High-Frequency Traders, News and Volatility

High-Frequency Traders, News and Volatility * Victor Martinez † Ioanid Ro¸su ‡ August 19, 2011 Abstract We model high-frequency traders (HFTs) as informed traders who dislike taking directional bets. They receive a continuous stream of information about a particular asset, which we call news, possibly by compiling relevant information from other market variables. We show that in the presence of news, HFTs generate most of the volatility and trading volume in the market, in contrast with other dynamic asymmetric information models with strategic trading, in which the contribution of informed traders to volume and volatility is very small. The model yields patterns in volatility and volume even under perfect agreement among informed traders. In particular, a higher precision of news generates more price volatility and trading activity, but only marginally higher market illiquidity. Keywords: Insider trading, Kyle model, noise trading, trading volume, algorithmic trading, informed volatility, price impact, inventory, risk aversion. *We thank Kerry Back, Laurent Calvet, Thierry Foucault, Johan Hombert, Pete Kyle, Stefano Lovo, Jiang Wang; seminar participants at HEC Paris; and conference participants at the Society for Advancement of Economic Theory, Portugal for valuable comments. † Baruch College, CUNY, Zicklin School of Business, Email: victor martinez@baruch.cuny.edu. ‡HEC Paris, Email: rosu@hec.fr. 11 Introduction The empirical literature on asset price volatility has shown that a signi?cant component of volatility is due to informed trading. 1 Yet, since the landmark paper of Kyle (1985), various theoretical models of strategic trading with asymmetric information have produced only a very small component of price volatility and trading volume due to informed traders, with the most part produced by the noise traders. 2 In fact, in the limit case when the time interval goes to zero, Kyle (1985), Back and Pedersen (1998), and Back, Cao, and Willard (2000) show that informed traders contribute to the price process by adding only a drift component, while the volatility component is generated solely by noise traders. How can we reconcile this discrepancy between theory and reality? This question is even more relevant when we consider the emergence of algorithmic trading and high-frequency trading, which have been identi?ed as informed traders in several studies, and which have reduced trading intervals sometimes to the level of milliseconds. Hendershott and Riordan (2009) ?nd that algorithmic traders account for about 50% of the trading volume in the 30 DAX stocks on the Deutsche Boerse, while they appear to be quickly processing information contained in order ?ow and price movements in that security as well as other securities across markets. Hendershott, Jones, and Menkveld (2011) ?nd that in 2009 algorithmic traders accounted for 73% of trading volume on the NYSE, while improving price e?ciency overall. Brogaard (2011) replicates these results for the subset of high-frequency traders (henceforth HFTs), and shows that these have superior information to other categories of traders. Despite this information advantage, HFTs rarely accumulate inventory over more than one day, typically switching between being long and short in a stock several times a day. If we compare the theoretical and the empirical literature on HFTs and informed trading, we face a stark dilemma. Empirically, there is signi?cant evidence that HFTs are informed traders. But then existing theoretical models imply that the contribution of HFTs to price volatility and trading volume should be very small, in contradiction with the empirical evidence. Our paper provides a solution to this dilemma. We model HFTs 1 See, e.g., French and Roll (1986) and Barclay and Warner (1993). 2 The asset pricing literature, e.g., Campbell and Kyle (1993), or Wang (1993), has avoided this issue by considering equilibria in which traders are price takers, i.e., they do not internalize the price impact of their trading. 2as informed traders that maximize their expected pro?t, but additionally are inventory averse, i.e., they dislike taking directional bets. They receive their information gradually, by a continuous stream of information, which we call news. This information structure is essentially the same as that of Back and Pedersen (1998). Then we show that, under plausible conditions, almost all volatility and trading volume are due to HFTs. We further show that the model yields patterns in price volatility and trading volume even though HFTs have the same information in our model. The model has two main ingredients. The ?rst is that the HFTs receive their information gradually, by a continuous stream of signals. These signals can be interpreted, as suggested by Back and Pedersen (1998), as a summary statistic of all the relevant public information which is related to the asset’s value. The fundamental value of the asset is assumed to be moving over time, although this is not strictly necessary. 3 The view of a large part of the market microstructure literature, starting with Kyle (1985), is that the fundamental (or liquidation) value is constant over time, and that it takes time for the market to discover that value. In reality, there is no reason why the demand and supply curves that determine the true value of the asset should be constant. The second ingredient is that HFTs are inventory averse, i.e., they favor taking non-directional bets over strategies that increase expected inventory. In the absence of inventory aversion, we show that informed traders (HFTs) only trade with a drift but with no volatility component, in agreement with Kyle (1985), Back and Pedersen (1998), and Back, Cao, and Willard (2000). 4 But we show that these classical equilibria are not robust in the presence of even a small inventory aversion, as long as the number of HFTs is su?ciently large. Thus, we have a “trembling hand” phenomenon: if HFTs cannot perfectly compute their expected utility, even a small deviation from risk neutrality induces them to contribute to a large component of volatility and volume. 3 For example, if we de?ne the fundamental value of GM as the liquidation value of GM at some distant point in the future, then we can de?ne news as a summary statistic re?ecting the price of the market index, energy prices, or any other relevant ?nancial variables that are correlated with the value of GM. The news variable then would change very frequently, even if the true value of GM did not. 4 Back, Cao, and Willard (2000) remark that it may be optimal for informed traders to include a stochastic component if their orders are correlated, but that such correlation is not feasible in practice with market orders (see Footnote 6 in their paper). However, in our paper the market orders of the informed traders are correlated, because they receive correlated signals about a moving fundamental value. The authors thank Kerry Back for pointing this out. 3Some extra care is required in setting up the model. To focus on the main intuition, we choose the simple case in which all HFTs receive the same stream of signals about the asset (e.g., HFTs interpret news in the same way). But we must be careful not to run into the problem noticed by Holden and Subrahmanyam (1992), that informed traders who receive the same static signal reveal their information so fast that no equilibrium exists in continuous time. 5 For that reason, we introduce a small correction in the utility function of the HFTs near the asset liquidation date, to prevent their building inventory too fast towards the end. We argue that the main results of the paper do not depend on the equilibrium behavior near the liquidation date, and thus are robust to our modeling choices. The contributions of the paper are threefold. First, HFTs are shown to generate a large part of volatility and trading activity. This is supported by the evidence discussed above regarding algorithmic trading and high-frequency trading. There is also indirect evidence: for many ?nancial assets, trading is dominated by institutions, and it is unlikely that institutions are noise traders. Our results show that this is perfectly consistent with rationality. Of course, because of the “no trade” result of Milgrom and Stokey (1982), we still need a certain amount of noise (or liquidity) trading, but we show that the necessary relative contribution of noise trading is very small. Second, we provide some clari?cation for the concept of news. In this paper, we interpret news as a stream of signals which are relevant, i.e., correlated, to the fundamental value. 6 If we consider the example of GM, the stream of signals may be obtained by extracting the relevant part about GM from the prices of other car companies, or from the S&P futures prices, or from the exchange rate USD/EUR. As long as these variables are correlated with the true value of GM, our results show that HFTs should incorporate them in their trading demands. This in turn may have implications on the comovement of asset prices that is due to news. 5 In contrast, Back, Cao, and Willard (2000) show that there exists an equilibrium when multiple informed traders receive imperfectly correlated static signals. Thus, ideally we would like HFTs to receive di?erent streams of information. But then we would run into the problem of forecasting the forecasts of others, as pointed out by Foster and Viswanathan (1996). 6We do not distinguish between private and public news. In the case of algorithmic traders, Hendershott, Jones, and Menkveld (2011) argue that trading is based on the interpretation of public news, e.g., by quickly changing limit orders as soon as some public information in other assets becomes available. 4A consequence of this interpretation of news is that one can obtain signi?cant patterns in trading volume and price volatility without assuming di?erences of opinions, as in Banerjee and Kremer (2010). For example, we show that volume and volatility increase when the signals become more precise, e.g., after news announcements. This is because with more precise signals, HFTs act more aggressively, and therefore increase both the price volatility and trading volume. Thus, the intuition of Kim and Verrecchia (1991) also works in a strategic model of trading even without any di?erences of precision of information among informed traders. In agreement with Kim and Verrecchia (1994), the market illiquidity (price impact) also increases with signal precision, although the e?ect is weak when the number of HFTs is large. Indeed, when HFTs trade more aggressively, they increase the information asymmetry between HFTs and market makers, thus increasing market illiquidity. But there is an partially o?setting e?ect: more aggressive trading by HFTs induces market makers to learn more quickly about the moving asset value. This reduces the level of asymmetry, thus making the market more liquid. We also ?nd that price volatility and trading volume are essentially independent of the composition of the market, i.e., on the number of informed traders or the amount of noise trading. Instead, price volatility depends only on the intrinsic characteristics of the fundamental value and the structure of news, i.e., the news precision and the initial news asymmetry. Third, we clarify our understanding of noise trading. In our model, we can interpret noise traders as HFTs who think their stream of signals is correlated with the fundamental value, when in reality it is not. This is essentially what Black (1986) suggests. Thus, HFTs are very similar to noise traders—except that the HFTs are correct in their inferences. Since it is di?cult to estimate correlations in practice, it is not hard to accept that some traders may not perceive correlations correctly. 7 Our paper also makes a methodological contribution. Since the trading strategies of informed traders are functions of time, ?nding the trading intensities that maximize 7Another interpretation of noise traders is that they are simply the slow HFTs. If HFTs disseminate public news and trade as quickly as possible on that interpretation, the slow HFTs try to imitate the quick HFTs, but in reality they trade on stale information. However, since the innovation in news does not get fully incorporated into prices right away, there is some room for slow traders. 5expected pro?t falls naturally under the framework of calculus of variations, as described by Gelfand and Fomin (2003). The other papers in the literature have solved this type of problems in di?erent, more ad hoc ways. E.g., Back (1992) and Back, Cao, and Willard (2000) use an approach that involved guessing the solution and solving the associated Hamilton-Jacobi-Bellman equation. Our method provides a constructive way of searching for the solution. The paper is organized as follows. Section 2 describes the model. Section 3 describes the resulting equilibrium price process and trading strategies. Section 4 discusses empirical implications of the model. Section 5 concludes. 2 The Model To describe the sources of uncertainty in the model, consider three independent Brownian motion processes, Bj with j = 1, 2, 3. Trading takes place in continuous time, t ? [0, 1]. There exists a single risky asset that pays no dividends, and liquidates at t = 1. The liquidation value, v1, can be written as v1 = v0 + R 1 0 dvt , with dvt = sv dB1,t . (1) The fundamental value vt can be thought as the best estimate of v1 at time t given all possible information. The parameter sv is called the fundamental volatility. There are three types of market participants: noise traders, high-frequency traders (HFTs), and market makers. Noise traders trade an exogenous amount dut at each t, given by dut = su,t dB2,t , (2) where we allow the noise trading volatility su,t to be time dependent. There are N HFTs who learn gradually about the fundamental value of the asset. For simplicity, we assume that HFTs have identical information at all times. 8 The information is released gradually by a process called the news stream, or simply news. 8 If HFTs get di?erent signals, we run into the problem of forecasting the forecasts of others: see, e.g., Foster and Viswanathan (1996). 6At t = 0, HFTs observe s0, a noisy signal of v0, which from the point of view of the other market participants has variance S0. The parameter S0 is called the initial news asymmetry. Subsequently, at each t, they observe a noisy signal dst of the form dst = dvt + d?t , with d?t = s? dB3,t , (3) such that the volatility s? is constant. We call the parameter a = s 2 v s2 v+s2 ? the news precision. In the particular case when a = 1 (or s? = 0) and S0 = 0 (or s0 = v0), the news stream is precise, i.e., HFTs perfectly observe the fundamental value vt at all times. HFTs trade in order to take advantage of their superior information. At each t, they form an expectation about the fundamental value, w s t = E s t (v1) = E(v1|F s t ), (4) where E s t denotes the expectation conditional on F s t , the information of the HFTs, which consists of the news stream (st )t?[0,t] , along with all the public information, Ft , to be de?ned below. For i = 1, . . . , N, denote the asset holdings of HFT i, by x i t . As in Back, Cao, and Willard (2000), we only consider trading strategies of the form dx i t = ? i t dt + µ i t dst , with (5) ? i t = a i tPt + ß i tw s t . (6) Given this strategy, we de?ne U s i,t , the expected utility of HFT i at t: 9 U s i,t = E s t Z 1 t v1 - Pt - dPt fA ? i t dt + µ i t dst , with fA = (1 - A) 1 + ke,t (1/?t) 0 ß i t , (7) A = 1, e = 0, ke,t = 0 if t ? [0, 1 - e] and ke,t > 0 if t ? (1 - e, 1]. 9Note that, unlike in Kyle (1985), or Back, Cao, and Willard (2000), the term dPs cannot be omitted, because the market order dxs has a stochastic component. 7