Evaporating Liquidity∗Stefan Nagel†Stanford University, NBER, and CEPRJuly 2011AbstractThe returns of short-term reversal strategies in equity markets can be interpreted asa proxy for the returns from liquidity provision. Analysis of reversal strategies showsthat the expected return from liquidity provision is strongly time-varying and highlypredictable with the VIX index. Expected returns and conditional Sharpe Ratios increaseenormously along w ith the VIX during times of financial market turmoil, such as thefinancial cr isis 2007-09. Even reversal strategies formed fr om industry portfolios (whichdo not y ield high returns unconditionally) produce high rates of return a nd high SharpeRatios during times of high VIX. The results point to withdrawal of liquidity supply, andan a ssociated increase in the expected returns from liquidity provision, as a main driverbehind the e vaporation of liquidity during times of financial market turmoil, consistentwith theories of liquidity provision by financially co nstrained intermediaries.∗I thank Miguel Ferreira, Terrence Hendershott, Charles Jones, Ron Kaniel, Ian Martin, Konstantin Mil-bradt, Dimitry Vayanos, and seminar participants at the Un iversity of Amsterdam, University of BritishColumbia, Columbia University, Federal Reserve Bank of New York, University of Maastricht, Princeton,Rice, Stanford, the American Finance Association Meetings, the NBER Summer Institute, and the GutmannCent er Symposium at WU Vienna for usefu l comments.†Stanford University, Graduate S chool of Business, 518 Memorial Way, Stanford, CA 94305, e-mail:[email protected] IntroductionLiquidity evaporated in many sectors of financial markets during the financial crisis 2007-09.In some markets, such as those for “toxic” asset-backed securities, trading activity reportedlycame to a complete halt.1There are at least two possible explanations for this disappearanceof market liquidity. One is that the crisis amplified asymmetric information problems. Forexample, Gorton and Metrick (2010) argue that large adverse shocks strongly increased theinformation sen s itivity of securitized debt. According to this view, th e reduction in liquidityis a symptom for aggravated adverse selection problems. An alternative and complementarytheory is that the market turmoil strained th e inventory-absorption capacity of the market-making sector, either because of a surge in liquidity demand from the public, or becausemarket makers reduced liquidity supply in response to elevated levels of risk, tighter fundingconstraints, and reduced competition. According to this second view, the conditions duringthe crisis raised the expected return from liquidity provision.This paper studies this second channel using data from equity markets. The main objec-tive is to estimate the extent by which the expected r eturn from liquidity provision rises intimes of financial market turm oil. The notion of “liquidity providers” ad opted in this paperis broad and not restricted to designated market makers. Liquidity provision in equity mar-kets is increasingly performed by algorithmic traders and other quantitative investors thatperform, effectively, a market-making role, but without being officially designated as marketmakers (Hendersh ott, J on es, and Menkveld (2011)). Even individual investors could performa liquidity provision role to some extent (Kaniel, Saar, and Titman (2008)).To construct a proxy for the returns from liquidity provision, I examine reversal strategiesthat buy stocks that went down over the prior days, and sell stocks that went up du ring theprior days, as in Lehman (1990) and Lo and MacKinlay (1990). This p attern of buying andselling in reversal strategies resembles the trading of a market maker who sells when thepublic buys (which tends to coincide with rising prices), and who buys when the public sells1See Brunnermeier (2009) for a review.1(which tends to coincide with falling prices). Setting up a model in which the public tradesfor liquidity and informational reasons, and in which market makers have limited risk-bearingcapacity, I show that reversal strategy returns closely track the returns earned by liquidityproviders . Effectively, reversal strategies use lagged returns as a noisy proxy for unobservedmarket maker inventory imbalances. They profit from the transitory price impact of orderflow and the negative serial correlation in price changes that arises from market makers’aversion to absorbing inventory. Price imp act due to private information, in contrast, ispermanent and does not induce negative serial correlation (Glosten and Milgrom (1985)),which allows me to isolate the variation in the expected returns from liquidity provision fromadverse selection effects.2The focus of this paper is to examine w hether there is predictable time-variation in thereturns from liquidity provis ion. Recent work on risk-taking of financial intermediaries sug-gests that the VIX index of implied volatilities of S&P500 index options is a natural candidatepredictor. The theories in Gromb and Vayanos (2002) and Bru nnermeier and Pedersen (2009)predict that higher volatility tightens funding constraints of market makers and thereby re-duces their liquidity-provision capacity. Adrian and Shin (2010) argue that risk-managementconstraints reduce the risk appetite of financial intermediaries in times of high VIX. Ang,Gorovyy, and van Inwegen (2011) and Ben-David, Fran zoni, and Moussawi (2011) find thathedge funds lose assets under man agement and reduce leverage in times of market turmoiland high VIX. Motivating evidence also comes from a recent literature that finds the VIX tobe related to various asset-pricing phenomena that may be related to risk-taking of financialintermediaries, such as corporate bond liquidity (Bao, Pan, and Wang (2011)), foreign ex-change carry trades (Brunnermeier, Nagel, and Pedersen (2008)) or sovereign credit-defaultswaps (Longstaff, Pan, Pedersen, and Singleton (2010)).Figure 1 illustrates some of the key fin dings of the paper. The solid line plots a three-2In Glosten and Milgrom’s model, greater adverse selection leads to a wider bid-ask spread, bu t transactionprices always follow a martingale (i.e., th ere is no bid-ask bounce), and market makers, as well as reversalstrategies, earn zero expected return.2Jan1998 Jan2000 Jan2002 Jan2004 Jan2006 Jan2008 Jan201000.0020.0040.0060.0080.01Average return per dayJan1998 Jan2000 Jan2002