Asymmetric Information (2)

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1 Asymmetric nformation (2) John Y. Campbell Ec2723 November 2013 John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

2 Outline Market microstructure The study of trading costs Bid-ask spread vs. market impact Models of the bid-ask spread Fixed costs and inventory costs (Roll 1984) Asymmetric information (Glosten-Milgrom 1984) Market power from search costs (Du e-garleanu-pedersen 2005) A model of market impact (Kyle 1985) A model of active asset management (Berk and Green 2004) John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

3 Market Microstructure Market Microstructure The eld of market microstructure studies the cost of trading nancial assets. How to measure this cost? Commission Bid-ask spread Market impact What types of assets are expensive to trade? What types of traders pay higher costs? John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

4 Market Microstructure Components of Transactions Costs n illiquid markets, brokers match buyers and sellers, and help them agree on a price, in exchange for a commission. As markets become more liquid, commissions become less important. Dealers or marketmakers typically take one side of each transaction. Marketmakers post o ers to sell high at the ask and buy low at the bid. The di erence is the bid-ask spread. n many markets, outside investors can compete with marketmakers by posting limit orders. n this case the minimum di erence between posted buy and sell limit orders is the "inside spread". Posted o ers apply only for modest trade sizes. Larger trades move prices against them as marketmakers adjust their posted prices, or increasingly less favorable limit orders are executed. This is market impact. John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

5 The Bid-Ask Spread Three Models of the Bid-Ask Spread 1 Marketmakers incur xed costs of doing business, and costs of holding inventory. 2 Marketmakers are concerned about trading with better informed investors, and set bid and ask prices to protect themselves (Glosten and Milgrom 1984). 3 Marketmakers have some monopoly power because of customer search costs (Du e, Garleanu, and Pedersen 2005). John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

6 The Bid-Ask Spread Determinants of the Bid-Ask Spread (1) Marketmakers incur xed costs of doing business, and costs of holding inventory Higher cost per trade when trading volume is low Higher inventory cost for volatile stocks Bid-ask bounce creates negative autocorrelation in transactions prices (Roll 1984) John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

7 The Bid-Ask Spread Fixed Costs and nventory Costs John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

8 The Bid-Ask Spread Determinants of the Bid-Ask Spread (2) Marketmakers are concerned about trading with better informed investors, and set bid and ask prices to protect themselves (Glosten and Milgrom 1984) Ask is expected fundamental value conditional on current information and the arrival of a buy o er Bid is expected fundamental value conditional on current information and the arrival of a sell o er f buys and sells are equally likely, midpoint is current expected fundamental value Then a buy moves the new midpoint to the old ask, and a sell moves the new midpoint to the old bid. John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

9 The Bid-Ask Spread Asymmetric nformation John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

10 The Bid-Ask Spread Determinants of the Bid-Ask Spread (3) Easley, Kiefer, O Hara, and Paperman (Journal of Finance 1996) elaborate on the Glosten-Milgrom model. Buy and sell arrivals are persistent within the trading day when information events occur. With probability α, an information event occurs and is negative with probability δ, positive with probability 1 δ. f it is negative, sells arrive at rate ε + µ, while buys arrive at rate ε. f it is positive, the arrival rates of buys and sells are reversed. With probability 1 α, no information event occurs and buys and sells occur at equal rates ε. Easley et al. estimate these parameters using the distribution of the total numbers of buys and sells across days. Stocks with higher α and µ relative to ε have a higher probability of informed trading αµ/(αµ + 2ε), and should have higher average spreads. John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

11 The Bid-Ask Spread EKO HP Model John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

12 The Bid-Ask Spread EKO HP Model John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

13 The Bid-Ask Spread EKO HP Model John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

14 The Bid-Ask Spread EKO HP Model John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

15 The Bid-Ask Spread Determinants of the Bid-Ask Spread (4) Broader implications of the Glosten-Milgrom model: n bad times, debt instruments become illiquid because it is worth generating private information about borrowers repayment capacity (Gorton). Traders who can show they have no private information pay lower spreads. A third model of the spread: Marketmakers have some monopoly power because of customer search costs (Du e, Garleanu, and Pedersen 2005) Sophisticated customers have lower search costs and get better execution This works against the Glosten-Milgrom e ect, since sophisticated customers more likely to have private information. John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

16 Market mpact A Model of Market mpact (1) Kyle (1985) is the classic model of market impact. An asset has an ex post value v which is distributed normally with mean p 0 and variance Σ 0. Noise traders have demand u which is distributed normally with mean zero and variance σ 2 u. A single insider observes v and chooses a demand x = X (v). John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

17 Market mpact A Model of Market mpact (2) Risk-neutral marketmakers observe x + u and set a price at which they are willing to buy or sell this amount, p = P(x + u) = E[v j x + u]. The informed investor makes a pro t π = (v p)x. The investor chooses his demand x to maximize expected pro t given the inside information, E[π j v]. John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

18 Market mpact A Model of Market mpact (3) n equilibrium, both the informed investor and the marketmakers follow linear strategies. The informed investor trades with aggressiveness β: X (v) = β(v p 0 ). The marketmakers set the price as a linear function of order ow, with coe cient λ: These coe cients are given by Thus β = 1/2λ. σ 2 β = u P(x + u) = µ + λ(x + u). Σ 0 µ = p 0, 1/2, and λ = 1 σ 2 1/2 u. 2 Σ 0 John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

19 Market mpact A Model of Market mpact (4) To derive these results, take the linear pricing rule as given and solve the informed investor s problem: The solution is where α = Max E[π j v] = E(v µ λ(x + u))x = (v µ λx)x. µ/2λ and β = 1/2λ. x = α + βv, John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

20 Market mpact A Model of Market mpact (5) Now consider the marketmaker s problem. With normally distributed shocks and a linear strategy of the informed investor, the marketmaker chooses a pricing function to minimize the variance of the pricing error: Min E[(v P(x + u)) 2 ] = E[(v µ λ(x + u)) 2 ] The solution to this problem sets = E[(v µ λ(α + βv + u)) 2 ]. λ = βσ 0 β 2. Σ 0 + σ 2 u Substituting in β = 1/2λ, we get the desired solution. John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

21 Market mpact Properties of Equilibrium (1) Greater volatility of noise trading increases the aggressiveness of the insider Analogy with Grossman-Stiglitz model f we substitute the insider s trading out of the equilibrium price function, we nd that p = µ + λ(x + u) = µ + λ(α + βv + u) = 1 2 (p 0 + v) + λu. Thus one-half of the insider s information gets into the price. The informativeness of the price in this model is independent of the volatility of noise trading, just as in the Grossman-Stiglitz model. John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

22 Market mpact Properties of Equilibrium (2) The expected pro t of the insider, conditional on knowing v, is E[π j v] = β 2 (v p 0) 2 = 1 2 σ 2 1/2 u (v p 0 ) 2, which is increasing in the distance of the information v from its unconditional mean. Unconditionally, the insider s expected pro t is E[π] = 1 2 σ 2 u Σ 0 Σ 0 1/2 Σ 0 = 1 2 σ p u Σ0, which is proportional to the standard deviations of noise trading and the inside information. The insider s expected pro t is also the total expected loss of the noise traders, since the marketmakers set prices to avoid losing money on average. John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

23 Market mpact Properties of Equilibrium (3) The reciprocal of λ can be interpreted as the market depth, the order ow needed to raise the market price by one dollar. We have 1 λ = 2 σ u p Σ0, so the market is deep when there is more noise trading and less inside information. f noise traders can choose when to trade, they would like to trade when other noise traders do, because they bene t from market depth. Even though the total losses of noise traders increase with the volume of noise trading, the loss per noise trader decreases. n a continuous-time version of this model, λ remains constant over time, while β increases and becomes in nite as the public revelation of the information approaches. Thus all private information enters the price eventually. John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

24 Market mpact Berk and Green on Mutual Fund Managers The Kyle model distinguishes between informed investors who pro t, marketmakers who break even, and noise traders who lose. Similar distinction in Berk and Green (2004). Equilibrium with skilled (informed) fund managers, mutual fund investors who break even, and other active stock traders who lose to the fund managers. Fund managers charge a fee that is a xed fraction of assets under management. nvestors judge managers skill by past performance and update their beliefs rationally. Successful funds attract in ows, but in ows reduce the performance that results from any degree of skill because there are diminishing returns to skill (perhaps because of market impact). n equilibrium, fund investors rationally chase performance, but past performance does not predict future performance. Fund managers are rewarded for their skill, but fund investors break even. John Y. Campbell (Ec2723) Asymmetric nformation (2) November / 24

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