chapter 5

C H A P T E R 5 Adverse Selection, Trading, and Spreads 5.1 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. Some economists have suggested that more than half of the U.S. economy is currently engaged in activities that are producing and analyzing information products. In fact, revenues obtained by the New York Stock Exchange from selling trading data exceed its trading-fee based revenues. 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. In Chapter 3, we discussed slippage and market impact models, describing how prices move against traders who execute large orders due to the perceived information content of those orders. Here, particularly in our discussion of the Bagehot (1971), Kyle (1985), and Glosten and Milgrom (1985) models, 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 mini- mize losses). This chapter is concerned primarily with problems that arise when traders and other market participants have inadequate, different (asymmetric information availabil- ity), and costly access to information. In this chapter, we discuss information and informa- tion asymmetries in a trading context. Adverse Selection Adverse selection originally referred to the tendency of higher risk individuals to seek insurance coverage. More generally, adverse selection refers to precontractual 117 Financial Trading and Investing © 2013 Elsevier Inc. All rights reserved. opportunism where one contracting party uses his private information to the counter- party’s disadvantage. For example, the adverse selection problem can arise when a woman planning a pregnancy purchases health insurance, when a car rental customer secretly planning a trip through a Golan Heights minefield buys comprehensive insurance on the car, or when a pyromaniac purchases fire insurance. In all three cases, the agent (insured or customer) has private information with respect to the higher anticipated costs of the insurance coverage or lease, but pays a “pooling” premium for the incident or casualty coverage. Obviously, this private information affects the behavior of insurers and other insured clients, in what might otherwise be taken to be a suboptimal manner, referred to as the adverse selection problem. 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 numer- ous buy (sell) orders originating from the same trader are likely to be perceived as being motivated by special information. Trade counterparties are likely to react by adjusting their offers (bids) upwards (downwards), resulting in slippage as we discussed in Chapter 3. This market impact or slippage is the market’s reaction to the adverse selection problem. In this chapter, we will consider the impact of the adverse selection problem on order sizes, security prices, and the spread. 5.2 NOISE TRADERS Noise traders trade on the basis of what they falsely believe to be special information or misinterpret useful information concerning the future price or payoffs of a risky asset. Noise traders make investment and trading decisions based on incorrect perceptions or analyses of the market, perhaps creating opportunities for more sophisticated investors and traders. In many models of markets, noise traders are often assumed to have no useful information or at least react inappropriately to useful information concerning a security’s fundamentals. But, do noise traders distort prices? If noise traders trade in large numbers, if their trading behavior is correlated, or if their effects cannot be mitigated by informed and rational traders, they may well distort prices from fundamental values. In many mod- els, individual investors are presumed to be noise traders and that their psychology (see Chapter 10) and poor access to information inhibit their trading success. In 1953, the economist 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 (1965) argued that when irrational trading does occur, security prices will not be significantly affected because more sophisticated traders will react quickly to exploit and eliminate any devia- tions from fundamental economic values. Figlewski (1979) suggested that it might take irrational investors a very long time to lose all their money and for prices to reflect secu- rity intrinsic values, but nonetheless, those traders who choose their portfolios irrationally are doomed in the long run. 118 5. ADVERSE SELECTION, TRADING, AND SPREADS FINANCIAL TRADING AND INVESTING Noise traders are useful, perhaps even necessary, for markets to function. Without noise traders, markets would be informationally efficient. Prices would always fully reflect infor- mation (to the extent market frictions are absent). 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 motiva- tion 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 such that no trades would ever be executed. However, noise traders do impose on other traders the risk that prices might move unpredictably, irrationally, and without reference to relevant information. In some instances, 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. In fact, arbitrageurs might sometimes need to ask themselves the following important question: “Does my ability to remain solvent exceed the asset price’s ability to remain irrational?” We will discuss this issue more in Chapter 6. 5.3 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 frame- work, trading is a zero-sum or neutral game. Investors with special information or super- ior analytical skills will earn abnormal returns; uninformed investors will lose more than they make. In fact, the more frequently an uninformed trader trades, the more he can be expected to lose, and these trading losses are reflected as informed trader profits.1 Market makers observe buying and selling pressure on prices and set prices accordingly, often making surprisingly little use of fundamental analysis when making their pricing deci- sions. Kyle’s (1985) theoretical model describes the trading behavior of informed traders and uninformed market makers in an environment with noise traders. Kyle: Informed Traders, Market Makers, and Noise Traders The Setting and Assumptions 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 informa- tion. Will they trade? Not if one trader believes that a second will trade only if the second 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 1See Barber and Odean (2000, 2001, 2002) and Barber et al. (2009) who find that more aggressive (frequent) traders underperform risk-adjusted benchmarks. We discuss these and related findings in Chapter 10. 1195.3 ADVERSE SELECTION IN DEALER MARKETS FINANCIAL TRADING AND INVESTING 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 infor- mation that we do. Thus, 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 and uninformed traders, and seek to set security prices that enable them to survive even without the special information enjoyed by informed traders. Kyle models how informed traders will use their information to max- imize their trading profits given that their trades yield useful information to market makers. Furthermore, market makers will seek to learn from the informed trader’s trading behavior, and the informed trader’s trading activity will seek to disguise his special infor- mation from the dealer and noise traders. Consider a one-time-period single auction model involving an asset that will pay in one time period vBN(p0; Σ0); that is, the future liquidation payoff v is normally distributed with mean value p0 and variance Σ0. Thus, 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, so that Σ0 reflects the informed trader’s value advan- tage. There are three trader types—a single informed trader with perfect information, many uninformed noise traders, and a single dealer or market maker who acts as an inter- mediary in all trades. All are risk neutral, there is no spread, and money has no time value. Market makers and noise traders seek to learn from the actions of the informed trader, who seeks to disguise himself and his special information in a batch market (mar- kets accumulate orders before clearing them). Thus, the informed trader seeks to deter- mine x, an appropriate share purchase (sale) volume that maximizes his trading profits based on his superior information: π5E[(v�p) xjv] where p is the market price of the asset. That is, the informed trader seeks to maximize his expected trading profits given his perfect knowledge of v and the price p that he pays (or receives) for x shares of the stock. Noise traders and the market maker will observe total share purchases X5 x1 u, where u reflects noise trader transactions, bidding up the price of shares p as X increases. The mar- ket maker cannot distinguish between informed trader demand x and noise trader demand u, but does correctly observe total demand X. Nonetheless, X will be correlated with x, hence, the informed trader needs to exercise care in deciding on his transactions volume x to protect himself from price slippage (see Chapter 3). Thus, neither the dealer nor the noise traders will know which trades or traders are informed, but they seek to dis- cern informed demand x from the noisy signal X representing total demand. Noise traders submit market orders for u shares randomly, such that their orders con- tain no useful information content. In fact, noise trader activity will obscure information provided by the informed trader, which enables informed traders to disguise the informa- tion content of their trading from the dealer and noise traders. Noise traders will demand u shares, where u is distributed normally with mean E[u]5 0 (they are as likely to sell as to buy) and variance σ2u: uBNð0; σ2uÞ. Thus, σ2u is the variance of uninformed investor demand. Informed traders do not know how many shares uninformed traders will buy or sell, but the informed trader does know the parameters of the distribution of the demand. 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 (the extent to which X 120 5. ADVERSE SELECTION, TRADING, AND SPREADS FINANCIAL TRADING AND INVESTING is positive or negative at various price levels), and sets the price p at which the total order flow X5 x1 u is executed and clears. Thus, the market maker observes X, and then sets the price as a function of the sum of informed and uninformed investor demand: p5E [vjx1 u]. The Informed Trader’s Problem: Profit Maximization Kyle’s Bayesian learning model assumes that informed investor demand x can be expressed as a simple linear function of v: x5α1βv, where α and β are simple coeffi- cients whose traits will be discerned and examined shortly. Similarly, the security’s price p, set by the market maker or dealer, is also assumed to be a simple linear function of demand: p5μ1λ(x1 u), where μ and λ are also simple coefficients whose traits will also be examined shortly. Thus, informed investor demand x is a linear function of true secu- rity value v and the security price p is a linear function of the sum of informed and unin- formed investor demand X5 (x1 u).2 Recall that the informed trader’s primary problem is to determine the optimal purchase (or sale) quantity x so as to maximize the expected value of his trading profits: maxx E½π�5E½ðv2 pÞxjv�5E½ðv2μ2λ ðx1 uÞÞxjv� 5E½ðvx2μx2λx22λuxÞ� (5.1) To maximize the informed trader’s profits, find the derivative of expected trading profits E[π] with respect to informed investor demand x and set equal to zero: @E½π� @x 5 v2μ2 2λx2λu5 0 (5.2) Also recall that that the distribution of u implies that E[u]5 0 since uninformed inves- tors randomly buy and sell. Next, note that λ must be positive for the second-order condi- tion (the second derivative must be negative (22λ, 0)) to hold for maximization. We will demonstrate this later. Finally, we rearrange terms to obtain: 2λx5 v2μ (5.3) x5 2 μ 2λ 1 1 2λ v (5.4) which is linear in v as Kyle proposed it would be. Now, we see that our coefficients α and β are simply: α5 2 μ 2λ ; β5 1 2λ Thus, the informed trader linear demand function x5α1βv5 2 μ 2λ 1 v 2λ is set based on the dealer pricing function. 2Readers who would prefer not to read this derivation might wish to skip to the numerical illustration at the end of this section. 1215.3 ADVERSE SELECTION IN DEALER MARKETS FINANCIAL TRADING AND INVESTING Dealer Price Setting But, to gain insight into what the informed trader linear demand function implies, we need to better understand our coefficients α and β. To explore this, we will examine the trading of the dealer or market maker who observes total order flow X5 x1 u, and sets a single market clearing price p or E[v] as a function of total demand p5E[vjx1 u] where x5α1βv. Note here that the dealer increases the price of the security as total demand x1 u increases. Since v and X are normally distributed, we will apply the projection theo- rem to p as follows3: p5E v½ �1 COV½v; x1 u� VAR½x1 u� � � x1 u2E x1 u½ �½ � (5.5) This dealer pricing function has a straightforward interpretation. First, the sensitivity of the dealer price to total share demand x1 u is a function of the covariance between the stock’s value and total demand for the shares COV[v, x1 u]. Thus, if the dealer believes that total demand x1 u for the stock increases dramatically with its intrinsic value v (unknown to him, but known to the informed trader), the price that the dealer sets for shares will be very sensitive to total demand. Thus, if the informed trader is known to dominate trading in the marketplace, the dealer will set the price of the security mostly or entirely as a function of total demand for the security. This sensitivity to total demand will diminish as uninformed demand volatility increases. As total demand deviates more from expected demand, the price of shares will increase. Informed Trader Demand and Dealer Price Adjustment Since x5α1βv, and Σ0 is the variance of or uncertainty associated with asset payoffs v, the variance of informed trader demand VAR[x] will equal β2Σ0. This means that VAR½x1 u�5β2Σ01 σ2u, which means that we can write the dealer pricing equation as: p5E v½ �1 COV½v; x1 u� β2Σ01σ2u " # x1 u2α2βE v½ �½ � (5.6) Now, recall that β is the slope of a line plotting a random dependent variable X or (x1 u) with respect to an independent random variable v. That is, β5COV[v, x1 u]/VAR[v]5 COV[v, x1 u]/Σ0, which means that COV[v, x1 u]5βΣ0, and we can write this equation as: p5E v½ �1 βΣ0 β2Σ01σ2u " # x1 u2α2βE v½ �½ � (5.7) 3The projection theorem has many applications in finance, such as to the capital asset pricing method (CAPM) and arbitrage pricing theory (APT). Many students are first exposed to it in econometrics when seeking an unbiased estimator in an econometrics setting. Generally, the projection theorem states that the relationship between some random dependent variable y and an independent random variable x is y5E y � � 1 COV½y; x� VAR½x� � � x2E x½ �½ � 122 5. ADVERSE SELECTION, TRADING, AND SPREADS FINANCIAL TRADING AND INVESTING Recall that Kyle suggested a linear relationship between the security price and its demand: p5μ1λ(x1 u). This implies a slope λ equal to: λ5 βΣ0 β2Σ01σ2u " # (5.8) which implies μ5 p1λ(2x�u) and μ5E½v�1λ½2α2βE½v�� (5.9) Next, we will use α and β coefficients from above to demonstrate that μ5E[v]: μ5E v½ �1λ μ 2λ 2 1 2λ E v½ � � � 5E v½ �1 μ 2 2 1 2 E v½ � � � 5 1 2 E v½ �1 μ 2 5E v½ � (5.10) Now, we will rewrite λ, substituting in for β: λ5 βΣ0 β2Σ01 σ2u " # 5 1 2λΣ0 1 2λ � �2Σ01σ2u " # (5.11) We will use a bit of algebra to simplify this expression for λ, starting by multiplying λ and the right-hand side of Equation (5.11) by the denominator of the right-hand side of the equation: λ 1 2λ � 2 Σ01σ2u " # 5 1 2λ Σ0 (5.12) Next, we will simplify the left-hand side and then multiply both sides by λ and simplify further by subtracting 14Σ0 from both sides: 1 4λ � Σ01λσ2u � � 5 1 2λ Σ0 (5.13) 1 4 � Σ01λ2σ2u5 1 2 Σ0 (5.14) λ2σ2u5 1 4 Σ0 (5.15) λ5 ffiffiffiffiffiffiffiffiffiffi 1 4 Σ0 σ2u s 5 1 2 ffiffiffiffiffiffi Σ0 σ2u s (5.16) First, we see that it is obvious that λ is positive and that our second-order condition for profit maximization has been fulfilled. More importantly, λ can be taken to be the dealer price adjustment for total stock demand; that is, λ can be considered to be the illiquidity adjustment. The ratio Σ0=σ2u is the ratio of informed trader private information resolution to the level of noise trading. Thus, dealer price adjustment is proportional to the square root of this ratio, increasing as private information Σ0 is increasing and decreasing as 1235.3 ADVERSE SELECTION IN DEALER MARKETS FINANCIAL TRADING AND INVESTING noise trading σ2u increases. This means that if the dealer determines that the informed trader resolves a substantial level of risk relative to the amount of noise trading, the level of dealer price adjustment λ will be large. Now, we can write ou