSFT: 5 minutes Insert Presentation Title 6 September 2, 2012

7. GOOG: 5 minutes Insert Presentation Title 7 September 2, 2012

8. Five minute chart comparison Visually, one can immediately distinguish GOOG from MSFT Quote differences MSFT quotes are stable for long periods of time MSFT quotes move in discrete jumps GOOG quotes move more continuously Trade differences MSFT trades much more frequently (and since average daily dollar trade volume is similar, trade sizes must be smaller) Many MSFT trades occur within the spread, frequently at the mid-quote GOOG trades less frequently, usually at one side of the spread Q: What drives these differences? A: Market microstructure Minimum price variant is nominally $0.01 in both cases, which economically is 20x larger for MSFT than GOOG Insert Presentation Title 8 September 2, 2012

9. What is Market Microstructure? Market microstructure is a branch of finance concerned with the details of how exchange occurs in markets. [�] The major thrust of market microstructure research examines the ways in which the working processes of a market affects determinants of transaction costs, prices, quotes, volume, and trading behavior. [Source: Wikipedia] Insert Presentation Title 9 September 2, 2012

10. What is Market Microstructure? My words: Study of how trading actually occurs Many economic and financial models assume that price is known Price function of supply and demand In reality, depends on information and strategy Why you should care (as a quant)? Microstructure affects transaction costs Understanding microstructure can generate alpha or lower costs Microstructure itself can be studied using quantitative techniques Insert Presentation Title 10 September 2, 2012

11. Market Making Provide liquidity (immediacy) to the rest of the investing public Always willing to buy or sell at certain prices Difference is called the spread Problem: information asymmetry with respect to the rest of the world

12. Questions about market making How should market makers set their quotes? How/why do they (not) make (any) money?

13. An Economist�s View of Prices

14. Features of this Model Mathematically simple Intuitively makes sense for most markets Accurate way to view many markets Increasing demand yields increasing price Increasing supply yields declining price � but it misses the key features about how prices are formed in financial markets

15. An Aside: Poker Simple one card poker, single suite deck 2 players each ante $1 Each player gets a card face down (they can see their own card) Cards are ranked as normal Game proceeds as follows:

16. One card poker game

17. Analysis of the Game If you could see the other persons card... Strategy is trivial Game is �fair� But with hidden information... Strategy is extremely nontrivial (the full game has been solved in this case but it�s hard) The game is no longer fair. �Bluffing� (concealing your private information) plays a role See www.cs.cmu.edu/~ggordon/poker/ for more information Thought question: who has the advantage?

18. What Assumptions Fail? Simple supply/demand curve analysis assumes everyone has perfect information In reality, information is revealed through the trading process Traders come to the marketplace with heterogenous information and sophistication, much like poker

19. Classic Microstructure Models Roll model: simplest model which incorporates market mechanics but no information/strategy Sequential trade model (Glosten-Milgrom style): incorporates information asymmetry but no strategy Kyle model: includes information asymmetry and strategy Reference: Hasbrouck �Empirical Market Microstructure�

20. Roll Model for Prices Incorporates some notions that market mechanics and organization structure influence short term prices Assumes fundamental security price follows a random walk Trading occurs through dealer quotes Spread is constant Enables estimate of spread from trade prices

21. Roll Model Trade Prices Fair price m follows driftless random walk Trades occur at dealer bid/offer quotes, spread is 2c Each trade is independent and uninformative

22. Changes in trade price I

23. Changes in Trade Price II

24. Examples

25. Glosten-Milgrom Model Roll model is too simple Captures some mechanical aspects of trading Totally ignores information content Sequential trade models include some aspects of information asymmetry Glosten-Milgrom (1985) and many descendants We refer to Hasbrouck (EMM as cited earlier) for a simplified version

26. Sequential Trading Setup Trading occurs at time t=0 in an asset with publicly unknown value: either V0 or V1 at time t=1. Traders trade by placing market orders against marker maker quotations B = bid A = ask Two types of traders: I: informed. These traders know the true value and trade on that basis U: uninformed. These traders (often called �noise� or �liquidity� traders) trade in a random direction Dealers place quotes to compete p/l to 0. Proportion of I to U is known to everyone.

27. STM: mechanics Security value is either V0 or V1 with probability d or 1-d respectively Random trader arrives at market and is I or U with probability m or 1-m respectively I traders trade in the direction of final value U traders trade randomly

28. STM Mechanics

29. STM: How do dealers set quotations? As wide as possible... Will not trade at an expected loss. But because of competition, quotes will be competed down to expected P/L ~ 0 So, ask will be expected P/L realized from next trade conditioned on it being a BUY This is a key point! Market makers should set their quotes at the expected terminal value conditioned on their quote getting hit

30. STM: analysis of ask P/L dealer gets from customer BUY: A-V So, A=expectation of V conditioned on BUY

31. Observations Dealers always lose to informed and profit from uninformed. Analysis of the bid is similar

32. Iterating the model This discussed a one period example This can be iterated to handle sequences of trades as well We assume each trader comes to the market only one time Trade prices are reported publicly Dealers all update their d on this basis We don�t worry about inventory/risk concerns

33. Updating d The only state that changes over time is d Computing new d after a first BUY order

34. Conclusions from model Trade prices form a martingale Trades occur at bid/offer prices These prices are expectation of terminal value conditioned on trade occurring at them B then S cancel out Order flow is not symmetric and is correlated over time (used to estimate probability of informed trading) Eventually dealers have excellent estimate of terminal value Prices gravitate towards one side or the other, spreads narrow Trades have price impact Important for empirical research Measure of information asymmetry

35. Example

36. Thought question Regulatory proposal: solve the high frequency �problem� by imposing a minimum duration on limit orders Q: What will the impact be of such a regulatory change? A: It will increase the amount of information in the marketplace for others to trade against the limit order (for example, looking at futures prices) In other words, the proportion of informed orders m increases Hence, spreads widen Insert Presentation Title 36 September 2, 2012

37. Roll model v. STM Roll model simply captures mechanics of dealer market with fixed edge per trade STM gets at deeper notion of information in trade Models reach incompatible conclusions In Roll model, trade prices are mean reverting In STM, trade prices are a Martingale

38. Strategic Trading In this sequential trade model, traders arrive at the market only once They don�t need to worry about disguising their information from the dealers and other market participants Dealers eventually learn the payoff (V0 or V1) Strategic trade models address this shortcoming (bluffing in poker)

39. Kyle Model Liquidity traders net order flow u One informed trader sees value v and submits x Market maker observes y=u+x, sets price p MM fills net order imbalance at price p

40. Analysis of Kyle Model Informed trader hypothesizes linear price response function from market maker MM hypothesizes linear demand function from IT Under normality assumption these turn out to be optimal

41. Single Period Analysis IT hypothesis: P/L for IT IT maximizes expected profit:

42. MM Strategy Hypothesis: Solving: Conclusion: Knowing y, how to compute expectation of v? Apply bivariate conditional expectation to y and v

43. Discussion of IT Trading IT order flow function: Trades in direction of terminal value More uninformed flow leads to more trading Less uncertainty on v leads to less trading Expected P/L:

44. Market Maker Pricing Pricing function: Perturbs p0 based on observed order flow

45. Iterated Auctions This can be repeated with MM updating distribution of v each round Price is a Martingale: MM sets it as expectation of v conditioned on order flow observed up to that point Informed trader slices orders into market over time, order flow tends to be on the same side (knowing IT�s order flow at any instant determines v). However, total order flow has no autocorrelation: Intuition: price changes and total order flow are linearly related, so price being a Martingale implies order flow is uncorrelated

46. Limitations Roll model hopelessly simplistic Order flow and trades do reveal information Ignoring this will lead to large losses GM and Kyle models explain how information asymmetries influence the spread and MM P/L But they take the information asymmetry as given, in reality the spread and trade prices/order flows are what can be observed. Electronic markets prices are usually discrete

47. Needed: somthing in the middle

48. Adverse Selection Basic practical problem for MM is to combat adverse selection Roll model too simplistic Glosten-Milgrom and Kyle models focus on how AS arises from underlying (unobservable) information asymmetries Desired: a model that focuses on the observable component of adverse selection Main point: limit orders are always filled when you�re wrong, but only selectively when you�re right Reasons for adverse selection Informed incoming market orders Competition among market makers

49. Simple AMM Model �Fair� price is 1 stage binary tree Liquidate at time 1 at f.v. Probability of price increase is p Spread is 2s We place a buy limit order Probability of fill is q if price rises Probability of fill is 1 if price falls

50. Compute the P/L

51. Simple Observations P/L increases with q. �Fill rate� P/L increases with s. �spread� P/L increases with p. �alpha� -- most of the time!

52. Why decreasing p? Q:How could we benefit from price falling when we�re buying? A: Spread can more than compensate for alpha if large enough Example: q=0, then only fills occur when price drops. P/L=(1-p)(s-1) Decreasing p increases overall fill rate

53. Special Case: No Alpha No alpha, ie p=1/2 Breakeven occurs when fill rate q is sufficiently high

54. Special Case: s=1/2 s=1/2 This looks like many limit order books if f.v. is assumed to be the midquote In words, no liquidity rebate or fee

55. Lessons from the Model P/L of automated market making is a tradeoff between three quantities Spread: s (obvious) Alpha: p (somewhat obvious) Fill rate: q (subtle but perhaps most important) Math that goes into maximizing these p: predictive models of price (regression, machine learning, etc) q: modeling fills rates, queues, etc

56. Break Even Spread

57. Multi-period Extensions So far a single period model dictates when it makes sense to post a limit order or not String these together to get a multi-period model Forecasts should not be viewed as static: p has some dynamics Interesting to see what happens when q also varries dynamically

58. AMM Model Dynamics Price is a binary process with transition probabilities that vary stochastically as function of state variable p p itself is binary process. Transition probabilities are a function of p itself, mean reverting Probability of adverse fill is modeled similarly to p

59. AMM Model Dynamics

60. Apply HJB Equations above give 3d state space (p, q and position s) Assume terminal time T with specified quadratic value function V(T,s,p,q) = -k s2 Use HJB to go backwards in time to fill in value function for t<T

61. Numerical Examples

62. Conclusions�