1. V. ADVERSE SELECTION, TRADING AND LIQUIDITY

2. 5.1. Market Microstructure, Liquidity and Spreads
Market microstructure is concerned with the markets for transaction services.
Liquidity refers to the ability to easily transact without causing significant price changes.
Adverse selection occurs when a party to a contract uses her superior information to the disadvantage of her counterparty.

3. Asset Pricing and the Bid-Ask Spread
The familiar Gordon stock pricing model:
Consider a market with transactions costs as a constant relative spread s = (Pa - Pb)/P
The stock is traded  times per year
Revised Gordon model (Amihud & Mendelson, 1986):

4. Amihud & Mendelson, 1986: Illustration
A stock traded twice per year with an average spread of 3% paying annual dividends equal to $1 discounted at 5% is valued under each of our two frameworks as:
A reduction in the spread from 3% to 1% would significantly increase the stock price:

5. 5.2. Information and Trading
The economics of information is concerned with how information along with the quality and value of this information affect an economy and economic decisions.
Information can be inexpensively created, can be reliable and, when reliable, is valuable.
The simplest microeconomics models assume that information is costless and all agents have equal access to relevant information.
But, such assumptions do not hold in reality, and costly and asymmetric access to information very much affects how traders interact with each other.
Investors and traders look to the trading behavior of other investors and traders for information, which affects the trading behavior of informed investors who seek to limit the information that they reveal.
Here, we discuss the market mechanisms causing prices to react to the information content of trades (market impact or slippage), and how traders and dealers can react to this information content to maximize their own profits (or minimize losses).
This chapter is concerned primarily with problems that arise when traders and other market participants have inadequate, different (asymmetric information availability) and costly access to information.

6. Adverse Selection
Adverse selection refers to pre-contractual opportunism where one contracting party uses his private information to the other counterparty’s disadvantage.
In a financial trading context, adverse selection occurs when one trader with secret or special information uses that information to her advantage at the expense of her counterparty in trade.
Trade counterparties realize that they might fall victim to adverse selection, so they carefully monitor trading activity in an effort to discern which trades are likely to reflect special information.
For example, large or numerous buy (sell) orders originating from the same trader are likely to be perceived as being motivated by special information, resulting in slippage.

7. 5.3. Noise Traders
Noise traders trade on the basis of what they falsely believe to be special information or misinterpret useful information.
Noise traders make investment and trading decisions based on incorrect perceptions or analyses.
Do noise traders distort prices? Maybe yes if:
noise traders trade in large numbers
their trading behavior is correlated
their effects cannot be mitigated by informed and rational traders
Milton Friedman suggested that traders who produce positive profits do so by trading against less rational or poorly informed investors who tend to move prices away from their fundamental or correct values.
Fama argued that when irrational trading does occur, security prices will not be significantly affected because sophisticated traders will exploit and eliminate deviations from fundamental economic values.
Figlewski [1979] suggested that it might take irrational investors a long time to lose their money and for prices to reflect security intrinsic values, but they are doomed in the long run.

8. Noise Traders and Market Function
Noise traders might be useful, perhaps even necessary for markets to function.
Without noise traders, markets would be informationally efficient and maybe no one would want to trade.
Even with asymmetric information access, informed traders can fully reveal their superior information through their trading activities, and prices would reflect this information and ultimately eliminate the motivation for information-based trading.
That is, as Black [1986] argued, without noise traders, dealers would widen their spreads to avoid losing profits to informed traders so that no trades would ever be executed.
However, noise traders do impose on other traders the risk that prices might move irrationally.
This risk imposed by noise traders might discourage arbitrageurs from acting to exploit price deviations from fundamental values.
Prices can deviate significantly from rational valuations, and can remain different for long periods.
Arbitrageurs might ask themselves the following question: “Does my ability to remain solvent exceed the asset price’s ability to remain irrational?”

9. 5.4. Adverse Selection in Dealer Markets
Bagehot [1971] described a market where dealers or market makers stand by to provide liquidity to every trader who wishes to trade, losing on trades with informed traders but recovering these losses by trading with uninformed, noise or liquidity motivated traders.
The market maker sets prices and trades to ensure this outcome, on average.
The market maker merely recovers his operating costs along with a "normal return.“
In this framework, trading is a zero sum or neutral game; uninformed investors will lose more than they make to informed traders.
Market makers observe buying and selling pressure on prices, set prices accordingly, often making surprisingly little use of fundamental analysis when making their pricing decisions.
The theoretical model of Kyle [1985] describes the trading behavior of informed traders and uninformed market makers in an environment with noise traders.

10. Adverse Selection and the Akerlof Lemon Problem
Suppose two rational traders have access to the same information and are otherwise identical. They have no motivation to trade.
Now, suppose they have different information. Will they trade? Not if one trader believes that the other will trade only if the other has information that will enable him to profit in the trade at the first trader’s expense.
Rational traders will not trade against other rational traders even if their information differs. This is a variation of the Akerlof Lemon Problem.
So, why do we observe so much trading in the marketplace? Most of us believe that others are not as informed or rational as we are or that others do not have the same ability to access and process information that we do.

11. Kyle [1985]: Informed Traders, Market Makers and Noise Traders
Kyle examines trading and price setting in a market where some traders are informed and others (noise or liquidity traders) are not.
Dealers or market makers serve as intermediaries between informed an uninformed traders,
Dealers set security prices that enable them to survive even without the special information enjoyed by informed traders.
Kyle models how informed traders use their information to maximize their trading profits given that their trades yield useful information to market makers.
Furthermore, market makers will learn from the informed trader’s trading, and the informed trader's trading activity will seek to disguise his special information from the dealer and noise traders.

12. The Kyle Framework
Consider a one-time period single auction model involving an asset that will pay in one time period v~N(p0; Σ0)
p0 is the unconditional expected value of the asset.
Variance, Σ0, can be interpreted to be the amount of uncertainty that the informed trader’s perfect information resolves
There are three risk-neutral trader types:
a single informed trader with perfect information
many uninformed noise traders
and a single dealer or market maker who acts as an intermediary between all trades.
There is no spread and money has no time value.

13. Market Participants in the Kyle Framework
Market makers seek to learn from informed trader actions who seeks to disguise his information in a batch market (markets accumulate orders before clearing them).
The informed trader determines x, an appropriate share transaction volume that maximizes trading profits: π = E[(v - p) x│v]where p is the market price of the asset.
The market maker will observe total share purchases X = x + u where u reflects noise trader transactions, bidding up the price of shares p as X increases.
The market maker cannot distinguish between and u, but does correctly observe total demand X.
The dealer does not know which trades or traders are informed, but will try to discern informed demand x from noisy signal X.
Noise traders submit market orders for u shares randomly.
Noise traders demand u shares, where u is distributed normally with mean E[u] = 0 and variance σu2: u~N (0; σu2).
Informed traders do not know how many shares uninformed traders will trade, but does know the parameters of the distribution of the demand.

14. The Kyle Market Process
Informed and noise traders submit their order quantities x and u to the market maker in a batch market.
The market maker observes the net market imbalance X sets p such that total order flow X = x + u clears.
The market maker observes X then sets the price as a function of the sum of x and u: p = E[v│x + u].

15. Informed Trader Demand
The informed trader knows the true value of the stock and would like to use his information advantage to purchase (v > E[v] ) or sell (v < E[v] ) an infinite number of shares.
He cannot, because the market maker observes the total demand X = [x + u] for the stock. Slippage will result from an X that differs from 0.
When the market maker observes a large total demand X, she infers, with error, a high informed demand level x, and accordingly increases the market price p of the stock, decreasing the informed trader's profits.
Thus, the informed trader's demand is linearly related to the informed trader's informational advantage v - E[v]  but inversely related to the uncertainty 0 resolved by informed trader demand relative to the noise σu2 associated with uninformed trader demand:
Thus, the informed trader's purchase demand for shares increases at a constant rate as his informational advantage v - E[v] and uninformed trader camouflage σu2 increase, but decreases with his anticipation that the market maker expects his uncertainty advantage improves 0.

16. Dealer Price Setting
Thus, the market maker institutes price revisions leading to slippage in the market price p.
The market maker sets a price that is linearly related to total demand X = [x + u] for the stock, directly related to the uncertainty 0 resolved by informed trader demand relative to the noise σu2 associated with uninformed trader demand:
Thus, the market price of the stock set by the market maker equals its expected value plus its total demand multiplied by a sensitivity factor  related to the proportion of uncertainty presumed to have been resolved by the informed trader.
Thus,  (sometimes referred to as Kyle's lambda) is the sensitivity of the dealer price to order flow; 1/ measures the depth of the market (the order flow needed to cause the price to change by $1) for the stock.

17. Illustration: Kyle's Adverse Selection Model
Suppose that the unconditional value of a stock in a Kyle framework is normally distributed with an expected value equal to E[v] = $50 and a variance equal to Σ0 = 30.
An informed trader has private information that the value of the stock is actually v = $45 per share.
Uninformed investor trading is random and normally distributed with an expected net share demand of zero σu2 equal to 5,000.
The dealer can observe the total level of order volume X = x + u where u reflects noise trader transactions and x reflects informed demand, but the dealer cannot distinguish between x and u.
The ability of the informed trader to camouflage his activity is directly related to σu2 and inversely related to x.

18. Illustration: Kyle's Adverse Selection Model
E[v] = $50 Σ0 = 30 v = $45 σu2 = 5,000
What would be the level of informed trader demand for the stock? We solve for x as follows:
We solve for the price level as follows, assuming that u = 0:

19. 5.5. Adverse Selection and the Spread
Walrasian markets assume perfect and frictionless competition and symmetric information availability.
In security markets, imperfect competition, bid-offer imbalances and frictions often reveal themselves in bid-offer spreads.
Here, we are concerned with the determinants of the bid-offer spread.

20. Some Determinants of the Spread
The evolution of prices through time should provide insight as to what affects the spread.
If market frictions were the only factors affecting the spread, we should expect that, in the absence of new information, execution prices would bounce between bid and ask prices.
Frictions such as transactions costs will tend to be either leave execution prices unchanged or to change in the opposite direction.
Thus, transactions costs tend to induce negative serial correlation in asset prices.
Asymmetric information produces positive serial correlation in asset prices.
Transactions executed at bid prices would cause permanent drops in prices to reflect negative information and transactions executed at offer prices would cause permanent increases in prices to reflect positive information.
Thus, the extent to which information distribution is asymmetric will affect the serial correlation of asset prices.
Inventory costs (such as unsystematic risk from the dealer’s inability to diversify) will tend to cause negative serial correlations in price quotes.
Transactions at the bid will tend to cause risk averse dealers to reduce their bid quotes as they become more reluctant not to over-diversify their inventories.
Similarly, transactions at the ask will tend to cause dealers to raise their quotes as they become more reluctant not to under-diversify their inventories.
Inventory costs and transactions costs will tend to lead towards negative serial correlation in security prices.
Asymmetric information availability will lead towards positive serial correlation in security prices as transactions communicate new information.

21. The Demsetz [1968] Immediacy Argument
Order imbalances impose waits on impatient traders requiring immediacy.
The costs of providing immediacy to liquidity traders include order processing costs (transactions costs), information and adverse selection costs, inventory holding costs, costs of absorbing inventory risks and costs of providing trading options.
The bid-offer spread provides the dealer compensation for assuming these costs on behalf of the market.
In the Demsetz [1968] analysis, buyers and sellers of a security are each of two types, one of which who wants an immediate transaction and a second who wants a transaction, but can wait.
Buy and sell orders arrive to the market in a non-synchronous fashion, causing order imbalances.
An imbalance of traders demanding an immediate trade forces the price to move against themselves, causing less patient traders to pay for immediacy.
The greater the costs of trading, and the greater the desire for immediacy, the greater will be the market spread.

22. Glosten and Milgrom [1985] Information Asymmetry Model
The Glosten and Milgrom [1985] adverse selection model assumes that dealer spreads are based on the likelihood π that an informed trader will trade.
Trades arrive to the market maker, each with some random chance of originating from either an informed or uninformed trader.
The asset can take on one of two prices, a high price PH and a low price PL, each with probability ½.
Uninformed traders will not pay more than PH for the asset and they will not sell for less than PL.
Risk neutral liquidity traders value the asset at (PH + PL)/2.

23. Glosten and Milgrom [1985] : Setting the Spread
When setting his quotes, the dealer needs to account for the probability that an informed trader will transact at his quote, and will set his bid price Pb and ask price Pa as follows:
Pb = πPL + (1 – π)(PH + PL)/2
Pa = πPH + (1 – π)(PH + PL)/2
The spread is simply the difference between the ask and bid prices:
Pa - Pb = π(PH - PL)
Thus, in the single-period Glosten and Milgrom model, the spread is a function of the likelihood that there exists an informed trader in the market and the uncertainty in the value of the traded asset.
The greater the uncertainty in the value of the traded asset as reflected by (PH + PL)/2, and the greater the probability π that a trade has originated with an informed trader, the greater will be the spread.

24. The Stoll [1978] Inventory Model
A dealer needs to maintain inventories in assets in which he makes a market to sell to investors as well as cash to purchase assets from investors.
Suppose that a dealer currently without inventory in a particular asset trades so as to maximize his expected utility level.
Assume that the dealer's wealth level could be subject to some uncertain normally distributed security return r whose expected value is zero and variance σ2.

25. Stoll [1978]: Expected Utility and the Bid Price
The dealer is willing to quote a bid price Pb to purchase this security with consensus price P:
E[U(W – Pb + (1+r)P)] = U(W)
E[U(W + (P - Pb) + rP)] = U(W)
The dealer’s expected utility after the security purchase is a function of his current level of wealth W, his bid price Pb and his uncertain return. Our problem is to solve this equality for Pb.
We start by performing a Taylor series expansion around the left side of the equality:
E[U(W) + (P - Pb + rP)(U’(W)) + ½(P - Pb + rP) 2(U”(W)) + …] = U(W)
Since E[r] = 0, E[rP]U’(W) can be dropped from the equality and σ2 = E[(P - Pb + rP)2]:
E[U(W) + (P - Pb)(U’(W)) + ½(σ2)U”(W) + …] = U(W)

26. Risk Aversion and the Bid
Drop left-hand side higher order terms not explicitly stated in the above equality:
(P - Pb)(U’(W))  - ½(σ2)U”(W)
(P - Pb)  - ½(σ2)U”(W)/ U’(W)
(P - Pb)  ½(σ2)ARA
where -U”(W)/U’(W) is the dealer’s Arrow-Pratt Absolute Risk Aversion Coefficient (ARA).
The greater the dealer’s risk aversion, or the greater the uncertainty associated with the asset, the greater will be the discount associated with his bid.

27. Risk Aversion and the Bid
Drop left-hand side higher order terms not explicitly stated in the above equality:
(P - Pb)(U’(W))  - ½(σ2)U”(W)
(P - Pb)  - ½(σ2)U”(W)/ U’(W)
(P - Pb)  ½(σ2)ARA
where -U”(W)/U’(W) is the dealer’s Arrow-Pratt Absolute Risk Aversion Coefficient (ARA).
The greater the dealer’s risk aversion, or the greater the uncertainty associated with the asset, the greater will be the discount associated with his bid.

28. Inventory and the Bid
The dealer maintains an initial inventory Wp of securities Wp = W0. The dealer borrows and lends at the riskless rate r, assumed to be zero.
This initial inventory of securities Wp is an optimal portfolio that maximizes the dealer's utility U(W) subject to his initial wealth constraint:
E[U(Wp(1+rp) – (P - Pb) + rP)] = U(W)
where ri is the uncertain return on the tradable asset i and rp is the uncertain return on the optimal portfolio Wp.
Expand the left side of this equation around E[U(Wp)], assume that E[r] = E[rp] = 0, and drop higher order terms:
E[U(Wp) + (P - Pb)(U’(Wp)) + ½(σ2)U”(Wp) + 2×½×E[rP×rpWp]×U"(Wp)…] = U(W)
The covariance of cash flows between profits on the optimal portfolio and the tradable asset i is 2×½×E[rP×rpWp] = σi,P. Simplifying and solving for (P - Pb), we find that the dealer’s bidding discount from the consensus price is:
(P - Pb) = σI,PARA + ½(σ2)ARA
The dealer will decrease his bid as his inventory of securities increases and as the covariance between inventory returns and asset returns increases.

29. Obtaining the Stoll Ask Price
Similarly, the premium based the dealer’s ask or offer price Pa is obtained as follows:
(Pa - P) = -σI,PARA + ½(σ2)ARA
Thus, the dealer will increase his offer premium as his inventory of securities decreases and as the covariance between his inventory returns and the asset returns decreases. The bid-offer spread is simply the sum of the bid discount and offer premium:
(Pa - Pb) = (σ2)ARA
The greater the dealer’s risk aversion, or the greater the uncertainty associated with the asset, the greater will be the dealer’s spread. The dealer’s inventory level does not affect the size of the spread.

30. The Copeland and Galai [1983] Options Model
A bid provides prospective sellers a put on the asset, with the exercise price of the put equal to the bid.
An offer provides a call to other traders.
Thus, when the dealer posts both bid and offer quotes, the spread is, in effect, a short strangle provided to the market.
Both legs of this strangle are more valuable when the risk of the underlying security is higher.
An options pricing model can be used to value this dealer spread.
Ultimately, this "implied premium" associated with this dealer spread is paid by liquidity traders who trade without information.
Informed traders make money at the expense of the dealer, who ultimately earns it back at the expense of the uninformed trader.
The Copeland and Galai model, as presented here, does not have a mechanism to allow trading activity to convey information from informed traders to dealers and uninformed traders. Nonetheless, in the Copeland and Galai option-based model, the spread widens as the uncertainty with respect to the security price increases.