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We build a model that helps to explain why increases in liquidity—such as lower bid–ask spreads, a lower price impact of trade, or higher turnover–predict lower subsequent returns in both firm-level and aggregate data. The model features a class of irrational investors, who underreact to the information contained in order flow, thereby boosting liquidity. In the presence of short-sales constraints, high liquidity is a symptom of the fact that the market is dominated by these irrational investors, and hence is overvalued. This theory can also explain how managers might successfully time the market for seasoned equity offerings, by simply following a rule of thumb that involves issuing when the SEO market is particularly liquid. Empirically, we find that: (i) aggregate measures of equity issuance and share turnover are highly correlated; yet (ii) in a multiple regression, both have incremental predictive power for future equal-weighted market returns.

A growing body of empirical evidence suggests that liquidity predicts stock returns, both at the firm level and in the time series of the aggregate market. Amihud and Mendelson (1986), Brennan and Subrahmanyam (1996), and Brennan et al. (1998) find that measures of increased liquidity, including a low price impact of trade, low bid–ask spreads and high share turnover, are associated with lower future returns in cross sections of individual firms. More recently, Chordia 2000 and Chordia 2001, Hasbrouck and Seppi (2001), and Huberman and Halka (2001) document that there is considerable time-variation in market-wide liquidity, and Amihud (2002) and Jones (2002) show that these market-wide movements in liquidity also forecast aggregate returns.1 The traditional explanation for why liquidity might affect expected returns is a straightforward one (Amihud and Mendelson, 1986; Vayanos, 1998). Investors anticipate having to sell their shares at some point in the future, and recognize that when they do so, they will face transactions costs. These costs can stem either from the inventory considerations of risk-averse market makers or from problems of adverse selection.2 But in either case, when the transactions costs are greater, investors rationally discount the asset in question by more. This story would seem to fit most naturally with the purely cross-sectional results. In particular, if we compare two stocks, and one is observed to have permanently lower bid–ask spreads and price impacts than the other, as well as higher turnover, it is plausible that the more liquid stock would have a somewhat higher price, and hence lower expected returns. It is less clear whether the same story can be carried over without modification to explain the time-series results for the aggregate market. First of all, we do not have a well-developed understanding of what drives the common time-series variation in measures of liquidity. For example, though it is a possibility, it seems more of a stretch to argue that there are large swings in the degree of asymmetric information about the market as a whole. Second, as Jones (2002) shows, and as we verify below, the predictive power of aggregate liquidity for market returns, particularly for equal-weighted returns, is large. In a univariate regression, a one-standard-deviation increase in stochastically detrended turnover (equivalent to turnover going from, say, the 1932–1998 mean of 30 percent up to 42 percent in a given year) reduces expected returns on the CRSP equal-weighted index over the next year by approximately 13 percent. In this paper, we develop an alternative theory to explain the connection between liquidity and expected returns.3 Our focus is on understanding why time-variation in liquidity, either at the firm level or for the market as a whole, might forecast changes in returns. We implicitly accept the premise that the traditional theory is best suited to explaining why permanent cross-firm differences in liquidity are associated with permanent cross-firm differences in expected returns. 4 Our model rests on two sets of assumptions—one about market frictions, and the other about investor behavior. With respect to the former, we assume that there are short-sales constraints. With respect to the latter, we posit the existence of a class of irrationally overconfident investors, where we think of overconfidence as a tendency to overestimate the relative precision of one's own private signals. In our setting, this form of overconfidence has two distinct manifestations. First, when overconfident investors receive private signals, they tend to overweight them; this leads to “sentiment shocks” that can be either positive or negative. Second, when overconfident investors observe the trading decisions of others, they tend to underreact to the information contained in these decisions, since they (erroneously) consider others to be less well-informed than they are. This aspect of overconfidence lowers the price impact of trades, thus boosting liquidity generally.5 Given these assumptions, our story goes as follows. At some initial date, the irrational investors receive private signals about future fundamentals, which they overreact to, generating sentiment shocks. The short-sales constraint implies that irrational investors will only be active in the market when their valuations are higher than those of rational investors—i.e., when their sentiment is positive and when the market is, as a result, overvalued. When the sentiment of irrational investors is negative, the short-sales constraint keeps them out of the market altogether. At a subsequent date, there is a round of trading by an informed insider. Since the irrational investors also tend to make the market more liquid in the face of such informed trading, measures of liquidity provide an indicator of the relative presence or absence of these investors, and hence of the level of prices relative to fundamentals. This theory also provides a novel perspective on a set of issues in corporate finance which have been the focus of much work recently. Stigler (1964), Ritter (1991), Loughran and Ritter (1995), Speiss and Affleck-Graves (1995), and Brav and Gompers (1997), among others, find that firms that issue equity have low stock returns in the subsequent few years—this is the so-called “new issues puzzle”. Baker and Wurgler (2000) uncover an analogous pattern in the aggregate data: if economy-wide equity issuance is high in a given year, the market as a whole performs poorly in the next year. The usual interpretation of these facts is that the managers making issuance decisions are “smart money”: they have a better estimate of the long-run fundamental value of their firms than is embodied in the current market price, and they purposefully time their financing decisions to exploit this advantage.6 We do not dispute that this smart-money mechanism may be part of what is going on. After all, in Graham and Harvey (2001), managers place market timing high on their list of reasons to issue equity. However, our model offers a potentially complementary way of rationalizing these phenomena, without requiring a high degree of managerial timing ability. Whether or not managers make an attempt—smart or misguided—to come up with independent estimates of fundamental value, their financing decisions may still convey information about future returns, if they follow a simple and plausible rule of thumb. In particular, suppose that managers are more willing to issue equity in periods when the market for new offerings is more liquid, in the sense of there being a reduced adverse price impact upon the announcement of a new issue.7 If they behave this way, their financing choices will be a passive mirror of market liquidity, and will thus, for the reasons outlined above, tend to forecast returns. Again, this mechanism can work even if managers never bother to take a stand on the relationship between prices and long-run fundamental value. We view the contribution of this paper to be primarily a theoretical one, and as such do not attempt to provide a definitive empirical test of the model. Nevertheless, we do briefly examine some aggregate data on turnover, equity issuance and stock returns, and document the following patterns. First, consistent with the corporate-finance element of our theory, there is a very strong correlation between turnover in a given year and the share of equity in total external finance. The simple correlation coefficient between the two variables is as high as 0.64 (in the period prior to the deregulation of the brokerage industry), and the strength of this relationship is largely unaffected by standard controls for valuation levels, such as the dividend-price ratio, and past returns. Thus our premise that equity issuance is a mirror of market liquidity seems to be borne out in the data. Second, both turnover and the equity share have considerable forecasting power for year-ahead returns, especially when we focus on an equal-weighted, as opposed to a value-weighted index. This is true when each variable is considered separately from the other; in this respect we are just confirming the earlier work of Jones (2002) and Baker and Wurgler (2000). Moreover, in spite of their high correlation with one another, each plays a significant role when they are entered in the regressions together, and the overall explanatory power for future returns is substantially augmented. In the context of our model, this can be thought of as reflecting the notion that both turnover and the equity share are noisy measures of “true” market liquidity. The third message that we take away from our brief empirical exercise is that the forecasting power of turnover appears to be large in economic terms. As already noted, in a simple univariate regression, a one-standard-deviation increase in detrended turnover implies a downward revision in year-ahead equal-weighted expected returns of roughly 13 percent. While we do not have a specific calibration of the effects that might be generated by a more traditional model, and while the standard error associated with our point estimate is large, this estimate would appear to cast doubt on the notion that the time-variation in expected market returns arises solely from the reaction of rational investors to fluctuations in trading costs. The rest of the paper proceeds as follows. In Section 2, we develop our basic model, which shows how measures of secondary-market liquidity such as price impact and turnover can forecast returns. In Section 3, we extend the model to incorporate firms’ equity issuance decisions, and demonstrate how these too can forecast returns. In Section 4, we discuss some of the model's implications in light of existing evidence, and in Section 5, we present our own empirical results. Section 6 concludes.

The basic idea of this paper is that, in a world with short-sales constraints, market liquidity can be a sentiment indicator. An unusually liquid market is one in which pricing is being dominated by irrational investors, who tend to underreact to the information embodied in either order flow or equity issues. Thus high liquidity is a sign that the sentiment of these irrational investors is positive, and that expected returns are therefore abnormally low. The model we have used to formalize this idea is admittedly very simplistic. For example, it lacks any real dynamic element, and hence cannot speak to issues such as the horizon over which return predictability plays itself out. The model also requires—in addition to the short-sales constraints—a strong assumption, namely that the same investors who are subject to sentiment swings are also the most prone to underreact to certain kinds of subtle news. While one can appeal to a variety of a priori arguments and experimental evidence to motivate the plausibility of this assumption, we believe that our use of it is ultimately best defended on the grounds of the explanatory mileage that it yields. In particular, the model is able to provide a unified explanation for a wide range of liquidity-related phenomena in stock markets. Many of the individual findings— from the return-forecasting power of measures of trading activity and trading costs, to the new issues puzzle and the existence of hot issue markets—have heretofore been rationalized separately, each with a story of its own. But as our preliminary empirical work suggests, these facts are intimately related to one another. So it is natural to want to be able to understand them within the context of a single conceptual framework. This paper has been a first attempt at developing such a framework; it would seem that there is room for much more to be done in this vein. Ranging further afield, one might ask whether our liquidity-as-sentiment approach can also shed some light on the workings of other, more ‘‘real’’ asset markets, such as those for physical corporate assets or for houses. Many of these real markets are also characterized by a strong link between prices and measures of both trading volume and liquidity. This link has been studied by Shleifer and Vishny (1992) , Stein (1995) , and Pulvino (1998) , all of whom assume rational investors and emphasize instead the roles of borrowing constraints and asset specificity. But perhaps investor sentiment also has some part to play in explaining the joint behavior of prices and liquidity in these other types of asset markets. 30 It would be interesting to develop this conjecture more completely, and to see whether it yields any novel empirical predictions