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Using a comprehensive sample of trades from Schedule 13D filings by activist investors, we study how measures of adverse selection respond to informed trading. We find that on days when activists accumulate shares, measures of adverse selection and of stock illiquidity are lower, even though prices are positively impacted. Two channels help explain this phenomenon: (1) activists select times of higher liquidity when they trade, and (2) activists use limit orders. We conclude that, when informed traders can select when and how to trade, standard measures of adverse selection may fail to capture the presence of informed trading.An extensive body of theory suggests that stock illiquidity, as measured by the bid-ask spread and by the price impact of trades, should be increasing in the information asymmetry between market participants (Glosten and Milgrom (1985), Kyle (1985), Easley and O'Hare (1987)). Based on this literature, there have been many attempts to measure trading costs empirically, and to decompose such costs into different components such as adverse selection, order processing, and inventory costs (Glosten (1987), Glosten and Harris (1988), Stoll (1989), Hasbrouck (1991a)). Empirical measures of adverse selection typically rely on an estimate of the persistent price impact of trades to capture the amount of private information in trades.

FOS S1. DETERMINISTIC GROWTH RATE OF NOISE TRADER VOLATILITYIN GENERAL, WHEN NOISE TRADING VOLATILITY IS STOCHASTIC (ν = 0) and there is predictability (m t = 0), then price impact is stochastic and negatively correlated (in changes) with noise trading volatility. However, price volatility and the posterior variance of the fundamental value (Σ t ) are both deterministic and only depend on the unconditional expected path of noise trading volatility. For illustration, Figure S1(a) plots the paths of the posterior variance (Σ t ) for three cases of constant growth rate m = 0 5, m = 0, and m = −0 5. It is remarkable that irrespective of ν t (and thus of realized shocks to noise trading, i.e., of realized volume), private information is revealed following a deterministic path, which only depends on the expected rate of change in noise trading volatility, despite the fact that the strategy of the insider is stochastic. This is, of course, the result of the offsetting effect noise trading volatility has on price impact. If the level of noise trading variance increases (decreases) unexpectedly, then the insider trades more (less) aggressively, but price impact decreases (increases) one for one, making price dynamics and information arrival rate independent of the volatility level. Instead, if noise trading variance is expected to increase on average because m > 0, for example, then the insider is expected to scale back his trading initially and to trade more aggressively later on. As Figure S1(a) shows, this leads to private information getting into prices more slowly initially, and then faster later on. So posterior variance follows a deterministic concave path if noise trading volatility is expected to increase, but a convex path if it is expected to decrease. As a result, the equilibrium price process exhibits deterministic time-varying volatility. Price volatility increases (decreases) exponentially if noise trading volatility is expected to increase (decrease).In Figure S1(b), we plot the expected optimal trading rate of the insider normalized by the initial undervaluation (E[θ t |v F 0 ]/(v − P 0 ) from equation (27) in the paper) for different levels of constant m. As we can see, when noise trading volatility is unpredictable (m = 0), then we expect the insider to trade at a constant rate as in the Kyle model. Instead, if noise trading volatility is expected to increase (m > 0), then, unconditionally, we expect the insider to trade more aggressively on average in the future when more noise trading will occur. In fact, when m > 0, the insider initially scales back his expected trading relative to the m = 0 case despite the fact that he starts out with the same level of noise trader volatility (σ 0 ) in both cases and indeed, despite the fact that the

Using a manually collected data set of all proxy contests from 1994 through 2012, I show that proxy contests play an important role in hostile corporate governance. Target shareholders benefit from proxy contests: the average abnormal returns reach 6.5% around proxy contest announcements. Proxy contests that address firms’ business strategies and undervaluation are most beneficial for shareholders. By contrast, proxy contests that aim at changing capital structure and governance do not lead to higher firm values. Relative to matching firms, future targets are smaller, they have higher stock liquidity, higher institutional and activist ownership, lower leverage and market valuation, and higher investments. Whereas most of these characteristics predict proxy contests in time series, prior to proxy contests, targets also experience poor stock performance, decreases in investments, increases in cash reserves and payouts to shareholders, and increases in management’s entrenchment. These changes in corporate policies are consistent with targets’ attempts to affect the probability of a proxy contest. This paper was accepted by Amit Seru, finance.

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