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Quantitative Trading and Market Structure Princeton Quant Trading Conference 2012 Insert July 17, Presentation 2015 Title July 17, 2015 1 Tale of Two Stocks (March 2012, #s are approx) MSFT GOOG ADV 58,000,000 3,000,000 Price $32 $650 Implied Volatility 21% 26% Market Cap $270B $212B Absolute spread 0.01 0.2 Relative spread 3bps 3bps Beta 0.90 1.06 Insert Presentation Title July 17, 2015 2 Annual Price Chart: MSFT Insert Presentation Title July 17, 2015 3 Annual Price Chart: GOOG Insert Presentation Title July 17, 2015 4 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 July 17, 2015 5 MSFT: 5 minutes Insert Presentation Title July 17, 2015 6 GOOG: 5 minutes Insert Presentation Title July 17, 2015 7 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 July 17, 2015 8 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 July 17, 2015 9 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 July 17, 2015 10 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 Questions about market making » How should market makers set their quotes? » How/why do they (not) make (any) money? An Economist’s View of Prices 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 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: One card poker game High Card Wins P2 Player 1 Wins P1 P1 P2 High Card Wins High Card Wins Player 2 Wins 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? 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 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” 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 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 Changes in trade price I Changes in Trade Price II Observation: Covariance is always negative, thus trade prices are inherently mean reverting. Empirically, a lot of HF data are MR but most of these effects cannot be traded. Examples Roll Model can be used to estimate spreads from trades Spreads on 12/1/2008 Roll Model (Trades) Quotes MSFT 0.011 0.0092 GOOG 0.288 0.233 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 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. 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 STM Mechanics m 0 B 1 S .5 B .5 S 1 B 0 S .5 B .5 S I V0 1-m d U V 1-d m I V1 1-m U 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 STM: analysis of ask » P/L dealer gets from customer BUY: A-V » So, A=expectation of V conditioned on BUY Observations » Dealers always lose to informed and profit from uninformed. » Analysis of the bid is similar 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 Updating d » The only state that changes over time is d » Computing new d after a first BUY order 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 Example Terminal Value 1 Terminal 1 Value Proportion of 20.00% Proportion Traders of Informed Informed 20.00% Traders 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 July 17, 2015 36 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 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) 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 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 Single Period Analysis » IT hypothesis: » P/L for IT » IT maximizes expected profit: MM Strategy » Hypothesis: » Solving: » Conclusion: » Knowing y, how to compute expectation of v? Apply bivariate conditional expectation to y and v 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: Market Maker Pricing » Pricing function: » Perturbs p0 based on observed order flow 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 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 Needed: somthing in the middle Complex Kyle Model Glosten-Milgrom ???? Roll Model Simplistic 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 Simple AMM Model 51 » “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 p 50 1-p t=0 49 t=1 Compute the P/L 51 p 50 1-p 49 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! 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 Special Case: No Alpha » No alpha, ie p=1/2 » Breakeven occurs when fill rate q is sufficiently high 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 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 Break Even Spread 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 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 AMM Model Dynamics •Price transition probabilities given by logistic function of underlying state variable p •p follows mean reverting binary process •Similar model for adverse selection probabilities 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 Numerical Examples Conclusions…