Trading and Returns under Periodic Market Closures

This paper studies how market closures affect investors' trading policies and the resulting return-generating process. It shows that closures generate rich patterns of time variation in trading and returns, including those consistent with empirical findings: (1) U-shaped patterns in the mean and volatility of returns over trading periods, (2) higher trading activity around the close and open, (3) more volatile open-to-open returns than close-to-close returns, (4) higher returns over trading periods than over nontrading periods, (5) more volatile returns over trading periods than over nontrading periods. It also shows that closures can make prices more informative about future payoffs. WE MODEL A COMPETITIVE STOCK MARKET with periodic closures in which investors trade for both allocational and informational reasons. We use the model to study how market closures intrinsically affect investors' trading behavior and the return-generating process. The purpose of this analysis is to increase our understanding of the time variation in security trading and returns that are associated with regular market closures, such as the intraday and intraweek patterns in stock returns, volatility, and trading volume. We consider a stock market in which the exogenous information flow is homogeneous over time and the market closes periodically. When the market is open, investors trade the stock either to rebalance their overall portfolio of assets, which also includes other illiquid assets, or to speculate on future stock payoffs using their private information. In particular, investors adjust their asset portfolio by trading the stock in order to hedge the risk of illiquid assets. We refer to these trades as hedging trades and those motivated by private information as speculative trades. When the market is closed, " Hong is from the Graduate School of Business, Stanford University, and Wang is from the Sloan School of Management, Massachusetts Institute of Technology, and NBER. The authors thank Jennifer Huang for programming assistance and an anonymous referee for many valuable suggestions. They also thank Glenn Ellison, John Heaton, Craig Holden, Andrew Lo, Steve Slezak, Jeremy Stein, Rene Stulz (the editor), the NBER Asset Pricing Lunch Group, and participants of seminars a t the London School of Economics, New York University, Princeton University, the University of California a t Los Angeles, the University of Houston, the University of Illinois, the University of Pennsylvania, the 1995 WFA meetings, and the Indiana University Symposium on the Organization of Financial Trade and Exchange Mechanism for comments. Hong acknowledges support from an NSF Fellowship and Wang acknowledges support from a Batterymarch Fellowship, NSF grant SES-9414112, and the Laboratory for Financial Engineering a t MIT. 298 The Journal of Finance investors hold on to their closing positions from the previous trading period despite their desire to trade as new information arrives. Consequently, investors optimally adjust their trading strategies during the trading period (in anticipation of and following market closures), which gives rise to time variations in equilibrium returns. Market closures impact the economy in two ways: they preclude investors from trading in the market, and they prevent investors from learning about the economy by observing market prices and trading activities. The lack of trading increases the risk of holding the stock over closures, causing investors to reduce their hedging trade at the market close. The anticipated decrease in investors'hedging trade tends to make the stock price decrease over time as a larger premium is demanded on the stock, and tends to make the stock price less sensitive to investors'hedging needs. The lack of market prices as a source of information gives rise to time variation in the information asymmetry among investors. While information asymmetry increases during the closure, it often decreases as trading continues after the market reopens. The decrease in information asymmetry tends to make the stock price increase as a smaller premium is demanded on the stock, and tends to make the stock price more sensitive to investors' private information on future payoffs as more private information is impounded into the price. The actual time variation in the stock price is determined by the interaction of these two effects: the effect of time-varying hedging trade and the effect of time-varying information asymmetry. The interaction between these two effects can generate a rich set of patterns in stock returns. For example, when the effect of time-varying hedging trade dominates, both the mean and volatility of stock returns decrease over time during the trading periods. When the effect of time-varying information asymmetry dominates, both the mean and volatility increase over time. For some parameter values, the effect of time-varying hedging demand dominates around market open and the effect of time-varying information asymmetry dominates around market close. In this case, both the mean return and return volatility are U-shaped during the trading periods, higher around the open and close and lower during midperiod. Additionally, when decreasing information asymmetry causes the stock price to increase during the day, the return over trading periods is higher than the return over nontrading periods. Also, trading reveals investors' private information, which moves the price; hence returns over the trading periods tend to be more volatile than returns over the nontrading periods. Furthermore, the information accumulation during a market closure gives rise to high trading volume at the open, and the reduction in investors'hedging positions at the end of a trading period can give rise to high trading volume at the close. The interaction between investors' hedging trade and the market's information flow also gives rise to other interesting phenomena. For example, as investors adjust their hedging trade in anticipation of future market closures, the endogenous information flow in the economy also changes. As the level of hedging trade decreases at the close, price changes are more likely 299 Trading and Returns under Periodic Market Closures to be caused by speculative trade, and hence are more informative about investors' private information on future payoffs. As a result, closures can make market prices more informative about stock payoffs by reducing the level of "noise" in stock prices from hedging trade. There is an extensive literature on the empirical patterns of stock returns and trading activities associated with market closures. These patterns include the following. a. Intraday mean return and volatility are U-shaped.1 b. Intraday trading volume is U-~haped .~ c. Open-to-open returns are more volatile than close-to-close returns." d. Weekend returns are lower than weekday return^.^ e. Returns over trading periods are more volatile than returns over nontrading periods." Many of these patterns are robust with respect to different market inicrostructures (such as the NYSE, Nasdaq, and the interbank market of currencies). The observed patterns have generated strong interest in developing theoretical models to understand them. Admati and Pfleiderer (1988, 1989) and Foster and Viswanathan (1990, 1993) analyze how investors' discretion in timing their liquidity trade can lead to endogenous concentration of trades and price changes. Their models, however, leave the actual timing of concentration in trade and price changes undetermined. Additional assumptions on the time-variation of liquidity trade and/or information arrival are needed in order to produce the empirical patterns that are punctuated by closures. Brock and Kleidon (1992) point out the link between time-variation in market activity and closures. They solve for investors' optimal marketmaking policies under periodic market closures. Unfortunately, their analysis is in a partial equilibrium setting and cannot speak to the equilibrium patterns in return and trading. Using a noisy rational expectations equilibrium setting, Slezak (1994) examines the impact of closure on equilibrium returns by comparing two equilibria, the one with closure and the other without closure. The difference in prices between these two cases suggests that market closure may help to explain some of the observed patterns. Slezak's (1994) results, however, depend crucially on the exogenous specification of the liquidity trade. Under the assumption that the liquidity trade is constant over time, the higher risk (thus lower liquidity) before and after a closure leads to higher price volatility. If investors can instead allocate 'See, for example, Andersen and Bollerslev (1997), Gerety and Mulherin (1994), Harris (1986, 1988, 1989), Kleidon and Werner (1996), Lockwood and Linn (1990), Rogalski (1984), Smirlock and Starks (1986), and Wood, McInish, and Ord (1985). See, for example, Chan et al. (1996) and Jain and Joh (1988). See, for example, Amihud and Mendelson (1987, 1991), Cao, Choe, and Hatheway (1995), Chan et al. (1996), and Stoll and Whaley (1990). See, for example, French (1980), Gibbons and Hess (1981), and Keim and Stambaugh (1984). "ee, for example, Amihud and Mendelson (1991), Barclay, Litzenberger, and Warner (1990), Fama (1965), French and Roll (1986), and Oldfield and Rogalski (1980). 300 The Journal o f Finance their trade accordingly, they may actually cut back their liquidity trade at the close, causing price volatility to decrease, not increase. Moreover, the intuition from comparing two different equilibria (with and without closure), though helpful, is inconclusive in explaining the actual time patterns. After all, these patterns appear in a single, intertemporal equilibrium, and hence need to be derived as the outcome of such an equilibrium. Our model differs from existing models in several dimensions. First, we explicitly model investors' allocational and informational trades simultaneously. This stands in contrast to the noisy rational expectations models in the literature, in which allocational trade (liquidity trade) is exogenously specified. As we show in the paper, the fact that investors can choose the timing and size of their allocational trades is important in understanding the equilibrium return and trading pattern^.^ Second, we focus on how market closures intrinsically affect investors' trading behavior and the return-generating process. In particular, we examine how closures generate endogenous time-variation in trading activity, information arrival, and price movements. Third, we derive the time patterns of return and trading activity from a single intertemporal equilibrium, which is different from Slezak (1994) who relies on a comparative static analysis of stationary equilibria.? Fourth, we assume a competitive market and avoid strategic and market microstructure issues. By analyzing periodic market closures, we focus on those effects on equilibrium returns and trading activities that are solely associated with closures. We show that only periodic market closures are needed to qualitatively generate all the empirical patterns mentioned above. The paper proceeds as follows. Section I describes the model. Section I1 defines the notion of equilibrium and Section I11 discusses the general solution of equilibrium. Section IV analyzes how market closures affect investors' hedging trade and equilibrium returns. Section V further examines the effect of information asymmetry on trading activity and stock returns. Section VI concludes. The Appendixes provides technical details and proofs. " Admati and Pfleiderer (1988, 1989) and Foster and Viswanathan (1990, 1993) allow some of the liquidity traders to time their trade of given sizes. But they do not provide a complete justification for the behavior of liquidity traders. For example, trade sizes are exogenously specified and not all investors can time their trade. See also Spiegel and Subrahmanyan (1995). Our model differs from Slezak (1994) in several other ways as well. In our model, two things are present during market closures: new information (both public and private) on asset payoffs and shocks to investors' allocational demand for stock. In Slezak's model, only the former is present. Thus, in the absence of any new information on stock payoffs (public and/or private), investors still desire to trade during a closure in our model but not in Slezak's model. In other words, in the absence of new information on stock payoffs, a closure in our model still affects the equilibrium, but a closure in Slezak's model does not. In this sense, the closure in Slezak's model is more like a pure information event such as a news arrival. Furthermore, in our model, the repeated nature of closures is important in generating the return patterns. In particular, what happens around the market close is related to past and future openings of the market, and what happens around the open is related to closures in the past and future. In Slezak (1994), there is a single closure, the open is not affected by the future close, and the close is not affected by past open. 301 Trading and Returns under Periodic Market Closures