# Markus K. Brunnermeier

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1 Institutional tut Finance Financial Crises, Risk Management and Liquidity Markus K. Brunnermeier Preceptor: Dong BeomChoi Princeton University 1

2 Market Making Limit Orders Limit order price contingent order Limit buy order: buy as soon as price drops to \$x. bid Limit sell order: sell as soon as price rises to \$x. ask Stand ready to trade at a certain price Grant somebody else the option to execute a transaction Stop orders 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 1-2

3 Market Making Market maker NYSE: monopolistic specialist (all orders go through him) NASDAQ: multiple competing dealers ECNs: (pure electronic limit order book) OTC/upstairs mrkt: bilateral relationship Black pools: After various mergers, distinction is less black and white 1-3

4 Event tree One-period Snapshot p t+1,1 p t p t+1,2 p t+1,3 p t+1 is random variable 1-4

5 Setting Bid and Ask Prices 1. Market Maker faces only liquidity traders (practice) Fundamental stays constant p t is driven by random liquidity needs of liquidity traders ask bid Fundamental follows random walk v t+1 = v t + ε t+1, where E[ε t+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 1-5

6 Setting Bid and Ask Prices 2. Market Maker faces informed traders Only informed traders extreme case v = 0 or 1 with equal probability all traders are informed traders (know whether v =0 or 1) Whatis the ask price? What isthe bid price? 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)] v=1 v=0 1-6

7 Setting Bid and Ask Prices 2. Market makerfaces Liquidity traders and informed traders [See Glosten Milgrom (1985)] μ v=1 ι informed liquidity 1 α buy sell buy sell a = E[v buy order] b = E[v sell order] 1-μ v=0 ι informed liquidity 1 α buy sell buy sell Bayesian updating! 1-7

8 Bayesian Updating Bayes Rule 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]= Pr [buy v=1] ]μ μ + Pr [buy v=0] ](1 μ) 1-8

9 Noise, noise, noise, Asymmetric information causes adverseselectionselection 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 spread) Fellow students might be noise traders 1 signal for every 3 4 time of trading (why?) Assuming that others are rational is dangerous: (see e.g. Keynes Beauty contest game) 1-9

10 Profits & Positions in simulations Relative profits Market Markers should do well when fundamentals are relatively flat Sim 1, 2, and 3 Market takers should do well otherwise Sim 4 (too much gambling on Sim 5) Market maker s positions Move against the price 1-10

11 Where will this head Only tradeafterbuying after and receiving an extreme signal No noise traders Market makers face more adverse selection and set wider bid ask spread Ultimately, Market Breakdown Nobody bids for market making rights (zero value for privilege) 1-11

12 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) (indep. of v). Ask price: a = 1/(1 2α), if α < 1/2 market breaks down for larger α Homework: Analysis for bid 1-12

13 Limit order Granting an option (selling an option) pick on me when you want One has to charge an option premium Market making rights are worthless when there areno noise/liquidity traders Lose to informed traders Gain from noise traders 1-13

14 Informed Trading 1. Acquiring Information What is the value of information? 2. Trading based on Information Trading is limited by Risk appetite i (previous lecture with CARA utility) Price impact If I trade more aggressive the market maker will learn my information and adjust the price 1-14

15 Endogenous info acquisition Value of signal (conditional on knowing realization) Intermediate signals are worthless Very high (go long) and very low (go short) are worth the most Take expectations bf before - knowing signal Payoff is very skewed (5.00) only extreme signal realizations are valuable Value of strangle (put + call) use Black-Scholes More valuable for higher vol. (see Excel file) 1-15 Put Call

16 Price Impact of Informed Trades Strategic t Trading: Kyle Kl (1985) model dl asset return v N(p 0, Σ 0 ) Agents (risk neutral) Insider who knows v and submit market order of size x Noise trader who submit marketorders of exogenous aggregate size u N(0, σ 2 u) Market maker sets competitive price after observing net order flowx=x+u Timing (order of moves) Stage 1: Insider & liquidity traders submit market orders Stage 2: Market Maker sets the execution price Repeated trading in dynamic version 1-16

17 Kyle (1985) on one page 1-17

19 In sum Asymmetric information causes adverseselectionselection 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 spread) Market breakdownwithout noise traders Value of information is (ex ante) highest when fundamental volatility is high (since only extreme signals pay off) strangle analogy 1-19

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