Institutional

st tut o a Finance
a ce
Financial Crises, Risk Management a

Markus K. Brunnermeier

Preceptor: Dong Beom Choi

Princeton University
Market Making – Limit Orders
Limit order – price contingent order
Limit buy order: “buy as soon as price drops to $
Limit sell order: “sell as soon as price rises to $x.

Stand ready to trade at a certain price

Grant somebody else the option to execute a
S
Stop orders
d
Stop sell order: “sell as soon as price drops to $x
(cut losses!)
Stop buy order: “buy as soon as price rises to $x
Market orders – non‐contingent order
Market Making
Market maker

NYSE: “monopolistic”
p specialist
p
(all orders go through him)

NASDAQ: multiple p competing p g “deal

ECNs: (pure electronic limit order book)

OTC/upstairs
/ p mrkt: bilateral relationsh
Black pools:
After various mergers, distinction is less black and
Event tree
0 1 2 3

One--p
One

pt

pt+1 is r
Setting Bid and Ask Prices
1. Market Maker faces only liquidity traders (prac
Fundamental stays constant
pt is driven by random liquidity needs of liquidity trader
ask
bid

Fundamental follows random walk

vt+1 = vt + εt+1, where E[εt+1]=0
Differences:
One has to adjust bid and ask price in each period
(cancel old limit orders and set new limit orders)
Asset volatility
What determines bid‐ask spread?
Monopolistic power of market maker
(Bertrand competition if there are multiple market makers
Volatility of asset if market makers are risk averse
Stochastic process of liquidity traders needs
Setting Bid and Ask Prices
2. Market Maker faces informed trade
Only informed traders ‐ extreme case
v = 0 or 1 with equal probability
all traders are informed traders
(know whether v =0 or 1)
What is the ask price? What is the bid pric
set by uninformed market maker
Suppose ask: a = ¾ and bid: b = ¼ .
Does the market make or lose money with a
bid ask spread of ½
Market Break‐Down – No Trade!
Liquidity traders and informed traders
[See Glosten‐Milgrom (1985)]
Setting Bid and Ask Prices

2
2. Market maker faces
Liquidity traders and informed traders
[See Glosten‐Milgrom (1985)] buy
1
informed
ι sell
v=1 buyy
α
μ liquidity a=
sell b=
buy
1-μ
informed B
ι 1 sell
v=0 buy
α
liquidity
sell
Bayesian Updating
Bayes’ Rule
Bayes

Example: a = E[v|buy] =1*Pr[v=1|buy] + 0

Pr [buy|v=1] = ι∗1 + (1 ‐ ι) α
Pr [buy|v=0] = ι∗0 + (1 ‐ ι) α
Pr [[buy]= y| ] μ + Pr [[buy|v=0]
y] Pr [[buy|v=1] μ
y| ] ((1 ‐μ
Noise noise
Noise, noise, noise,
noise …
Asymmetric information causes adverse s
Informed traders
buy only if asset is undervalued and
sell only if asset is overvalued
Market maker loses (even with bid ask spread)
noise traders
Market makers wins from them (due to bid‐ask sp
Fellow students might be noise traders …
1 signal for every 3‐4 time of trading (why?)
Assuming that others are rational is dangero
(see e.g. Keynes Beauty contest game)
Profits & Positions in simulation
Relative profits
Market Markers should do well when f
are relatively flat
Sim 1, 2, and 3
Market takers should do well otherwis
Sim 4 (too much gambling on Sim 5)
Market maker’s
maker s positions
Move against the price …
Where will this head …
Only trade after buying and receivin
extreme signal
No noise traders
Market makers face more adverse se
and d set wider
id bid‐ask
bid k spreadd
Ultimately, Market Breakdown
Nobody bids for market making righ
((zero value for privilege)
p g )
Example of Market Breakdown
Risk‐neutral competitive market makers
v is distributed with pdf
i.e. cdf is
xxx
α = prob. of informed trader
Noise traders’ private valuation has pdf of f(v) (in

Ask price: a = 1/(1‐2α), if α < 1/2

market breaks down for larger α
H
Homework:
k Analysis
A l i for
f bid
Limit order
Granting an option (selling an option
“pick on me when you want”
One has to charge an “option
option premium
Market making rights are worthless
when there are no noise/liquidity trad
Lose to informed traders
Gain from noise traders
Informed Trading
1
1. Acquiring Information
What is the value of information?
2. Trading based on Information
Trading is limited by
Risk‐appetite
Ri k i (previous
( i l
lecture with
i h CARA
Price impact
If I trade more aggressive the market ma
information and adjust the price
Endogenous info acquisition
Value of signal (conditional 25 00
25.00
on knowing realization)
20.00
Intermediate signals are
worthless 15 00
15.00
Very high (go long) and very
low (go short) 10.00

are worth the most.

5.00
Take
k expectations before
b f
knowing signal -
20.00 30.00 40.00 50.00 60.00 70.00

Payoff
y is veryy skewed (5.00)

only extreme signal

realizations are valuable Value of strang
use Black-Scho
More valuable
(see Excel file)
Price Impact of Informed Trades ‐
Strategic
St t i Trading:
T di KyleK l (1985) modd
(p0, Σ0)
asset return v ∼ N(p
Agents (risk neutral)
Insider who knows v and submit market orde
Noise trader who submit market orders of ex
aggregate size u ∼ N(0, σ2u)
Market maker sets competitive price after ob
order flow X=x+u
Timing (order of moves)
Stage 1: Insider & liquidity traders submit ma
Stage 2: Market Maker sets the execution pr
Repeated trading in dynamic version
Kyle (1985) – on one page
Kyle (1985)
Equilibrium:

Illiquidity
decreases with noise trading, σu2
increases with info‐advantage of informed trader,

Multi‐period version
A
Aggressive
i trading
t di leads
l d to
t adverse
d price
i mo
in current trading round
In any future trading around (before public annou
In sum
Asymmetric information causes adverse s
Informed traders
buy only if asset is undervalued and
sell only if asset is overvalued
Market maker loses (even with bid ask spread)
noise traders
Market makers wins from them (due to bid‐ask sp
Market breakdown without noise traders
Value of information
is (ex‐ante) highest when fundamental volati
(since only extreme signals pay off) – strangle