Do arbitrageurs amplify economic shocks?

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Abstract

We test the hypothesis that arbitrageurs amplify economic shocks in equity markets. The ability of speculators to hold short positions depends on asset values. Shorts are often reduced following good news about a stock. Therefore, the prices of highly shorted stocks are excessively sensitive to shocks compared with stocks with little short interest. We confirm this hypothesis using several empirical strategies including two quasi-experiments. In particular, we establish that the price of highly shorted stocks overshoots after good earnings news due to short covering compared with other stocks.

Introduction

We examine whether arbitrageurs amplify exogenous economic shocks in asset markets. This issue is related to a large literature dating back to Friedman (1953) on the role of speculators in affecting asset price dynamics. A number of theories suggest that asset prices are excessively sensitive to economic news when arbitrage is limited in various ways such as leverage constraints or agency problems arising from delegated money management.1 For instance, the market turmoil of 1998 is widely viewed as having been exacerbated by the forced selling of assets by Long Term Capital Management and other hedge funds that were pursuing similar strategies. The turbulence in the summer of 2007 has been attributed to the forced selling by many multi-strategy quantitative funds.2 And throughout the current crisis since the collapse of Lehman Brothers in September 2008, many market observers have pointed to the forced unwinding of highly levered trades as an explanation for the collapse and extreme volatility of financial markets.3

Despite the wide acknowledgment of the importance of this amplification mechanism in financial markets, relatively little systematic evidence exists on whether fundamental shocks are magnified by such speculative activity. An understanding of the effects of speculators on asset price dynamics has never been more important from both academic and public policy perspectives.

We tackle this issue in the context of short arbitrage in equity markets by examining if the presence of short arbitrage in a stock heightens the reaction of its price to quarterly earnings news. There are a couple of reasons that short selling in equity markets is a useful setting to study this issue. First, plentiful panel data are available on the amount of short selling, and most short sales are undertaken by professional speculators such as hedge funds as opposed to retail investors. This stands in contrast to the difficulty of measuring levered long speculative positions in equities. Second, in practice, the ability of arbitrageurs to hold on to short positions depends on asset values. Shorts are often reduced (increased) following good (bad) news about a stock for a variety of reasons. This has been confirmed by earlier work on this mechanism (see, e.g., Lamont and Stein, 2004). Short sales tend to be highly levered transactions that require having enough funds in the margin account.

The financial press often speaks of short covering (the cutting down of short positions through the purchase of shares) causing excess volatility in markets. One example is for the Internet stock eBay, which reported better earnings than expected in the summer of 2005. Its stock price soared dramatically the same day. The press pointed to short covering as a likely source of the price movement (see Nassar, 2005). On October 28, 2008, hedge funds shorting the car maker Volkswagen (VW) were forced to cover their short positions when news came out that Porsche had bought up much of VW's remaining free float. Shares in the German car maker, which began the day trading at €420 a share, hit an intraday high of €1,005.01, valuing the company at €296.06 billion ($370.4 billion) based on ordinary stock, which was more than that of the world's next largest company at the time, Exxon Mobil Corp's $343 billion market value. VW's share price reverted to €393 per share by November 3 after the hedge funds finished buying all the shares they needed to cover their speculative positions.

To capture this amplification mechanism caused by short covering, we begin by developing a simple three date model, based on Shleifer and Vishny (1997), of asset price dynamics in which arbitrageurs have a profitable opportunity to short an overpriced stock subject to positive sentiment.4 The key ingredient is that the ability of arbitrageurs to hold on to short positions depends on asset values (i.e., the past performance of these positions). An earnings announcement also could affect the sentiment for the stock. Our joint hypothesis is as follows: Suppose the firm has good earnings news, forcing arbitrageurs to short cover. This short covering will temporarily boost a firm's stock price as the extra buying pressure leads to an overshooting of price to earnings news that is reversed in the long run.

We derive three key predictions that we test using monthly data on short sales in US equities from 1994 to 2007. The first prediction is that the price sensitivity to earnings news is higher for a stock with positive short selling (i.e., arbitrage presence) than for a stock with no short selling (i.e., no arbitrageurs). We measure the sensitivity of the stock price to earnings news as the regression coefficient of the stock return around the earnings announcement date on the earnings surprise (or the difference between the earnings and the consensus forecast scaled by previous price). We define a highly shorted stock as one in the top 33% of the short ratio (short interest to shares outstanding) distribution for stocks in our sample for that quarter and a stock with little short selling as the rest of the stocks in our sample for that quarter. The premise behind this cutoff is that only those with substantial short ratios are likely to be subject to genuine valuation-motivated arbitrage activity.

We test this prediction by running a pooled regression of cumulative abnormal returns around (quarterly) earnings announcement dates (from one trading day before to one day after) on a high earnings surprise dummy variable (equal to one if the stock is in the top 33% of the earnings surprise distribution for stocks in our sample for that quarter and zero otherwise), a dummy variable for whether a stock is highly shorted before the earnings date and the highly shorted dummy interacted with the high earnings surprise dummy. The coefficient for the interaction term then reveals the difference in the sensitivity of the stock price to news between highly shorted stocks and stocks with little short interest.

In estimating this relation, we worry about unobserved heterogeneity; e.g., highly shorted stocks could be more in the media spotlight than other stocks and, hence, their prices respond more to news. To deal with this issue, we estimate this regression specification (and all the other specifications below) in a variety of ways such as controlling for a number of stock characteristics (e.g., interacting news with stock characteristics such as firm size and institutional ownership) and using stock fixed effects. Regardless of how we estimate this relation, we find that the price of a highly shorted stock is more sensitive to earnings news than a stock with little shorting. For stocks with little short interest, our basic results suggest that having a high earnings surprise leads to a higher cumulative abnormal return of about 3.27 percentage points (or 327 basis points). In contrast, for highly shorted stocks, the comparable figure is around 382 percentage points. The difference of 55 basis points (about 17% larger for highly shorted stocks) is economically and statistically significant. We verify that this relation (as well as all the other ones established below) is robust to a variety of different specification checks such as ways of measuring abnormal returns and earnings surprises.

The second prediction is that the change in the short interest ratio of a stock should be negatively correlated with the earnings surprise (e.g., a positive earnings surprise should lead to a fall in this ratio). Here, we are merely extending earlier work by Lamont and Stein (2004) and Savor and Gamboa-Cavazos (2005). They have already shown that the monthly short interest ratio falls on good news to stock prices and rises on bad news to stock prices. Ideally, we want to measure the sensitivity of changes in daily short interest to unexpected earnings announcements. Unfortunately, we can observe short interest only at a monthly frequency. Such monthly changes are a noisy and likely biased way to pick up the short covering effect around earnings dates. Therefore, we use a stock's abnormal turnover around the earnings announcement as a proxy for changes in the short interest ratio. Consistent with our model, we find that, for highly shorted stocks, abnormal turnover is more sensitive to earnings news than for little shorted stocks.5

Our third and perhaps most important prediction is that arbitrageurs are forced to cover short positions that would have been profitable; i.e., the stock price subsequently declines. This means that, for highly shorted stocks, a short position initiated after the event date should be more profitable after good earnings news forces short covering. We find that, for stocks with little shorting, good news leads to higher subsequent returns (from two days after to 126 trading days after the announcement) to holding the stock (about 157 basis points). This is consistent with the well-documented post earnings announcement drift (see, e.g., Bernard and Thomas, 1989, Bernard and Thomas, 1990). However, for highly shorted stocks, good news leads to excess returns of negative 110 basis points, 267 basis points lower than for little shorted stocks. In other words, a short position in these stocks initiated after good earnings news is profitable.

This third prediction cuts strongly against a number of alternative stories. For instance, one possible reason for price being more sensitive to news for highly shorted stocks is that short sales are informed bets that there are going to be negative earnings surprises. As a result, good news means these bets are wrong and price naturally reacts more to good news. If this alternative explanation is correct, then one would not expect to find that the greater price increase observed on the event date following good news is subsequently reversed (i.e., that the stock price declines in the months following the good news). This post-announcement return finding is difficult to reconcile with alternative explanations.

Finally, to better identify our amplification mechanism, we consider two quasi-experiments. Our first quasi-experiment is that the above findings ought to be stronger for NASDAQ stocks than NYSE stocks because historically it was easier to short NASDAQ stocks than NYSE stocks for regulatory reasons before 2007 (and particularly before 2001). We find empirical support for our hypothesis using this quasi-experiment. Our second quasi-experiment builds on the work of Hanson and Sunderam (2008), who show a striking increase in the short interest ratio concentrated among small stocks since the early 2000s. They argue that this is due to the rise of hedge funds. If our hypothesis is correct, then we expect to find that the destabilizing effects shown above ought to have increased among small stocks since 2002 compared with large stocks that did not witness such growth. Although our estimates are imprecise, we find that this is the case.

A growing literature tests the implications of limits to arbitrage models. Work most closely related to ours includes Savor and Gamboa-Cavazos (2005), who find that short sellers cover their positions after suffering losses and increase them after experiencing gains (measured using past returns). This relation is very strong for positions established due to perceived overvaluation; expected returns do not explain the documented short seller behavior. Similarly, Lamont and Stein (2004) show a strong negative correlation between market returns and the change in the aggregate short interest ratio.

The main innovation of our paper relative to these and other empirical papers in the literature is that we show that arbitrage activity directly influences asset prices through at least one channel: the amplification of fundamental shocks.6 The important point is that this paper is one of the first to directly show the economic mechanism that leads to destabilizing speculation in asset markets.7 However, the idea that short sales can influence stock price reaction to news is also in Reed (2007), who shows that short-sales constraints lead price to underreact to bad earnings news. We show in contrast that stock prices overreact to good news due to short covering.

Our paper is also closely related to empirical papers looking at the relation between leverage and asset prices.8 Lamont and Stein (1999) test a similar hypothesis to ours but in the context of the housing market. Their principal finding is that in cities where a greater fraction of homeowners are highly leveraged, house prices react more sensitively to city-specific shocks such as changes in per capita income. In contrast to their paper, our setting provides a tighter test of the amplification of fundamental shocks hypothesis.

Our paper proceeds as follows. We present a simple model to derive the main predictions in Section 2. The data are presented in Section 3 and the empirical findings in Section 4. We conclude in Section 5. All proofs are in the Appendix section.

Section snippets

Model

This section presents a simple three-period model based on Shleifer and Vishny (1997). Whereas Shleifer and Vishny (1997) look at levered longs by arbitrageurs in an initially underpriced stock, we consider the case of arbitrageurs shorting an initially overpriced stock. The model illustrates how an informed arbitrageur faced with leverage or risk management constraints must cut back on positions following adverse price moves and that such actions tend to amplify the price reaction to an

Data

The sample consists of quarterly observations of stocks that are listed on the NYSE, Amex or Nasdaq exchanges from 1994 through 2007. Observations are dropped if short interest, earnings data, or Institutional Brokers' Estimate System (I/B/E/S) forecast data are missing or if the earnings statement takes place outside the typical earnings announcement season, which we consider to be 30 to 90 calendar days following the end of the fiscal period. All of our cutoff criteria described below are

Sensitivity of price to earnings news

We begin by testing Proposition 1, which states that the earnings response coefficient should be higher for highly shorted stocks. We want to measure how the sensitivity of price to earnings news varies by whether a stock is actively shorted or not. We first measure the overall effect of unexpected earnings shocks on returns; i.e., the price to earnings sensitivity for the typical firm in our sample. This provides a benchmark. To this end, we estimate the following specification:CARi,t=α+β1UEHIG

Conclusion

We develop a simple model based on Shleifer and Vishny (1997) to examine whether arbitrageurs amplify fundamental shocks in the context of short arbitrage in equity markets. The key amplifying mechanism is that the ability of arbitrageurs to hold on to short positions depends on asset values: shorts are often cut following good news about a stock. The extra buying pressure from this short covering temporarily boosts the stock price. As a result, the prices of highly shorted stocks overshoot

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    We thank our referee Jay Ritter, Jerry Coakley, Karl Diether, Sam Hanson, Arvind Krishnamurthy, Michael Rashes, Pavel Savor, Jeremy Stein, Rene Stulz, and seminar participants at the Cambridge-Princeton Finance Conference, Ohio State University, Georgetown University, Wharton School of the University of Pennsylvania, National Bureau of Economic Research Behavioral Finance, Morgan Stanley, Oxford University, Queen Mary of the University of London, London School of Economics, Singapore Management University, National University of Singapore, Imperial College of London, European Financial Association Meetings, New York University Five Star Conference and the Reserve Bank of Australia for helpful comments.

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