Asymmetric Trading Costs Prior to Earnings Announcements: Implications for Price Discovery and Returns

Transcription

1 Asymmetric Trading Costs Prior to Earnings Announcements: Implications for Price Discovery and Returns Travis L. Johnson The University of Texas at Austin McCombs School of Business Eric C. So Massachusetts Institute of Technology Sloan School of Management March 2015 Abstract We show the cost of trading on negative news relative to positive news increases prior to earnings announcements. Our evidence suggests this asymmetry is due to financial intermediaries preference to reduce their exposure to risks associated with the announcements. The asymmetry creates a predictable upward bias in prices that increases pre-announcement and subsequently reverses, which confounds short-window announcement returns as measures of risk premia and earnings news. Our findings provide a link between trading behavior, return patterns, and the information content of prices around earnings announcements and help to explain puzzling evidence in prior research that announcement risk premia precede the actual announcements. JEL Classifications: G10, G11, G12, G14, M41 We thank Zhi Da, Emmanuel De George, Terry Hendershott, SP Kothari, Charles Lee, Russ Lundholm, Paul Tetlock and seminar participants at Cornell University, MIT, The University of Texas at Austin, London Business School, the 2014 Citi Quant Research Conference, Nasdaq Economic Research, and Stanford University for helpful feedback and suggestions. Portions of this research were previously included in a working paper titled Earnings Announcement Premia: The Role of Asymmetric Liquidity Provision, which has been split into multiple papers. Corresponding authors: Travis Johnson, travis.johnson@mccombs.utexas.edu, 2110 Speedway Stop B6600, Austin, TX and Eric So, ESo@mit.edu, E Main Street, Cambridge MA

2 Asymmetric Trading Costs Prior to Earnings Announcements 1 1. Introduction Market frictions play a crucial role in the determination of asset prices. Recognition of this role has given rise to a substantial literature on the implications of these frictions. Transaction costs are a classic example of market frictions that influence the price discovery process by reducing investors incentives to gather and trade on information. Due to this influence, studying the determinants of transaction costs is essential for understanding the dynamics and information content of market prices. The cost of trading a given security is directly related to the security s risk profile. This relation is in part driven by the impact of risk on the financial intermediary sector, which is comprised of broker-dealers, investment banks, and market-making firms, among others. Financial intermediaries provide liquidity to investors by serving as the trade counterparty in response to imbalanced demand between buyers and sellers. In doing so, they are forced to take temporary positions in the asset, referred to as inventory, and thus expose themselves to price fluctuations ( inventory risk ). The amount of compensation that financial intermediaries demand for providing liquidity depends on several factors, including their existing inventory positions as well as the riskiness of the asset. This study uses firms earnings announcements to examine how predictable changes in risk affect financial intermediaries willingness of provide liquidity to buyers versus sellers. Prior research shows that financial intermediaries are positively exposed to the market and hold positive average inventory positions, indicating they are likely exposed to increased risks associated with the announcements. 1 As a result of this exposure, we predict intermediaries demand greater compensation for providing liquidity to sell orders, which would exacerbate their exposure, relative to buy orders, which would shield them from announcement risks by helping them get flat (i.e., reduce exposure) before the release of earnings news. 1 For example, Brunnermeier and Pedersen (2009) reports that broker-dealer firms have median market betas above one. Adrian and Shin (2010) shows financial intermediaries leverage is highly procyclical because they expand their positions in response to market booms and contract their positions in response to market downturns. Similarly, studies using proprietary data on market makers inventory positions also show they tend to hold positive inventories (Madhavan and Smidt (1993) and Comerton-Forde et al. (2010)).

3 Asymmetric Trading Costs Prior to Earnings Announcements 2 To formalize our central hypotheses, we develop a simple model of liquidity provision prior to an information event involving a financial intermediary with positive exposure to the underlying asset. In our model, the intermediary anticipates traders strategies and chooses bid and ask prices to maximize their expected utility, after which risk-averse informed and uninformed traders choose optimal quantities. In equilibrium, the intermediary embeds a smaller liquidity provision premium into the ask than the bid, which helps reduce their inventory risk at the announcement by attracting greater demands to buy than sell. Our model shows that by asymmetrically providing liquidity, intermediaries induce an upward bias in pre-announcement prices because traders face lower costs of acting on good news compared to bad news. The announcement corrects this bias, which elicits abnormally low returns, but also commands a risk premium, which elicits abnormally high returns. Together, these offsetting effects cause abnormal returns to be concentrated prior to, rather than during, earnings announcements even in the presence of an announcement risk premium. Our model also yields several additional implications for trading activity, price dynamics, and the information content of prices, all of which we validate in our empirical tests. Empirically, we begin by documenting changes in liquidity provision prior to earnings announcements. As in Nagel (2012), we use short-term return reversals as a proxy for the compensation that financial intermediaries demand for providing liquidity, which are well suited to test our central hypothesis for at least three reasons. First, most models involving risk-averse intermediaries, including ours, predict that they extract compensation for providing liquidity by setting prices above (below) fundamental value in response to buy (sell) order imbalances, which subsequently revert toward fundamental value, resulting in negatively autocorrelated returns (i.e, return reversals). Second, adverse selection does not give rise to negative autocorrelation in returns (Glosten and Milgrom (1985)), which allows us to attribute pre-announcement increases in reversals to greater inventory risks rather than adverse selection. Finally, comparing the magnitude of reversals following positive versus negative returns allows us to measure asymmetries in costs of buying versus selling.

4 Asymmetric Trading Costs Prior to Earnings Announcements 3 Our first main result is that return reversals become increasingly asymmetric prior to firms earnings announcements. Specifically, return reversals associated with net selling pressure (i.e., recent losers) increase dramatically leading up to announcements, whereas no discernible trend exists for recent winners. These results are consistent with our model s prediction that intermediaries demand greater compensation for providing liquidity to sellers relative to buyers and, thus, that traders face higher costs of expressing negative news in preannouncement prices compared to positive news. This asymmetry increases starting several days prior to announcements, peaks at more than three times normal levels immediately before announcements, and reverts to normal levels after announcements. We provide further evidence of asymmetries in pre-announcement transaction costs by examining within-firm changes in intra-day price impact and quoted depth, conditional upon the fraction of trading volume that is buyer- versus seller-initiated. Our findings show preannouncement net selling is associated greater increases in effective spreads compared to net buying, consistent with traders incurring abnormally high price impact when selling prior to earnings announcements. Similarly, we show that pre-announcement quoted depth decreases in periods of net selling, which is consistent with financial intermediaries reducing liquidity provision in response to pre-announcement demands to sell. Our second main empirical result is that investors respond to asymmetric trading costs by trading more aggressively ahead of good news compared to bad news. Specifically, we show the association between earnings news and returns is weaker prior to, and stronger following, negative news announcements, indicating that pre-announcement prices incorporate more good news than bad news and that prices adjust following the announcement. Similarly, we show the majority of net buyer-initiated (seller-initiated) volume in earnings announcementmonths occurs before (after) the announcement. Finally, we show that pre-announcement abnormal trading volume positively predicts earnings news. All of these results corroborate our model s predictions and provide support for our main hypothesis that traders face lower costs of acting on good news compared to bad news prior to earnings announcements.

5 Asymmetric Trading Costs Prior to Earnings Announcements 4 Our third main result is that firms earn positive excess returns beginning an entire week before their earnings announcements, supporting our model s prediction that asymmetric trading costs give rise to a predictable upward bias in pre-announcement prices. This connection between asymmetric trading costs and pre-announcement returns helps explain the puzzling result in Barber et al. (2013) that earnings announcements elicit an idiosyncratic risk premium but that a significant portion of the premium is earned prior to the actual announcements. The Barber et al. (2013) result is puzzling because investors appear to earn abnormal returns before the spike in idiosyncratic at the announcement, which suggests an arbitrage opportunity. This paper establishes that even in the presence of a risk premium associated with an information event, researchers are likely to observe abnormal returns prior to the event due to predictable asymmetries in transaction costs. Our final main result is that while excess returns rise in terms of magnitude and significance ahead of earnings announcements, they are insignificant on announcement dates (t), and become significantly negative following the announcements (t+1). This return pattern supports our model s prediction that the contemporaneous realization of risk and risk premia at earnings announcements is offset by the reversal of the upward bias in pre-announcement prices. To our knowledge, this study is the first to show firms excess returns are only reliably positive prior to, but not during, their earnings announcements. Our results also suggest evidence of excess returns on announcement dates (t) in prior studies likely stems from mismeasurement of the date when earnings news is released. More broadly, our findings yield an important insight for the enormous literature spanning finance, accounting, and economics that studies firms earnings announcement returns: Short-window announcement returns are unreliable proxies for risk premia or earnings news. The reason is that short-window announcement returns are confounded by the growth and subsequent reversal of pre-announcement biases in prices. Moreover, because the bias accumulates starting several days prior to announcements, longer-window returns (e.g., weeks or months) are needed to measure risk premia or news associated with the announcements.

6 Asymmetric Trading Costs Prior to Earnings Announcements 5 To supplement our main findings, we test the cross-sectional implications of our model s prediction that greater uncertainty about earnings news gives rise to a larger upward bias in pre-announcement price discovery and returns. Similar to models involving short-sale constraints, our prediction is based on the idea that high uncertainty stocks are subject to more extreme opinions and that prices are more likely to reflect extreme positive opinions than extreme negative opinions due to greater costs of selling. Consistent with this prediction, we show that uncertainty proxies have a significant positive relation with pre-announcement returns up until t-1 but the sign of this relation flips on day t, becoming significantly negative on and following the announcement. This knife-edge result provides strong evidence of an upward bias in pre-announcement prices that reverses post-announcement. This pattern supports our friction-based explanation over a selective disclosure story (e.g., managers delay bad news) because prices should not be predictably upward biased in the absence of market frictions that prevent corrective selling pressure. To illustrate the implications of our cross-sectional tests, we examine various measures of announcement-window returns used in prior studies and show that the choice over alternative windows significantly impacts the size and significance of estimated risk premia. For example, using earnings volatility as a proxy for uncertainty, we show that measuring announcementwindow returns from t 1 to t results in an insignificant spread in announcement returns across high and low uncertainty firms (17 basis points, p-value = 0.12), whereas the estimated uncertainty premium jumps more than four-fold to 71 basis points and becomes highly statistically significant when returns are instead measured from t to t+1. This striking contrast is a reflection of our knife-edge results, which show that uncertainty proxies are positively related to pre-announcement returns (t-1) but negatively related to post-announcement returns (t+1). This evidence indicates that firm-level proxies correlated with uncertainty are likely to induce predictable variation in return patterns around earnings announcements and, as a result, cross-study variation in how researchers measure announcement-window returns is potentially more impactful than previously believed.

7 Asymmetric Trading Costs Prior to Earnings Announcements 6 The analyses in this paper offer a joint test of financial intermediaries exposure to earnings announcement risks and the implications of this exposure for how they provide liquidity. We focus on the sector as a whole, rather than a specific subsector, because liquidity is shaped by interactions between traders and intermediaries at several levels, including up-stairs markets, block-crossing, and traditional exchange trading (Kwan, Masulis, and McInish (2015)). To directly link our findings to the financial intermediary sector, our final tests explore the implications of intertemporal changes in the aggregate positions of financial intermediaries. These tests are motivated by evidence in Adrian and Shin (2010) and Adrian, Etula, and Muir (2014) that financial intermediaries are positively exposed to the market and procyclically adjust their balance sheet positions to reach a target level of leverage. As a result, we use changes in intermediaries balance sheets to capture their preference to expand versus contract their net positions and, thus, their willingness to provide liquidity to buyers versus sellers. Consistent with this intuition, we show that our main findings are more pronounced when intermediaries are scaling down their balance sheets, suggesting that our findings stem from the risk- and inventory-management practices of financial intermediaries. Taken together, our findings demonstrate how previously unlinked empirical evidence such as asymmetric reactions to good vs. bad news, predictable pre-announcement returns, and announcement risks are linked due to asymmetries in liquidity provision. Our findings indicate that anticipated information events elicit asymmetric costs of trading on positive versus negative news, which highlights a new channel through which announcement risks can impact the directional bias and information content of market prices and, as a result, may help to abnormal returns around other predictable events such as dividend (Kalay and Loewenstein (1985)) and macroeconomic announcements (Lucca and Moench (2014)). The rest of the paper is organized as follows. Section 2 provides a simple model of liquidity provision that yields several empirical predictions. Section 3 discusses our sample and the results of our main empirical tests. In Section 4, we extend our analysis by examining cross-sectional and time-series implications of main hypotheses. Section 5 concludes.

8 Asymmetric Trading Costs Prior to Earnings Announcements 7 2. Model In this section, we provide a model of intermediated trading before an information event with known timing. Our model conveys the intuition for the main result of our paper: frictions in the intermediary sector cause asymmetric trading costs prior to information events, which in turn cause a positive bias in pre-announcement price discovery and returns. The key frictions intermediaries face in the model are: 1) an exogenous preference for holding positive positions, and 2) an aversion to inventory risk. The former is consistent with the evidence in Brunnermeier and Pedersen (2009) and Adrian and Shin (2010) that brokerdealers assets are strongly pro-cyclical, as well as the evidence in Comerton-Forde et al. (2010) that market makers hold positive inventories 94% of the time, perhaps because it is costly to locate and/or borrow shares when providing liquidity to buyers. The latter is supported by the link between short-term reversals and liquidity provision in Chordia, Roll, and Subrahmanyam (2002) and Nagel (2012), perhaps because intermediaries employ trader-specific risk budgets for agency reasons. In our model, the intermediary chooses initial inventory and prices of liquidity that keep their inventory near an optimal target level determined by the tradeoff between the risk associated with non-zero inventory positions and an exogenous benefit from holding positive positions. Because inventory risks rise during volatility events such as earnings announcements, while the preference for positive positions remains constant, target inventory decreases prior to the announcement. In order to reduce their inventory towards the lower target, intermediaries provide liquidity asymmetrically, resulting in positive bias in pre-announcement price discovery. At the same time, consistent with the evidence in Patton and Verardo (2012) and Barber et al. (2013), our model includes a risk premium corresponding to the announcement, which elicits an abnormally large return on the announcement day. Combining these offsetting effects results in positive abnormal pre-announcement returns that only partially reverse in the announcement period.

9 Asymmetric Trading Costs Prior to Earnings Announcements Assumptions We study an asset with payoff ṽ = ṽ 1 + ṽ 0 at t = 0, where ṽ 1 = { 1, 1} corresponds to a normal time period information release and ṽ 0 = { σ, σ}, σ > 1, corresponds to a high volatility information release, such as an earnings announcement. We model two trading periods in order to illustrate that intermediaries behaving optimally will carry an undesirably high inventory from normal periods into the pre-announcement period. The positive innovations ṽ 1 = 1 and ṽ 0 = σ have probabilities z 1 and z 0, respectively. However, these innovations are exposed to priced risk, meaning agents value them using riskneutral probabilities y 1 and y 0 instead of z 1 and z 0. 2 We assume the asset has a positive risk premium, so investors price assets using risk-neutral probabilities that underestimate the probability of the good state: y 1 < z 1 and y 0 < z 0. For analytic convenience, we assume the risk-neutral probabilities are y 1 = y 0 = 1 2 and the risk-free rate is 0. There are three types of agents in the model: an intermediary M, informed traders I t, and uninformed traders U t. To avoid the complexity associated with dynamic trading strategies, we assume the traders at t = 1 are different from those at t = 2, and that all traders hold their positions until t = 0. The timeline in the model is as follows: Prior to t = 2 M chooses initial position Q 2 and ask and bid prices a 2, b 2. t = 2 I 2 and U 2 purchase quantities of shares x I, 2 and x U, 2, respectively. Prior to t = 1 ṽ 1 is revealed, M chooses ask and bid prices a 1, b 1. t = 1 I 1 and U 1 purchase quantities of shares x I, 1 and x U, 1, respectively. t = 0 ṽ 0 is revealed, all positions liquidated for ṽ 1 + ṽ 0. As in Glosten and Milgrom (1985), all trades clear through the intermediary exclusively. Therefore, each trader pays the ask price for any shares they buy, and receives the bid price for any shares they sell, regardless of the other trader s demand for shares. The t = 2 informed trader, I 2, receives a private signal about the realization of ṽ 1 but not ṽ 0. Their signal takes one of two values, s 2 = {g, b}, where P (ṽ 1 = 1 s 2 = g) = 2 We write E y and E z for expectations under the risk-neutral measure and physical measure, respectively.

10 Asymmetric Trading Costs Prior to Earnings Announcements 9 P (ṽ 1 = 1 s 2 = b) = p > 1. Informed traders have mean-variance preferences, where 2 both moments are under the risk-neutral measure, 3 and therefore I 2 s demand satisfies: x I, 2 ( s 2 ; a 2, b 2 ) = arg max E y (x (ṽ 0 p(x)) s 2 ) γ t Var y (x (ṽ 0 p(x)) s 2 ) (1) x (2p 1) a 2 2γ T if s (4p(1 p)+σ = 2 ) 2 = g (2) (2p 1) b 2 2γ T if s (4p(1 p)+σ 2 ) 2 = b. where γ T is the traders risk aversion, and the price function p(x) equals the ask a 2 for positive x (i.e., buying) and the bid b 2 for negative x (i.e., selling). The t = 1 informed trader I 1 gets a signal about the realization of ṽ 0. The signal takes one of two values s 1 = {g, b}, and has the same precision as s 2, meaning P (ṽ 0 = σ s 1 = g) = P (ṽ 0 = σ s 1 = b) = p > 1 2. The value of ṽ 1 becomes publicly known at t = 1, meaning the risk-neutral expected asset value conditional on s 1 is v 1 + (2p 1)σ or v 1 (2p 1)σ. Therefore, I 1 s demand satisfies: x I, 1 ( s 1 ; a 1, b 1 ) = v 1 +(2p 1)σ a 1 8γ T p(1 p)σ 2 if s 1 = g v 1 (2p 1)σ b 1 8γ T p(1 p)σ 2 if s 1 = b. (3) The uninformed traders in our model are not the usual price-insensitive noise traders. The crux of our story is that the intermediary uses asymmetric trading costs to attract buyers for their undesired inventory, which necessitates price-sensitive traders. Furthermore, in the presence of a price-insensitive uninformed trader, the intermediary would set enormous bidask spreads to profit from uninformed order flow and avoid the informed trader. We therefore model uninformed traders as mean-variance agents who behave as if they are informed. Their signals at times t = 2 and t = 1 are ũ 2 and ũ 1, respectively. The uninformed traders believe these signals inform them about ṽ 1 and ṽ 0, even though in reality they are 3 We use the risk-neutral measure to adjust for priced systematic risk and mean-variance preferences to adjust for the additional idiosyncratic risk traders are exposed to by taking concentrated positions.

11 Asymmetric Trading Costs Prior to Earnings Announcements 10 uninformative. Therefore uninformed trader demand satisfies: (2p 1) a 2 2γ T if ũ (4p(1 p)+σ x U, 2 (ũ 2 ; a 2, b 2 ) = 2 ) 2 = g (2p 1) b 2 2γ T if ũ (4p(1 p)+σ 2 ) 2 = b. v 1 +(2p 1)σ a 1 8γ T if ũ p(1 p)σ x U, 1 (ũ 1 ; a 1, b 1 ) = 2 1 = g v 1 (2p 1)σ b 1 8γ T if ũ p(1 p)σ 2 1 = b. (4) (5) The intermediary has mean-variance preferences, where both moments are under the risk-neutral measure, and chooses Q 2, a 2, b 2, a 1, and b 1 to maximize their expected utility. They choose Q 2, a 2, and b 2 prior to trade at t = 2 with foresight of how these choices will affect their inventory and liquidity provision in period t = 1. Prior to t = 1, they choose a 1, and b 1 that are optimal given the net inventory they carry forward after the initial round of trading Q 1 = Q 2 x I, 2 x U, 2, as well as the realization of ṽ 1. Expected profits for the intermediary come from trading at advantages prices: selling at a > ˆv and buying at b < ˆv, where ˆv is the conditional risk-neutral expected value of ṽ. They also consider two costs associated with inventory levels Q 1 and Q 0 = Q 1 x I, 1 x U, 1. The first is inventory risk, which affects Q 0 disproportionately because ṽ 0 is more volatile than ṽ 1. The second is a linear benefit (cost) ρ to holding positive (negative) inventory positions. The linear functional form, as opposed to a linear cost for negative inventories without a benefit for positive inventories, is analytically convenient but also proxies for the fact that positive inventories today are beneficial because they reduce the probability of negative inventories in the future. All together, the intermediary s objective function is: Expected trading profit { ( }}{ t= 1 ) U(Q 2, a 2, b 2, a 1, b 1 ) = E y x I,t (p(x I,t ; a t, b t ) ˆv t ) + x U,t (p(x U,t ; a t, b t ) ˆv t ) t= 2 ( γ ( M E y Q 1) 2 + σ 2 E ( )) y Q ρ (E y (Q 1 ) + E y (Q 0 )). }{{}}{{} Inventory risk Cost of negative inventory (6)

12 Asymmetric Trading Costs Prior to Earnings Announcements Results and empirical predictions This section presents our equilibrium results and corresponding empirical predictions. We provide a detailed solution of the model and prove our equilibrium results in Appendix A. We assume throughout that the intermediary has a benefit ρ > 0 of positive inventory positions and that the announcement news creates more volatility than normal news σ > 1. Result 1 (Asymmetric liquidity provision). In the pre-announcement period, the average ask price is closer to the mean asset value (i.e., v 1 ) than the average bid price: E z (a 1 v 1 ) < E z (b 1 v 1 ). (7) Moreover, negative price changes overshoot the fundamental value information revealed by the trade more than positive ones: E z (a 1 ) E z (ṽ buy) < E z (ṽ sell) E z (b 1 ). (8) Empirical Prediction 1. The compensation intermediaries demand for providing liquidity, as measured by return reversals, is higher for seller-initiated than buyer-initiated trades. Result 1 indicates that because, on average, the intermediary s inventory is above its optimal announcement level at t = 1, the intermediary asymmetrically provides liquidity by lowering both a 1 and b 1 to encourage demands to buy and discourage demands to sell, respectively. The second component of Result 1 states that positive price changes overshoot fundamental value to a lesser extent than negative ones, which reflects the fact that the intermediary embeds a smaller liquidity premium into the ask than the bid. Once the information is revealed at t = 0, prices converge (on average) to E z (ṽ buy) or E z (ṽ sell), so the differences a 1 E z (ṽ buy) and E z (ṽ sell) b 1 indicate the extent to which prices overshoot at t = 1 and reverse at t = 0. Empirical Prediction 1 states that these equilibrium price patterns will result in asymmetric pre-announcement return reversals. Thus, our main

13 Asymmetric Trading Costs Prior to Earnings Announcements 12 tests focus on asymmetries in daily return reversals, which are well suited for gauging changes in trading costs driven by overnight inventory risks associated with news releases; however we also consider alternative measures in subsequent tests. Result 2 (Asymmetric trading intensity). In the pre-announcement period, traders submit larger buy orders in equilibrium than sell orders: x I, 1 ( s = g) > x I, 1 ( s = b) (9) x U, 1 (ũ = g) > x U, 1 (ũ = b). (10) Empirical Prediction 2. Pre-announcement price discovery and trading volume are greater for positive news announcements than negative news announcements. Having established that trading costs are asymmetric prior the announcement, the remainder of our results focus on the implications of this asymmetry for price discovery and returns. Result 2 pertains to pre-announcement price discovery and states that, due to the asymmetric pricing of liquidity described in Result 1, traders optimally choose to place larger orders when receiving good news relative to bad news at t = 1. The first empirical prediction from Result 2 is that pre-announcement prices incorporate more earnings news ahead of positive news announcements than negative news announcements. The second prediction is that positive news announcements have greater pre-announcement trading volume than negative news announcements because the informed trader responds to higher costs of selling by trading more aggressively on positive signals than negative signals. To study the implications of asymmetric trading costs for returns before and after announcements, we first compute the average prices and returns in a frictionless benchmark wherein there is no information asymmetry and the asset trades at its risk-neutral expected

14 Asymmetric Trading Costs Prior to Earnings Announcements 13 value in each period. In this case, expected returns (price changes) are: E z ( p 1 p 2 ) = E z (ṽ 1 ) = 2 ( z 1 1 2), (11) E z ( p 0 p 1 ) = E z (ṽ 0 ) = 2 ( z 0 1 2) σ. (12) Note that expected returns in each period are positive and driven by the risk associated with the news in each period, 1 and σ, along with the difference between physical probabilities z t and risk-neutral probabilities y t = 1. Prices do not predictably decline as risk increases 2 because, if they did, rational investors would all sell at t = 2 before the decline occurred and repurchase their shares at t = 1 for a profit. We next compute expected returns in our model, which are a combination of the risk premia arising in the frictionless benchmark and an upward bias in pre-announcement prices due to asymmetric trading costs. Because the asset can trade at both the bid and the ask price simultaneously in each period, we compute returns using the expected volume-weighted average price in each period, producing the return pattern summarized in Result 3. Result 3 (Abnormal returns around announcements). Expected returns computed using expected volume-weighted average prices under the physical measure satisfy: E z ( p 1 p 2 ) = 2 ( ( ) ) z ρ 2p(1 p) + γ M 2 }{{} 8 (σ2 γ 1) T 4p(1 p)(1 + σ 2 ) + γ M γ T Normal risk prem. }{{} E z ( p 0 p 1 ) = 2 ( z 0 2) 1 σ ρ }{{} 8 (σ2 1) Announcement risk prem. Upward bias ( 2p(1 p) + γ M γ T 4p(1 p)(1 + σ 2 ) + γ M } {{ } Bias reverses γ T ) (13) (14) Empirical Prediction 3. Returns are abnormally positive prior to announcements and less positive or even negative following the announcement. Abnormal pre-announcement returns that reverse reflect an upward bias resulting from asymmetric trading costs, while abnormal pre-announcement returns that persist reflect an announcement risk premium.

15 Asymmetric Trading Costs Prior to Earnings Announcements 14 Equation (13) quantifies the two sources of pre-announcement abnormal returns in the model: a risk premium 2(z 1 1 ), which occurs in the frictionless benchmark as well, and 2 an upward bias caused by the asymmetric trading costs. Note that the upward bias is proportional to the benefit of positive inventory ρ multiplied by the increase in variance at the announcement (σ 2 1), both of which are positive by assumption. Result 3 depends critically on these two assumptions because they assure the intermediary s optimal inventory is positive but larger at t = 2 than t = 1. It may be initially puzzling why lower average a 1 and b 1 result in higher average prices, however, this stems from the equilibrium response of traders described in Result 2. Because traders with positive signals use larger trades than those with negative signals, many more trades happen at a 1 than b 1, both overall and in states where informed and uninformed traders have offsetting demands. The quantity effect outweighs the price effect because the intermediary is a net seller on average and sets bid and ask prices to assure that the average price they receive is above the frictionless benchmark. Similarly, Equation (14) quantifies the two sources of excess returns associated with the announcement itself: a risk premium 2(z 0 1 )σ, which is likely larger than the normal time 2 period premium 2(z 1 1 ), and a reversal of the upward bias in pre-announcement prices. 2 Comparing Equations (13) and (14) yields two important insights. First, even if there is an abnormally large risk premium at the announcement, returns measured in a narrow window around the announcement will be confounded by the reversal of the pre-announcement bias and therefore will understate the risk premium. Second, we can estimate the relative contribution of risk premia and the pre-announcement bias by examining the extent to which abnormal pre-announcement returns reverse. Specifically, long-window cumulative returns surrounding the announcement represent the risk premium, while the pre-announcement return that reverses post-announcement reflects the upward bias. Result 4 (Comparative statics). Average asymmetry in liquidity provision, pre-announcement return, and post-announcement reversal are all increasing in the intermediary s inventory Q 1, risk aversion γ M, cost of negative positions ρ, and the announcement risk σ.

16 Asymmetric Trading Costs Prior to Earnings Announcements 15 Empirical Prediction 4. Average pre-announcement asymmetry in liquidity provision, preannouncement returns, and post-announcement reversals are all greater when intermediaries have larger positive inventory positions, less risk-bearing capacity, higher costs of locating and borrowing shares, and/or the earnings announcement risk is higher. Our final result shows comparative statics for Result 3. The first two comparative statics predict that when the intermediary has a larger inventory or greater risk aversion they will be more aggressive in reducing inventory by asymmetrically providing liquidity, thereby increasing the temporary bias in pre-announcement prices p 1. Similarly, larger benefits from positive inventories result in larger pre-announcement inventory Q 1 and therefore greater asymmetric liquidity provision and pre-announcement biases in prices. Finally, for a given endowment and risk aversion, greater announcement risks raise the intermediary s desire to reduce inventory and, consequently, increases the average bias in pre-announcement prices. In summary, our model provides a friction-based explanation for asymmetries in preannouncement trading costs and yields several additional implications of this asymmetry for pre-announcement trading activity, price dynamics, and the information content of market prices, all of which we validate in our empirical tests below. 3. Empirical tests In this section, we first outline the construction of the sample used throughout our main empirical tests. We next document changes in liquidity provision, price discovery, and predictable variation in returns around earnings announcements Sample Selection We construct the main dataset used in our analyses from three sources. We obtain price and return data from CRSP, firm fundamentals from Compustat, and analysts forecasts of earnings from IBES. We eliminate firms that have been in the CRSP database for less than six months to ensure there is sufficient data to calculate historical return volatility and

17 Asymmetric Trading Costs Prior to Earnings Announcements 16 momentum. We also require that firms have coverage in the IBES database to calculate analyst-based earnings surprises, and eliminate firms with prices below $1 to mitigate the influence of bid-ask bounce on our calculation of return reversals as noted in Roll (1984). Our final sample consists of 215,754 quarterly earnings announcements over the 20 calendar years spanning from 1993 to Our main analyses examine changes in liquidity and equity prices surrounding the date of firms quarterly earnings announcements. Because we expect liquidity provision to significantly change on the date of the announcement, it is important that we correctly identify the announcement date to cleanly test our hypotheses relative to the arrival of news. To do so, we follow the procedure from DellaVigna and Pollet (2009) that compares Compustat and IBES announcement dates and assigns the earlier date as being correct. We also use the IBES time stamp to determine whether the announcement occurred after the market close and, when it does, we adjust the announcement date one trading day forward. DellaVigna and Pollet (2009) shows that their approach yields announcement dates that are more than 95% accurate by comparing their calculated date with news-wire time stamps and also more accurate than the dates in Compustat and IBES when either is used in isolation. To provide support for the accuracy of the announcement dates in our sample, Fig. 1 plots average daily abnormal idiosyncratic volatility in event time in the 21 trading days surrounding firms announcement dates, t, across three different sources of earnings announcement dates. Specifically, the top panel in Fig. 1 is plotted against the earnings announcement dates used in this study whereas the middle and bottom panels are plotted against Compustat and IBES announcement dates, respectively. Following Barber et al. (2013), we compute abnormal idiosyncratic volatility on day d by taking the square root of the ratio of the squared residual (from a firm-specific market-model regression with three lags) on day d and the average squared residual from t-51 to t-11, and subtracting one. Consistent with the findings in DellaVigna and Pollet (2009), the top panel of Fig. 1 shows that idiosyncratic volatility is concentrated on the announcement dates used in this study, which provides strong evi-

18 Asymmetric Trading Costs Prior to Earnings Announcements 17 dence that the announcement date in our sample correctly identifies the date of earnings news releases. By contrast, the middle and bottom panels of Fig. 1 show that idiosyncratic volatility increases on announcement dates proposed by Compustat and IBES but increases further and peaks on the subsequent day, indicating that the announcement dates in these databases are often one day too early. A likely reason for this is that many announcements occur after markets close, meaning an announcement made today is commonly reflected in tomorrow s close-to-close return. The findings in Fig. 1 help explain why we find no excess returns on announcement dates, whereas prior research finds significant excess returns on Compustat announcement dates (e.g., Ball and Kothari (1991) and Frazzini and Lamont (2007)). By using Compustat dates that are frequently one day too early, these studies record the return one day before the actual announcement, which is abnormally positive, as the announcement date return. As we discuss below, the proper identification of earnings announcement dates helps us to highlight the temporal separation between idiosyncratic announcement risks and pre-announcement abnormal returns and, in doing so, underscores a key asset pricing puzzle that our findings help to resolve Asymmetric Trading Costs Our first analyses examine changes in trading costs prior to earnings announcements. Based on Empirical Prediction 1, we expect the cost of liquidity to be asymmetric because financial intermediaries tend to hold net positive positions and thus providing liquidity to sellers would further increase their exposure to heightened inventory risks associated with the announcement, whereas providing liquidity to buyers would have the opposite effect. We are unable to directly observe the cost of liquidity and thus must instead make inferences based on observable market outcomes. Because intermediaries demand compensation for providing liquidity in the form of transitory price concessions, we use short-term return reversals as a proxy for the expected returns intermediaries demand for providing liquidity following Nagel (2012), although we also consider alternative proxies in subsequent tests.

19 Asymmetric Trading Costs Prior to Earnings Announcements 18 Table 1 contains average daily returns for firms within the lowest quintile of returns over the prior day ( losers ) and firms within the highest quintile of returns over the prior day ( winners ), in event time for the 21 trading days surrounding firms announcement dates. Table 1 shows that the average daily returns of firms in the lowest quintile are generally positive and significant, consistent with financial intermediaries receiving compensation for providing liquidity in periods of net selling by setting prices below fundamental value. Similarly, the average daily return for firms in the highest quintile are generally negative and significant. Consistent with the findings in Avramov, Chordia, and Goyal (2006), negative returns exhibit greater reversals than positive returns throughout the event window, suggesting that intermediaries are more averse to providing liquidity in response to selling pressure and thus demand asymmetric levels of compensation. The final column of Table 1 presents average levels of asymmetric liquidity provision, ALP, defined as the difference between returns earned from a long position in prior day losers and returns earned from a short position in prior day winners. ALP captures differences in reversal magnitudes across losers and winners and, thus, higher values of ALP indicate intermediaries demand greater compensation for providing liquidity to sellers relative to buyers. The average level of ALP increases beginning several days prior to the announcement, consistent with intermediaries often taking multiple days to unwind net positions (Madhavan and Smidt (1993)) and, thus, being averse to taking on additional inventory prior to high volatility events because doing so increases their risk exposure. Table 1 also shows that ALP steadily increases until t-1, suggesting that intermediaries are most averse to providing liquidity to sellers when there is the least time to unwind the position prior to the announcement. Finally, ALP changes sign on the date of the announcement and gradually reverses to normal levels, which is consistent with intermediaries being less averse to taking on inventories once earnings news is announced and inventory risks decline. 4 4 The change in the sign of the reversal strategy return around the announcement is consistent with the presence of post-earnings announcement drift as well as evidence in Tetlock (2010) that returns on non-news days tend to reverse whereas returns on news days tend to continue.

20 Asymmetric Trading Costs Prior to Earnings Announcements 19 Fig. 2 expands the results in Table 1 by plotting return reversals in the 60 trading days surrounding earnings announcements. The top panel separately plots the returns to the long and short legs of a three-day reversal strategy, which correspond to a short position in firms within the highest quintile of returns over the prior three-day window and a long position in firms within the lowest quintile. The reported strategy return is centered on the date shown on the X-axis such that the quantity on day d reflects the three-day cumulative strategy return from d-1 to d+1 from a long position in the lowest quintile of returns from d-4 to d-2 and a short position in the highest quintile of returns from d-4 to d-2. The top panel of Fig. 2 shows pre-announcement increases in return reversals are asymmetric: the increase is almost entirely driven by larger reversals following net selling pressure (i.e., the loser portfolio). The rapid ascension of reversals associated with the loser portfolio contrasts sharply with the flatter trend in reversals associated with the winner portfolio. These results support Empirical Prediction 1, suggesting that intermediaries steadily raise the compensation they demand when providing liquidity to sellers but do not change, or even decrease, the compensation they demand when providing liquidity to buyers. Using information from the top panel in Fig. 2, the bottom panel plots ALP in event time and documents a rapid pre-announcement increase in asymmetric liquidity provision. ALP increases more than three-fold immediately prior to the announcement, which is consistent with the magnitude of the increase in the daily ALP measure shown in Table 1. Fig. 2 shows that ALP dramatically decreases once the return-measurement period includes the announcement, which first occurs on day t-1. The pre-announcement increase in ALP suggests that traders face increasing costs of trading on negative news, relative to positive news, prior to announcements. However, a potential alternative explanation for the evidence in Fig. 2 is that changes in ALP stem from a positive bias in pre-announcement disclosure by managers (Kothari, Shu, and Wysocki (2009)), which could make positive pre-announcement price changes more likely than negative ones to be information-based and, therefore, less likely to reverse. We discuss this alternative explanation in Section 4.1.

21 Asymmetric Trading Costs Prior to Earnings Announcements 20 Table 2 contains descriptive statistics for each year of the sample. The number of firm-quarters gradually increases over time from a low of 6,774 in 1993 to a high of 12,472 in Following So and Wang (2014), we measure average pre-announcement asymmetry in liquidity provision from t-4 to t-2 and compare it with the average value in non-announcement periods from t-11 to t-31. The table also contains average values of ALP, the difference between ALP(t-4,t-2) and ALP(t-31,t-11), which are positive in every year except 2012 and significant at the 5% level in eight years. Additionally, the pooled mean of ALP is (t-statistic = 5.35) indicating the asymmetry is greater prior to earnings announcements than in non-announcement periods. These findings suggest the evidence in Lee, Mucklow, and Ready (1993) and So and Wang (2014) of greater costs of liquidity around earnings announcements are primarily driven by greater costs of selling. In Table 3, we provide further evidence of asymmetries in pre-announcement transaction costs by using intra-day data to examine the link between abnormal buy/sell behavior and within-firm changes in price impact and quoted depth. We calculate intraday order imbalances for each trading day as the difference between buyer- and seller-initiated volume, scaled by total volume, using the Lee and Ready (1991) algorithm applied to the Trade and Quote (TAQ) database. To mitigate the influence of firm-specific trends in buying-vs-selling behavior, we report standardized order imbalances by subtracting the average daily order imbalance from t-51 to t-11 and scaling by the standard deviation over that window. Table 3 contains results from regressing abnormal transaction cost measures on abnormal order imbalances (AOI), which are both averaged over t-4 to t-2. The three transaction cost measures we employ are (1) Amihud Illiquidity Ratio, ALR, defined as the ratio of absolute return to dollar volume, (2) effective spreads, calculated from intraday TAQ data as the average absolute distance between a transaction s price and the bid-ask midpoint quote, scaled by the midpoint quote, and (3) quoted depth, also calculated from TAQ as the average offer and bid size of intraday quotes. All three transaction cost proxies are also standardized by their mean and standard deviation from t-51 to t-11, which allows us to measure how order

22 Asymmetric Trading Costs Prior to Earnings Announcements 21 imbalances result in abnormal asymmetries in transaction costs for selling versus buying in the days leading up to firms announcements. Columns (1) through (4) of Table 3 show that pre-announcement net selling behavior is associated with an increase in effective spreads and ALR, which is consistent with traders incurring abnormally high price impact when selling compared to buying leading up to the announcements. Similarly, columns (5) and (6) show that pre-announcement quoted depth decreases in periods of net selling behavior, which is consistent with financial intermediaries becoming less willing to provide liquidity to sellers prior to the release of earnings news. Taken together, the evidence in Tables 1 through 3 provides support for Empirical Prediction 1 by demonstrating that the cost of selling prior to earnings announcements is abnormally high relative to the cost of buying. An implication of these findings is that transaction costs tilt traders incentives toward expressing positive relative to negative news into preannouncement prices. We empirically explore this implication in the following section Implications of Asymmetric Trading Costs In Tables 4 and 5, we test two implications of Empirical Prediction 2. The first implication of this prediction is that pre-announcement returns should lead earnings news to a greater degree when the news is positive because traders are more aggressive in impounding positive signals into prices. To establish asymmetries in price discovery, Panel A of Table 4 contains market-adjusted returns around earnings announcements in which firms report good news, defined as earnings at or above the consensus earnings forecast, and those where firms report bad news, defined as earnings below the consensus. For good news announcements, pre-announcement returns are positive for all days leading up to the announcement, increase in magnitude when approaching the announcement, and remain statistically significant throughout. By contrast, Table 4 also shows that pre-announcement returns start out as slightly negative several days prior to bad news announcements but attenuate over time, and become statistically insignificant in the days immediately prior to announcements. The market reac-

23 Asymmetric Trading Costs Prior to Earnings Announcements 22 tion to negative news is also nearly twice as large as the reaction to positive news on t and t+1. The larger reaction to negative news mitigates concerns that the absence of negative pre-announcement returns stems from negative news already being reflected in prices. To further illustrate differences in the return patterns of good and bad news announcements, the top panel of Fig. 3 plots the percentage of cumulative returns in the 21 days surrounding announcements. The figure highlights a stark contrast between the expression of good and bad earnings news in prices prior to the announcement. Pre-announcement prices continuously assimilate positive news but stop assimilating negative news in the days immediately prior to the announcement and instead incorporate the news on the announcement date. Similarly, the bottom panel of Fig. 3 plots the average cumulative returns in the 21 days surrounding announcements and shows that the majority of negative returns in the month of a bad news earnings announcement are earned once the news is released. Panel B of Table 4 provides further corroborating evidence by examining the direction of order flow around earnings announcements. The All column of Panel B presents pooled averages of abnormal order imbalances for all earnings announcements. The average order imbalance tends to be positive leading up to the announcement and peaks on day t-1, indicating that investors tend to be net buyers prior to earnings announcements. We also see that the average order imbalance flips sign and becomes negative following the announcement, indicating that investors tend to be net sellers after earnings announcements. The remainder of Table 4 partitions the sample based on the sign of the earnings news and shows that there is a large spike in directional trading prior to good news announcements, whereas no such spike exists for negative news announcements. Conversely, negative news tends to be followed by a longer trend of net selling after the announcement, whereas no such trend exists for positive news announcements. These patterns are consistent with the idea that investors are deterred from expressing negative news in prices prior to earnings announcements and instead trade on negative news after the announcement. 5 5 As modeled in Johnson and So (2012), when costs of selling shares in equity markets are high, traders may choose to capitalize on negative signals in option markets. We expect that traders buy options to

24 Asymmetric Trading Costs Prior to Earnings Announcements 23 A second implication of Empirical Prediction 2 is that informed traders respond to asymmetric trading costs by placing larger orders when they receive positive signals compared to negative ones and, as a result, pre-announcement trading volume should foreshadow positive earnings surprises. To test this prediction, Table 5 regresses pre-announcement returns and earnings news proxies on pre-announcement abnormal turnover, TO, defined as average daily volume scaled by total shares outstanding from t-4 to t-2 minus the corresponding average from t-51 to t-11. We use two proxies for earnings announcement news: SURP, defined as firms actual EPS minus the consensus analyst forecast immediately prior to the announcement, and scaled by beginning-of-quarter price, and SUE, standardized unexplained earnings, defined as the realized EPS minus EPS from four quarters prior, divided by the standard deviation of this difference over the prior eight quarters. The results in Table 5 confirm that abnormal pre-announcement turnover has a significant positive relation with contemporaneous returns and positively predicts both measures of earnings news, which is consistent with Empirical Prediction 2 that informed agents respond to asymmetric liquidity provision by trading more aggressively when impounding positive news into prices. Thus, our findings provide new evidence to the literature that trading volume increases asymmetrically ahead of announcements with good news compared to bad news, which reflects investors response to asymmetries in transaction costs Returns around Earnings Announcements In this section, we provide a test of Empirical Prediction 3, which predicts that increases in asymmetric liquidity provision prior to earnings announcements give rise to an upward bias in pre-announcement prices because traders face greater costs of trading on negative news than positive news. capitalize on their expectations of larger reactions to negative news, implying that higher pre-announcement option-implied volatilities should foreshadow negative news at earnings announcements. In untabulated tests, we calculate pre-announcement implied volatility, IV, calculated using calls in the Ivy OptionMetrics database and find that IV negatively predicts both earnings surprises and announcement returns, consistent with traders purchasing options in anticipation of negative news but being unable to incorporate negative information into pre-announcement equity prices.

25 Asymmetric Trading Costs Prior to Earnings Announcements 24 To test this Empirical Prediction 3, Table 6 presents time-series average returns in eventtime in the month (21 trading days) centered on firms quarterly earnings announcement dates. Our primary variable, RET, denotes daily market-adjusted returns. As a second measure of excess returns, AP denotes the announcement premium, defined as the firm s daily return minus the contemporaneous average return of all non-announcing firms in our sample. A firm is categorized as a non-announcer on day d if the firm did not announce earnings within the 21 trading days centered on d. Additionally, to mitigate the influence of static risk characteristics on returns, we also use within-firm variation in returns around announcements relative to non-announcement periods following Cohen et al. (2007). Specifically, AR is a firm s raw return on the specified date minus the average of its raw return from t-51 to t-11. Table 6 presents one of the main results of the paper. Specifically, the table shows that firms tend to earn significantly positive returns beginning on t-6, one week before their earnings announcements. Pre-announcement returns grow in magnitude and significance when approaching the announcement, peaking on day t-1. 6 In contrast, returns on the announcement date, t, are insignificant and considerably smaller in magnitude than returns earned on t-1. We also show that returns become significantly negative immediately following the announcement starting on t+1, which is consistent with our prediction that the preannouncement upward bias in prices reverses once earnings are announced and the relative costs of acting on negative news reverts to normal levels. The evidence in Table 6 is generally consistent with evidence in Barber et al. (2013) that the bulk of the monthly earnings announcement premium is earned prior to announcements. However, our findings also contrast with the finding in Barber et al. (2013) that the largest abnormal return occurs on the announcement date, t. By precisely measuring the earnings announcement date, to our knowledge our study is among the first to show that returns are only reliably positive prior to the arrival of earnings news. 6 Similar to the findings in Chari, Jagannathan, and Ofer (1988), Table 6 shows that market-adjusted returns are significantly positive starting on day t+7, though smaller than those corresponding to the preannouncement period. It is unclear why this pattern exists in returns net of the equal-weighted market.

26 Asymmetric Trading Costs Prior to Earnings Announcements 25 The bottom rows of Table 6 help quantify the relative magnitudes of pre-announcement and announcement returns by separately reporting average three-day pre-announcement returns from t-4 to t-2 and announcement-window returns from t-1 to t+1. Across all three return metrics, the mean and t-statistic of returns from t-4 to t-2 are just as large, if not larger, than those corresponding to t-1 to t+1. Table 6 also demonstrates that cumulative returns from t-1 to t+1 are only significantly positive because of large positive returns the day immediately prior to the announcement on t-1, rather than the returns being centered on the announcement day t. These findings are consistent with our model s prediction that the average three-day announcement-window return is likely to be downward biased because it reflects both risk-premia associated with the announcement and the reversal of the upward bias in pre-announcement prices. The evidence of significant pre-announcement returns in Table 6 is unlikely to be driven by an announcement risk premium in light of the evidence in Fig. 1 that idiosyncratic volatility is concentrated on the announcement date. A common thread among asset pricing models is that risk premia should be earned at the same time as the realization of the priced risk. However, our findings show that excess returns precede the realization of higher idiosyncratic volatility at the announcement by an entire week. More generally, the pre-announcement returns in Table 6 are unlikely to be compensation for an unspecified form of risk, for example caused by peer firms announcing their earnings, because of the post-announcement reversal. Excess returns due to risk premia do not subsequently reverse because if they did they would not provide compensation to long-term investors bearing the risk. Instead, the post-announcement reversal of pre-announcement excess returns is consistent with a friction-based, transitory bias in pre-announcement prices. To help characterize the economic significance of the pre-announcement price bias we document, Fig. 4 plots the fraction of cumulative return in the 21 trading days surrounding firms announcement date, where the cumulative return is scaled each day by the firm s total return over the 21 day period. As in Barber et al. (2013), we calculate the announcement

27 Asymmetric Trading Costs Prior to Earnings Announcements 26 premium as the cumulative difference in returns for announcers versus non-announcers. By construction, the fraction ends at one by the end of the 21 day period. However, a striking result from Figure 4 is that cumulative return peaks on t-1 at more than double the total 21 day return, indicating that the pre-announcement effect we document is economically large relative to the monthly announcement premium studied in prior research. As shown in Section 2, in the presence of an announcement risk premium but no market frictions, prices should be low pre-announcement, rise during the announcement in proportion to the realization of priced risk, and stabilize post-announcement. By contrast, our evidence shows that prices predictably increase pre-announcement, do not significantly change during the announcement, and decrease post-announcement. Our model and empirical results help to reconcile these sets of findings by highlighting the role of asymmetric trading costs in eliciting a pre-announcement upward bias in prices. Thus, an important implication of our return-based results is that they help solve the puzzle in Barber et al. (2013) that a significant portion of the monthly earnings announcement premium is earned prior to the announcements. Specifically, this paper establishes that even in the presence of a risk premium associated with an information event, researchers are likely to observe abnormal returns prior to the event due to predictable asymmetries in transaction costs. The contemporaneous realization of risk and risk premiums a cornerstone of standard asset pricing models is offset at the announcement by the reversal of upward biases in prices. 4. Additional analyses In this Section, we extend our main findings by examining both cross-sectional and timeseries implications of asymmetric costs of selling prior to earnings announcements Cross-Sectional Implications Our first tests explore our model s prediction that asymmetric liquidity provision is more pronounced among high uncertainty firms because their announcement returns are riskier. Specifically, Empirical Prediction 4 predicts that the extent to which intermediaries provide

28 Asymmetric Trading Costs Prior to Earnings Announcements 27 liquidity asymmetrically is increasing in σ, the volatility associated with news released at the announcement. To test this prediction, Table 7 contains average levels and changes in ALP across subsamples of high and low uncertainty firms. We use three firm-level proxies for uncertainty: EVOL, the firm s earnings volatility, defined as the standard deviation of quarterly earnings scaled by total assets over the prior eight quarters; VLTY, the firm s return volatility, defined as the standard deviation of daily market-adjusted returns from t- 51 to t-11; and AGE, the log of the number of months since the firm first appeared in CRSP. We expect that higher values of EVOL and VLTY and lower values of AGE indicate greater uncertainty about firms profitability and thus greater inventory risks and higher ALP. Consistent with changes in ALP stemming from inventory risks, Table 7 shows that the pre-announcement increase in ALP is pronounced among higher uncertainty stocks. When partitioning the sample based on EVOL and VLTY, we find that ALP is significantly positive for high uncertainty firms and insignificant for low uncertainty firms. Across all three uncertainty proxies, we find that ALP is greater among firms in the highest quintile of uncertainty than the lowest quintile. Although the return-based findings in Table 4 provide support for our model s predictions, they are also generally consistent with the hypothesis in Kothari, Shu, and Wysocki (2009) that managers pre-release good news and delay bad news. To distinguish these two non-mutually-exclusive hypotheses, we explore the relation between uncertainty proxies and the pattern in returns around earnings announcements. Our model predicts that the preannouncement upward bias in prices as well as the subsequent reversal will be pronounced among higher uncertainty stocks, which follows from greater asymmetries in trading costs. Moreover, for a given asymmetry in trading costs, we also expect that higher uncertainty firms are subject to more extreme opinions, exacerbating the upward bias in return because prices are more likely to reflect extreme positive opinions than extreme negative opinions. Panels A and B of Table 8 contain daily returns relative to the announcement date partitioned across quintile portfolios sorted by the three firm-level proxies for uncertainty

29 Asymmetric Trading Costs Prior to Earnings Announcements 28 used in Table 7. Panel A shows that prices generally increase from t-4 to t-2 but the increase is pronounced among high uncertainty stocks. Moreover, the magnitude of the difference in returns across high and low uncertainty stocks increases from t-4 to t-2, indicating that the uncertainty-return relation rises when approaching the announcement. Panel B of Table 8 shows that the uncertainty-return relation continues to rise until day t-1, where uncertainty proxies have the most robust positive relation with pre-announcement returns. However, Panel B also shows that the sign of the uncertainty-return relation flips on day t, becoming significantly negative on and following the announcement. These findings indicate that uncertainty is associated with a predictable upward bias in prices that begins to reverse immediately after the announcement. 7 Berkman et al. (2009) provides evidence that optimists create an upward bias in prices due to short-sale constraints and that earnings announcements help correct this bias by resolving speculative disagreement about firm value. Our findings extend those in Berkman et al. (2009) by identifying asymmetric liquidity provision as an alternative sell-oriented friction, similar to short-sale constraints, that rises pre-announcement in proportion to the uncertainty underlying the announcement. However, our findings help distinguish these possible explanations. Specifically, given the Berkman et al. (2009) hypothesis in which investors face short-sale costs and intermediaries have, on average, net-zero inventories, greater speculative demand from optimists should give rise to greater reversals following buying pressure because non-fundamental price changes tend to reverse. By contrast, our empirical results in Table 1 and Figure 2 show that the opposite holds. Thus, our findings offer an alternative interpretation of the evidence in Berkman et al. (2009), namely that rising pre-announcement prices are more likely to stem from increasingly asymmetric trading costs. 7 The pattern of rising pre-announcement prices and declining post-announcement prices among high uncertainty stocks shown in Table 8 is consistent with the findings in Trueman, Wong, and Zhang (2003) that show a qualitatively identical pattern for a sample of internet firms during the peak of the Tech Bubble for which uncertainty was likely to be high. Trueman, Wong, and Zhang (2003) interprets the returns as reflecting price pressure from investors seeking to hold internet stocks through their announcements. By contrast, our findings suggest prices are upwardly biased due to asymmetric liquidity provision and that this effect is pronounced among high uncertainty stocks posing greater inventory risks.

30 Asymmetric Trading Costs Prior to Earnings Announcements 29 To visualize the results from Table 8, Fig. 5 presents a longer-window view of the uncertainty-return relation in the 21 days surrounding the announcement. The difference in returns across high and low uncertainty firms is significantly positive and increasing ahead of the announcement but suddenly reverses signs, while remaining significant, on the announcement date. These knife-edge results provide clear evidence of a predictable upward bias in pre-announcement prices that reverses post-announcement. This reversal pattern supports our friction-based explanation because prices should not be predictably upward bias in the absence of a market friction that prevents corrective selling pressure. Moreover, due to this upward bias, prices must adjust further in response to the release of negative earnings news, indicating that evidence of an asymmetric reaction to negative news announcements is at least partially driven by greater costs of selling rather than selective disclosures as hypothesized in Kothari, Shu, and Wysocki (2009). Panel C of Table 8 illustrates an important implication of our findings for future research. Specifically, we study three common definitions of announcement-window returns used in prior studies and show the choice over alternative windows significantly impacts the size and significance of the relation between uncertainty proxies and announcement returns. For example, using the earnings volatility proxy, we show that measuring returns from t 1 to t results in an insignificant spread in announcement returns across high and low uncertainty firms (17 basis points, p-value = 0.12), whereas the uncertainty premium jumps more than four-fold to 71 basis points and becomes highly statistically significant (p-value = 0.00) when announcement-window returns are measured from t to t+1. The striking contrast in these estimates reflects our knife-edge results where uncertainty proxies are positively related to pre-announcement returns (t-1) but negatively related to post-announcement returns (t+1). This evidence indicates firm-level proxies correlated with uncertainty yield predictable variation in return patterns around earnings announcements, and that cross-study variation in how researchers measure announcement-window returns is potentially more impactful than previously believed, particularly when the construct of interest is related to uncertainty.

31 Asymmetric Trading Costs Prior to Earnings Announcements 30 In Section 3.4, we highlighted that longer-window returns are needed to assess risk premia associated with earnings announcements due to the accumulation and subsequent reversal of the upward bias in pre-announcement prices. To further illustrate this point, Figure 6 plots the average cumulative difference in returns across quintiles sorted by uncertainty, and its 95% confidence interval, in the 21 trading days surrounding firms announcement date. Using the proxies from Table 7, we characterize firms based on composite uncertainty proxy, IU, calculated as the sum of volatility (VLTY), earnings volatility (EVOL), and minus 1 times firm age (AGE), where all three measures are standardized each quarter to have a zero mean and unit standard deviation. The wide confidence interval in Fig. 6 shows there is no significant difference in cumulative returns across high and low uncertainty firms in the month surrounding firms announcements. However, the cumulative return spread does appear to be temporarily significant and positive immediately prior to the announcement. Combining this longer-window evidence with the shorter-window evidence from Table 8 demonstrates that a narrow focus on short-window earnings announcement returns may cause researchers to conclude that there is a significant uncertainty premium at announcements whereas the longer window view casts doubt on that interpretation because risk premiums should not immediately reverse after the realization of risk. At a minimum, our findings suggest researchers should consider both short- and longer-window returns (i.e., weeks or months) when estimating risk premiums associated with anticipated information events such as earnings announcements Time-Series Implications The analyses in this paper offer a joint test of financial intermediaries exposure to earnings announcement risks and the implications of this exposure for how the intermediary sector provides liquidity. We focus on the sector as a whole, rather than a specific subsection such as designated market makers, because an asset s liquidity is shaped by interactions between traders and intermediaries at several levels, including up-stairs markets, block-crossing, and traditional exchange trading. To directly link our findings to the financial intermediary

32 Asymmetric Trading Costs Prior to Earnings Announcements 31 sector, we examine asymmetric liquidity provision and pre-announcement returns when conditioning on changes in the aggregate balance sheets of financial intermediaries. These tests explore the time-series implications of Empirical Prediction 4 that our model s predictions should be most pronounced when intermediaries prefer to reduce their net positions. Adrian and Shin (2010) and Adrian, Etula, and Muir (2014) show financial intermediaries are positively exposed to the market and pro-cyclically adjust their balance sheet positions to reach a target level of leverage. As a result, we expect that time-series changes in the aggregate balance sheets of financial intermediaries reflects variation in their preference to expand versus contract their positions and, thus, their willingness to provide liquidity to buyers versus sellers. To test this prediction, Table 9 presents the averages of ALP and returns surrounding earnings announcements across calendar quarters partitioned by changes in broker-dealer leverage, LevFac, which is defined as the seasonally adjusted log change in the level of broker-dealer leverage as constructed in Adrian, Etula, and Muir (2014). Calendar quarters are ranked into quartiles within each calendar year to control for long-run trends in broker-dealer leverage, where the highest (lowest) quartile of LevFac corresponds to quarters with the greatest increase (decrease) in broker-dealer leverage within a given year. 8 Table 9 shows that our main findings are most pronounced in periods when financial intermediaries are scaling down their leverage by reducing their balance sheet positions. Specifically, Panel A shows that ALP is more than three times as large in quarters where intermediaries are reducing leverage (i.e., low LevFac quarters) compared to quarters where intermediaries are increasing leverage (i.e., high LevFac quarters). Similarly, Panel B shows the average excess pre-announcement return is 48 basis points (t-statistic = 4.289) in low LevFac quarters compared to just 7 basis points (t-statistic = 1.278) in high LevFac quarters. Note that this result cannot be explained by trends in the overall market because we use excess returns. Together, this evidence is consistent with pre-announcement asymmetries in trading costs being most pronounced when intermediaries prefer to reduce their net exposure. 8 In untabulated tests, we find even stronger results sorting the full time-series of quarters by LevFac.

33 Asymmetric Trading Costs Prior to Earnings Announcements 32 Related evidence in Table 10 contains results from regressing announcement returns on aggregate financial intermediary balance sheet growth, FIG. Adrian and Shin (2010) provides evidence that intermediaries primarily adjust their balance sheets through changes in their repo behavior. We use changes in repo behavior as an alternative proxy for intermediaries willingness to provide liquidity to buyers versus sellers that is more granular than the quarterly LevFac data. As in Adrian and Shin (2010), we obtain weekly data on aggregate repo behavior from the Federal Reserve Bank of New York and define FIG as the weekly change in total repurchase agreements (repos plus reverse repos), relative to the prior calendar week. We measure FIG in the week prior to firms earnings announcements and predict that it is positively related to the pre-announcement upward bias in prices and subsequent reversal. Columns (1), (3), and (5) of Table 10 provide strong corroborative evidence for our central hypotheses by showing that both the pre-announcement upward bias in returns and the subsequent reversal are most pronounced when financial intermediaries are scaling down their balance sheet positions, consistent with intermediaries being the most averse to providing liquidity to sellers when they prefer to reduce their net exposure. The symmetry in results across pre- versus post-announcement returns is consistent with intermediaries inducing a short-term upward bias in pre-announcement prices that subsequently reverses. Finally, columns (2), (4), and (6) of Table 10 combine our cross-sectional and time-series tests by examining the interaction effect between FIG and uncertainty. We predict that the link between financial intermediary balance sheet growth and returns is most pronounced among high uncertainty firms because their announcements engender greater risks. To test this prediction, we interact FIG with our composite information uncertainty measure, IU. Consistent with our prediction, columns (2) and (6) show that the relation between intermediary growth and returns is more pronounced among high uncertainty firms, indicating that extent of pre-announcement biases in market prices are shaped by time-series changes in financial intermediaries behavior, cross-sectional differences in announcement risks, and the interaction between the two.

34 Asymmetric Trading Costs Prior to Earnings Announcements Discussion: Relation to Prior Literature This study compliments and extends several strands of related literature. For example, by studying changes in financial intermediary behavior around earnings announcements, this study relates to prior research examining changes in transaction costs around information events such as earnings announcements. Studies such as Lee, Mucklow, and Ready (1993), Krinsky and Lee (1996), and So and Wang (2014) provide evidence that transaction costs increase prior to earnings announcements due to changes in adverse selection and inventory risks. Whereas these studies focus on the level of transaction costs, this study contributes to the literature by identifying asymmetries in transaction costs and the implications of these asymmetries for price discovery and returns. Our study also relates to prior research that documents differential market reactions to positive versus negative earnings news. These studies characterize the asymmetry as reflecting selective disclosures of good versus bad news ahead of the announcement (e.g., Kothari, Shu, and Wysocki (2009)), differences in market-level sentiment and uncertainty (e.g., Mian and Sankaraguruswamy (2012), Conrad, Cornell, and Landsman (2002)), and differences in ambiguity and credibility (e.g., Williams (2014)). This paper extends these studies by identifying an alternative, friction-based explanation for why investors respond more sharply to negative compared to positive news. Additionally, our findings show these effects should be most pronounced when uncertainty is high because uncertainty raises financial intermediaries incentives to asymmetrically provide liquidity, indicating that uncertainty is an important conditioning variable for studying asymmetric reactions to earnings news. Finally, our study relates to a vast literature studying returns and trading patterns around earnings announcements. Our findings contribute to the literature on risk premia associated with earnings announcements by helping to explain evidence of positive excess pre-announcement returns in prior studies (e.g., Frazzini and Lamont (2007), Barber et al. (2013)) and by identifying sources of measurement error in short-window announcement returns as proxies for earnings news or risk premia. This measurement error perspective

35 Asymmetric Trading Costs Prior to Earnings Announcements 34 provides a possible explanation for why prior research fails to find a significant association between non-diversifiable risk proxies and equity market returns (Barth and So (2014)). Additionally, our findings relate to studies that examine trading volume at earnings announcements as proxies for earnings news and/or investor disagreement (e.g., Bamber (1987), Garfinkel and Sokobin (2006)) by showing that asymmetrically liquidity provision creates an incentive to traders to delay trading on negative earnings news and, as a result, that abnormal pre-announcement trading volume positively predicts earnings news. 5. Conclusion The central contribution of this paper is that we provide both theoretical and empirical evidence that the costs of trading on negative news relative to positive news increases prior to earnings announcements, which shapes trading behavior, return patterns, and the information content of market prices. Our evidence suggests this asymmetry is due to financial intermediaries setting asymmetric prices for liquidity in order to reduce exposure to risks associated with the release of earnings news. An important implication of our findings is that they help resolve the puzzling evidence in prior studies that the earnings announcement premium reflects compensation for risk but a significant portion of the premium is earned prior to the release of earnings news. Our findings indicate that even if an information event commands a risk premium, researchers are likely to document increasing abnormal returns prior to the event due to predictable asymmetries in transaction costs. Additionally, our model and empirics show that the contemporaneous realization of risk and risk premia at earnings announcements is offset by the reversal of an upward biases in pre-announcement prices. As a result, our findings demonstrate that longer-window returns (i.e., weeks or months) are needed to measure the risk premia or news associated with earnings announcements.

36 Asymmetric Trading Costs Prior to Earnings Announcements 35 Appendix A. Model solution and proofs 1.1. Detailed model solution We solve the model by working backwards, beginning with the trading game at t = 1. The intermediary has initial inventory Q 1 that is determined by their choice of Q 2 and the trading game at t = 2, but at t = 1 it is no longer a choice variable. Given realization ṽ 1 = v 1, the two possible asset values are {v 1 σ, v 1 + σ}. The intermediary s problem in the subgame is therefore: a 1, b 1 = arg max a,b U (a, b Q 1, v 1 ) = U (a, b Q 1, v 1 ) (15) Expected trading profit {}}{ E ( y x I, 1 (p(x I, 1 ; a, b) ˆv 1 ) + x U, 1 (p(x U, 1 ; a, b) ˆv 1 ) ) (16) γ M σ 2 E ( ) y 2 Q 1 x I, 1 x U, 1 +ρ E ( ) y Q 1 x I, 1 x U, 1. } {{ } Inventory risk } {{ } Cost of negative inventory We begin by substituting trader demand functions from (2), (3), (4), and (5) into each of the three components of intermediary utility, relying on the following notation: The expected trading profit term satisfies: (2p 1) A 0,d 8γ T p(1 p)σ (17) 1 A 1,d 8γ T p(1 p)σ 2 (18) α a v 1 (19) β b v 1 (20) E y (trading profit) = E y [x i ( s 1 )(p(x i ( s 1 ; a, b)) ˆv) + x u (ũ 1 ; a, b)(p(x u (ũ 1 )) ˆv)] (21) = 1 4 [2(A 0,d A 1,d α)(α σ(2p 1)) + 2(A 0,d A 1,d α)α + 2( A 0,d A 1,d β)β + 2( A 0,d A 1,d β)(β σ(1 2p))] = A 0,d σ(2p 1) A 0,d(α β) A 1,d (α 2 + β 2 ). The expected inventory risk term satisfies: σ 2 E y ( (Q 1 x I, 1 x U, 1 ) 2 ) = σ2 4 [(Q 1 2A 0,d + 2A 1,d α) 2 + 2(Q 1 + A 1,d (α + β)) 2 + (Q 1 + 2A 0,d + 2A 1,d β) 2 ] (22) = A 0,v + A 1,v α + B 1,v β + A 2,v (α 2 + β 2 ) + C 2,v αβ,

37 Asymmetric Trading Costs Prior to Earnings Announcements 36 where: A 0,v σ ( ) 2 2A 2 0,d + Q 2 1 (23) A 1,v 2σ 2 A 1,d (Q 1 A 0,d ) (24) B 1,v 2σ 2 A 1,d (Q 1 + A 0,d ) (25) A 2,v 3 2 σ2 A 2 1,d (26) C 2,v σ 2 A 2 1,d. (27) Finally, the expected cost of negative inventory term satisfies: ρ E ( ) ( y Q 1 x I, 1 x U, 1 = ρ Q 1 + A 1,d (α + β) ) (28) Putting the pieces together, the marker maker s full objective function satisfies: U (a, b Q 1 ) = A 0,m + A 1,m α + B 1,m β + A 2,m (α 2 + β 2 ) + C 2,m αβ, (29) where: A 0,m A 0,d σ(2p 1) γ M σ ( 2 2A 2 0,d + Q 1) 2 + ρq 1 (30) A 1,m 3 2 A 0,d 2γ M σ 2 A 1,d (Q 1 A 0,d ) + ρa 1,d (31) B 1,m 3 2 A 0,d 2γ M σ 2 A 1,d (Q 1 + A 0,d ) + ρa 1,d (32) A 2,m A 1,d 3 2 γ Mσ 2 A 2 1,d (33) C 2,m γ M σ 2 A 2 1,d. (34) We solve the first-order conditions with respect to a and b and find the following prices: a 1 = M S 1 (35) b 1 = M S 1, (36) where: M 1 v 1 4p(1 p)γ ( M 4p(1 p) + γ σ 2 Q M 1 ρ ) γ T 2γ M σ 2 (37) S 1 12p(1 p) + 2 γ M γ T 8p(1 p) + γ M γ T (2p 1)σ. (38) Substituting a 1 and b 1 from (35) and (36) into the intermediary s utility function in

38 Asymmetric Trading Costs Prior to Earnings Announcements 37 equation (15), we have the following subgame expected utility as a function of Q 1 : U 1 (Q 1 ) = C 4p(1 p)γ Mσ 2 4p(1 p) + γ M γ T ( Q 1 ρ ) 2, (39) 2γ M σ 2 where C is a constant that does not depend on inventory Q 1. Note that expected subgame utility is maximized when excess inventory Q 1 ρ 2γ M is zero, leading to the interpretation σ ρ 2 of 2γ M as the target or optimal inventory for the announcement period. σ 2 Using the subgame equilibrium characterization, we solve for the intermediary s t = 2 optimal choice of Q 2, a 2, and b 2. Substituting (39) into (6), we have: U(Q 2, a 2, b 2 ) = Expected trading profit {}}{ E y ( x I, 2 (p(x I, 2 ; a 2, b 2 ) ˆv 2 ) + x U, 1 (p(x U, 2 ; a 2, b 2 ) ˆv 2 ) ) γ M E ( ) y 2 Q 2 x I, 2 x U, 2 +ρ E ( ) y Q 2 x I, 2 x U, 2 }{{}}{{} Inventory risk Cost of negative inventory ) 2 ( Q 2 x I, 2 x U, 2 + C 4p(1 p)γ Mσ 2 4p(1 p) + γ E y ρ M γ T 2γ M σ 2 }{{} Expected t= 2 utility. (40) Solving first-order conditions with respect to Q 2, a 2, and b 2 using a process similar to the one used for t = 1 yields the following solution: ( ) Q 2 = ρ 8p(1 p) + γ M γ T 2γ M 4p(1 p)(1 + σ 2 ) + γ (41) M γ T a 2 = 1 2 S 2 (42) b 2 = 1 2 S 2 (43) γ T K S 3(4p(1 p) + σ2 ) + 2 γ M 2(4p(1 p) + σ 2 ) + γ M γ T K (2p 1) (44) K 4p(1 p)(1 + σ2 ) + γ M γ T 4p(1 p) + γ M γ T. (45) 1.2. Proofs of equilibrium results Result 1 (Asymmetric liquidity provision). In the pre-announcement period, the average ask price is closer to the mean asset value (i.e., v 1 ) than the average bid price: E z (a 1 v 1 ) < E z (b 1 v 1 ). (46)

39 Asymmetric Trading Costs Prior to Earnings Announcements 38 Moreover, negative price changes overshoot the fundamental value information revealed by the trade more than positive ones: Proof. Eqs. (37) and (38) imply that: E z (a 1 ) E z (ṽ buy) < E z (ṽ sell) E z (b 1 ). (47) E z (a 1 + b 1 2v 1 ) = 2E z (M 1 v 1 ) = 8p(1 p)γ M 4p(1 p) + γ σ 2 M γ T Since liquidity provision at t = 2 is symmetric, we have that: ( ) E z (Q 1 ) = Q 2 = ρ 8p(1 p) + γ M γ T 2γ M 4p(1 p)(1 + σ 2 ) + γ M γ T ( E z (Q 1 ) ρ ). 2γ M σ 2 (48) > ρ 2γ M σ 2. (49) In words, before the pre-announcement trading period expected market market inventory is above the optimal Q 0, which necessitates asymmetric liquidity provision: E z (Q 1 ) > ρ 2γ M σ 2 Ez (a 1 + b 1 2v 1 ) < 0 (50) E z (a 1 v 1 ) < E z (v 1 b 1 ). Furthermore, since: E z (ṽ buy) = v ( 2 (2p 1)σ + 2 z 0 1 ) σ (51) 2 E z (ṽ sell) = v 1 1 ( 2 (2p 1)σ + 2 z 0 1 ) σ, (52) 2 we have: z ( < E z v 1 b 1 1 ( 2 (2p 1)σ + 2 z E z (a 1 ) E z (ṽ buy) = E z ( a 1 v (2p 1)σ 2 ( ) ) σ ) σ ) (53) = E z (ṽ sell) E z (b 1 ). Result 2 (Asymmetric trading intensity). In the pre-announcement period, traders submit larger buy orders in equilibrium than sell orders: x I, 1 ( s = g) > x I, 1 ( s = b) (54) x U, 1 (ũ = g) > x U, 1 (ũ = b). (55) Proof. Follows from Result 1 and the demand functions in Eqs. (3) and (5).

40 Asymmetric Trading Costs Prior to Earnings Announcements 39 Result 3 (Abnormal returns around announcements). Expected returns computed using expected volume-weighted average prices under the physical measure satisfy: E z ( p 1 p 2 ) = 2 ( ( ) ) z ρ 2p(1 p) + γ M 2 }{{} 8 (σ2 γ 1) T 4p(1 p)(1 + σ 2 ) + γ (56) M γ T Normal risk prem. }{{} E z ( p 0 p 1 ) = 2 ( z 0 2) 1 σ ρ }{{} 8 (σ2 1) Announcement risk prem. Upward bias ( 2p(1 p) + γ M γ T 4p(1 p)(1 + σ 2 ) + γ M } {{ } Bias reverses Proof. Since liquidity provision is symmetric at t = 2, average volume weighted average price p 2 equals the frictionless benchmark E y (ṽ) = 0. For a given inventory Q 1, we define the average price at t = 1, p(q 1 ), as the average across the four different demand combinations of the volume-weighted average price given that demand combination. This average satisfies: ( ) p(q 1 ) = E z (vwap) = v M 1 + (2p 1)σM 1 M 1 S 1 (2p 1)σ 1 2 S 1 γ T ) (57) (58) We can therefore substitute Eqs. (37) and (38) into (58), and simplify to: ( ) ( p(q 1 ) = v 1 8p(1 p)γ Mσ 2 (2p 1)σ S 16p(1 p) + 4 γ 1 + M γ T (2p 1)σ 1S Q 1 ρ ) 2γ 2 M σ 2 = v 1 + 2p(1 p) γ M ( γ T 16p(1 p) + 4 γ γ M M σ 2 Q 1 ρ ) γ T 2γ M σ 2 (59) We now take the expectation over possible Q 1, and use equation (50) for E z (Q 1 ). Since E z (Q 1 ) > ρ 2γ M, average excess inventory is positive, resulting in asymmetric liquidity σ 2 provision and, as a consequence, an upward bias in prices: p 1 E z (p(q 1 )) = 2(z ) + = 2(z ) + ρ 8 (σ2 1) ( 2p(1 p) + γ M γ T 16p(1 p) + 4 γ M γ T γ M σ 2 2p(1 p) + γ M γ T 4p(1 p)(1 + σ 2 ) + γ M γ T ) ( E z (Q 1 ) ρ ) 2γ M σ 2 (60). (61) The asset liquidates at t = 0 for ṽ, making the average price p 0 equal the frictionless benchmark 2(z 1 1) + 2(z 2 0 1)σ. Combining the equations for p 2 2, p 1, and p 0 yields the expected returns in (56) and (57).

41 Asymmetric Trading Costs Prior to Earnings Announcements 40 Result 4 (Comparative statics). Average asymmetry in liquidity provision, pre-announcement return, and post-announcement reversal are all increasing in the intermediary s inventory Q 1, risk aversion γ M, cost of negative positions ρ, and the announcement risk σ. Proof. From equation (59) it is clear that the average pre-announcement price conditional on Q 1 is increasing in Q 1. Furthermore, after some algebra, the average pre-announcement price in equation (61) is increasing in γ M, ρ, and σ. Finally, the asymmetry in liquidity provision, as measured by the difference: E z (v 1 b 1 ) E z (a 1 v 1 ) = 2E z (M 1 v 1 ) (62) = 8p(1 p)γ ( M 4p(1 p) + γ σ 2 E z (Q M 1 ) ρ ) (63) γ T 2γ M σ 2 is also an increasing function of γ M, ρ, and σ. = 4p(1 p)γ M 4p(1 p)(1 + σ 2 ) + γ M γ T ρ(σ 2 1), (64)

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44 Asymmetric Trading Costs Prior to Earnings Announcements 43 Figure 1: Event-Time Idiosyncratic Volatility Relative to Announcement This figure plots the time-series average of abnormal idiosyncratic volatility in event time in the 21 trading days surrounding firms earnings announcement date, t. The top panel is plotted against the earnings announcement dates used in this study, the middle panel is plotted against the earnings announcement dates as reported in Compustat, and the bottom panel is plotted against the earnings announcement dates as reported in IBES. We compute abnormal idiosyncratic volatility on day d by taking the square root of the ratio of the squared residual (from a firm-specific market-model regression estimated with three lags) on day d and the average squared residual from t-51 to t-11, and subtracting one. The sample for this analysis consists of 215,754 quarterly earnings announcements spanning 1993 through 2012.

45 Asymmetric Trading Costs Prior to Earnings Announcements 44 Figure 2: Event-Time Reversals Relative to Announcement The top panel plots the average three-day returns for firms within the highest and lowest quintile of returns over the prior three-day window. Quintiles are formed each calendar quarter using breakpoints from the prior calendar quarter. The figure is shown in event time, where day t corresponds to the earnings announcement date. The reported strategy return on day d reflects the three-day cumulative strategy return from d-1 to d+1 from a long position in the lowest quintile of returns from d-4 to d-2 and a short position in the highest quintile of returns from d-4 to d-2. The 95% confidence interval is constructed using the time-series of quarterly average returns. The bottom panel plots the difference in returns from buying firms within the lowest quintile of returns over the prior three-day window and the returns from selling those within the highest quintile. The sample for this analysis consists of 215,754 quarterly earnings announcements spanning 1993 through 2012.

46 Asymmetric Trading Costs Prior to Earnings Announcements 45 Figure 3: Returns for Good and Bad News Announcements The top panel in this figure plots the average percentage of cumulative returns in the 21 days surrounding an earnings announcement, where day t corresponds to the earnings announcement date, for good and bad news announcements. An announcement is labeled as good ( bad ) if the corresponding analyst-based earnings surprise, SURPRISE, is greater or equal to (less than) zero. SURPRISE equals the actual EPS number reported in IBES minus the last consensus forecast available immediately prior to the announcement, and scaled by beginning-of-quarter price. The bottom panel plots the average cumulative returns in the 21 days surrounding an earnings announcement. The sample for this analysis consists of 215,754 quarterly earnings announcements spanning 1993 through 2012.

47 Asymmetric Trading Costs Prior to Earnings Announcements 46 Figure 4: Cumulative Announcement Premium This figure plots the average percentage of the cumulative announcement premium, AP, in event time in the 21 trading days surrounding the announcement date, t. AP equals the firm s daily return minus the contemporaneous average return of all non-announcing firms. A firm is deemed a non-announcer on day d if the firm did not announce earnings within the 21 trading days centered on day d. For each day d relative to the announcement, we report the average cumulative AP from t-10 to d, scaled by the cumulative AP from t-10 to t+10. The sample for this analysis consists of 215,754 quarterly earnings announcements spanning 1993 through 2012.