Slide 1

Report
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
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Annual Price Chart: MSFT
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Annual Price Chart: GOOG
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Annual Chart Comparison
» Very hard to tell the difference between the two firms optically
» Essentially, prices behave similarly on a macro scale
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MSFT: 5 minutes
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GOOG: 5 minutes
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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
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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]
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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
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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
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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…

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