Adverse Selection In The Equity Loans Market

Peita Lin

July 25, 2016


We examine a form of adverse selection which arises when short sellers attempt to coordinate a price correction, but stock lenders learn by observing arbitrageurs’ arrivals and become better informed about the true timing of an imminent price correction. We refer to this concept as coarse clocks. We show how coarse clocks lead to an adverse selection problem in the market for equity loans, creating a type of strategic short sale constraint which limits arbitrage. We analyze the implications of a switch from the current over-the-counter stock loans market to a centralized exchange, and relate our findings to recent empirical research on short-selling risks.

Adverse Selection In The Equity Loans Market – Introduction

Some arbitrageurs have better information about firm fundamentals, while others are better at anticipating future market movements. The latter is commonly known as market timing. One insight originally proposed by Keynes (1936) is that in timing financial market movements, it may be far more rewarding to second guess when other investors believe prices will adjust. Acting on a pessimistic view is profitable only if a majority of other agents form the same beliefs, and coordinate to short sell the stock at the same time. Only then can there be a price correction for arbitrageurs to close their positions and take profits. Delays in price corrections can result from what Abreu and Brunnermeier (2002) refer to as synchronization risk, which differs from traditional notions of risk in that it refers to the strategic uncertainty surrounding the timing of other arbitrageurs’ actions, rather than uncertainty about firm fundamentals.

For arbitrageurs acting under strategic uncertainty, more precise information concerning the timing of others’ actions is key to mitigating synchronization risk. However, improved synchronization has a nasty implication for short sellers—when borrowing stocks, arbitrageurs inadvertently reveal their beliefs about the timing of the price correction to the stock lender. Since the lender may observe the frequency with which unique arbitrageurs arrive over a set time period, the lender gradually learns about the true timing of the price decline. Thus when arbitrageurs borrow stocks in a synchronized fashion, lenders infer that a price decline is imminent and take measures to avoid this outcome by increasing borrowing fees or recalling stock loans. The arrival of subsequent arbitrageurs imposes a negative information externality on earlier arbitrageurs as it allows lenders to recall stocks moments before arbitrageurs can profit from a price decline.

The purpose of this paper is to identify a form of adverse selection that occurs when arbitrageurs and lenders differ in their ability to discern the true timing of an imminent price correction. I refer to this concept as coarse clocks. Some agents have fine precise clocks, and are in the position to take advantage of agents with comparatively coarse clocks. Other agents, such as stock lenders, are uniquely positioned to learn and “fine-tune” their clocks. I show how the current structure of the equity loans market gives rise to coarse clocks, which expose arbitrageurs to an adverse selection problem. In doing so, I highlight how coarse clock-induced adverse selection can act as a hidden short sale constraint on many seemingly “obvious” arbitrage opportunities, inhibiting price discovery (Miller, 1977).

My model starts with the assumption that lenders are matched with multiple arbitrageurs who arrive sequentially over time. As in Abreu and Brunnermeier (2002), the price declines (only) when a critical mass (?) of arbitrageurs successfully borrow and short sell the stock. Lenders know that arbitrageurs’ arrivals follow a poisson process, but are unsure as to whether the parameter governing arrivals (?) is high or low. Lenders update their beliefs by observing the arrivals of arbitrageurs, becoming increasingly pessimistic in discrete jumps upon each arrival, while gradually becoming more optimistic over time when no borrowers arrive. When lenders’ belief about the arrival rate exceeds a certain pessimistic threshold, they recall loans and sell their stock. This threshold rule captures the idea that lenders are only concerned about a successful synchronized short-selling attack. My assumption that lenders behave according to this threshold rule can be empirically justified by the observation that lending fees do not appear to react to loan demand (Cohen, Deither and Malloy, 2007), except when there is an acute spike in borrowing demand (Kolasinski et al., 2013).

The theory produces a general negative result for arbitrageurs — improved synchronization amongst short sellers helps lenders learn rapidly, which intensifies coarse clock-induced adverse selection. This result alludes to Lamont’s (2012, p. 4) observations that short sellers have incentives to both publicly announce their short sales while maintaining secrecy since “the sooner one can convince other investors that the stock price is too high, the sooner the price will fall, minimizing holding costs and price risk. On the other hand, recall risk […] gives short sellers an incentive for secrecy, since holding costs generally rise when other investors are also trying to short.” Thus the distinguishing feature of my model is in its ability to capture short sellers’ aversion towards “obvious” arbitrage opportunities, such as the expiration of IPO lockups which exhibit abnormal price declines (Ofek and Richardson, 2000; Field and Hanka, 2001). Stock recalls disrupt arbitrageurs’ ability to collectively correct a mispricing, and more obvious arbitrage opportunities are more prone to the adverse selection problem.

My idea that lenders infer from borrowers’ arrival intensities the timing of price movements is related to Easley et al.’s (2012) concept of “volume clocks”. The idea is that orders tend to cluster across time so there are periods where there is furious activity in trading followed by prolonged periods of silence. Grouping trades into volume buckets rather than in chronological time periods may provide a more informative measure of order flow. Just as market makers learn from order flow and adjust bid-ask spreads in response to order flow toxicity (Glosten and Milgrom, 1985), stock lenders use arbitrageurs’ arrivals as an early warning signal of impending price corrections.

As lenders learn about the arrival rate ?, their posterior beliefs about bubble burst times shift relative to those of naïve arbitrageurs. I rank and establish stochastic dominance results between lenders’ and arbitrageurs’ posterior beliefs. This allows me to analyze how various short interest disclosure regimes may lead to more socially efficient outcomes for the loans market. In particular, I analyze how improving short interest disclosures can reduce the adverse selection problem but invite arbitrageurs to short sell more aggressively. I further discuss the implications of a switch from the current opaque over-the-counter (OTC) market structure to a more transparent stock loans exchange.

The structure of the rest of this paper is as follows. Section 2 provides an overview of the existing short-selling literature and the market structure for stock loans. Section 3 presents the baseline Abreu and Brunnermeier’s (2003) model where arbitrageurs follow symmetric strategies and do not compete with lenders when timing their short selling strategies. Section 4 introduces lenders and describes their information acquisition process. This is followed by a discussion on the comparative statics of lenders’ stopping times after allowing lenders to learn and earn lending fees. Section 5 analyses the impact of different short interest disclosure regimes on the timing behaviors of arbitrageurs and lenders. I introduce search frictions and link my results

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