The divergence of liquidity commonality in the cross-section of stocks

Abstract

This paper demonstrates that the cross-sectional variation of liquidity commonality has increased over the period 1963–2005. The divergence of systematic liquidity can be explained by patterns in institutional ownership over the sample period. We document that our findings are associated with similar patterns in systematic risk. Our analysis also indicates that the ability to diversify systematic risk and aggregate liquidity shocks by holding large-cap stocks has declined. The evidence suggests that the fragility of the US equity market to unanticipated events has increased over the past few decades.

Introduction

The literature on asset liquidity has received much attention in recent years. It is now widely accepted that the liquidity of financial assets changes over time, and that these time variations are governed by a significant common component in the liquidity across assets (see, e.g., Chordia, Roll, and Subrahmanyam, 2000; Hasbrouck and Seppi, 2001, Amihud, 2002, Korajczyk and Sadka, 2008). Current literature focuses on either the cross-sectional differences in asset liquidity or the existence of commonality. This paper studies the evolution of systematic liquidity in the cross-section of US stocks from 1963 through 2005, and the implications for asset returns.

Following Chordia, Roll, and Subrahmanyam (2000) we use the market model of liquidity to estimate the sensitivity of each firm's liquidity to variations in market liquidity. To proxy for the changes in liquidity we use the daily change in (the log of) Amihud's (2002) measure of firm's illiquidity. To the extent that the sensitivity to market liquidity is an indicator of systematic liquidity risk, we find that systematic liquidity, which we define as the sensitivity of the stock's liquidity to market liquidity, has decreased significantly for small-cap firms, but increased significantly for large-cap firms (size quintiles 1 and 5, respectively). We show that this increased divergence of systematic liquidity in the cross-section of firms can be explained by the patterns of institutional ownership over the sample period. Moreover, the temporal patterns of systematic liquidity have important implications for asset prices.

One of the key developments in the US equity market over our sample period is the substantial increase in institutional investing and index trading. The estimated percent of US shares held by institutional investors rose from 21% in 1965 to 35% in 1980 and 50% in 2002 (source: NYSE). It is well known that increases in institutional investing and index trading have played a key role in the increases of trading volume and liquidity levels of US equity markets.¹ What is less known is how they have affected the commonality in liquidity. We investigate the effects of the increased institutionalization of the US equity markets on the systematic liquidity of stocks. We use the CDA/Spectrum data on institutional ownership of common stocks from January 1981 until December 2005. We find that, in the cross-section of firms, the sensitivity of the stock's liquidity to aggregate liquidity shocks increases with institutional ownership. These results support the argument in Chordia, Roll, and Subrahmanyam (2000) that institutional trading is a significant source of commonality of liquidity among stocks. Furthermore, examining institutional ownership by type of institution, we find that liquidity betas increase with ownership by investment companies and investment advisors, but not with ownership by other types of institutions.

Moreover, the increases in institutional ownership over time can explain the divergence of liquidity commonality. Institutional investing and index trading have been more concentrated in large-cap stocks than in small-cap stocks. Institutional herding is also more prevalent in large-cap stocks, especially those included in the S&P500 index. Some institutions are required to satisfy the “prudent man” rule, which may lead them to under-invest in small-cap stocks that are viewed as less prudent (see Del Guercio, 1996). Moreover, since the S&P500 is the most widely followed index by index funds and index arbitrageurs, index trading, especially trading related to stock index-derivative contracts, is also much more prevalent in large-caps stocks than in small-cap stocks. Consequently, indexation and institutionalization often have different effects on the behavior of large firms’ shares than on the behavior of small firms’ shares.² Gompers and Metrick (2001) find that institutional investors tend to increase demand for large-cap stocks and decrease demand for small-cap stocks, and that these demand shifts can explain part of the decline in the small-firm premium embedded in equity returns. We find that differences between the percentages of institutional ownership (especially ownership by investment companies and investment advisors) of large and small stocks cause differences in their sensitivities to aggregate liquidity. This can explain why large firms’ stocks have become more sensitive to market liquidity shocks relative to small firms’ stocks.³

Another feature of institutional and index trading is the use of security baskets as possible means of trading.^4,5 The model of Gorton and Pennacchi (1993) predicts that equity basket trading increases the commonality in liquidity for the constitute stocks in the basket, but reduces liquidity commonality for individually traded stocks. Since they are a dominant fraction of institutional and index trading, large-cap stocks are more likely to be a part of basket trading than small-cap stocks. Thus, Gorton and Pennacchi (1993) can explain why we find that the sensitivity of large-cap stocks to systematic liquidity shocks has increased over our sample period, while the sensitivity of small-cap stocks’ liquidity to systematic liquidity has declined. Further supporting their model, we find that the liquidity betas of S&P500 stocks have increased significantly relative to the liquidity betas of non-S&P500 stocks, over our sample period.

We also study the implications of the time patterns in systematic liquidity for asset returns. It is widely accepted that trading activity affects prices. If the factor causing the trading activity and its price impact is market-wide, then trading activity could also affect the systematic risk of firms’ returns. There is a growing body of literature which predicts that aggregate variables can affect both firm systematic liquidity (liquidity beta) and firm systematic return (return beta). For example, Chordia, Roll, and Subrahmanyam (2000), Coughenour and Saad (2004), and Vayanos (2004) suggest that changes in market volatility affect systematic liquidity by creating correlated trading patterns among investors and affecting the supply of liquidity by market makers, across many stocks. Since trading activity affects stock prices, this can increase the comovement of stock returns. In addition, the models of Kyle and Xiong (2001), Vayanos (2004), and Brunnermeier and Pedersen (2008), as well as the empirical findings of Ang and Chen (2002) and Hameed, Kang, and Viswanathan (2006), suggest that market return affects both systematic liquidity and systematic return. The underlying idea is that market declines reduce the capital available to money managers and market makers and force them to reduce their stock holdings in a manner that increases commonality in liquidity as well as the correlations in asset returns. In these studies, market volatility and market return typically affect liquidity betas and return betas by affecting the liquidity in the market, which suggests that market illiquidity may be another potential determinant of liquidity commonality and return commonality. Consistent with the studies above, we find that market volatility, market return, and market liquidity affect both firms’ systematic liquidity and firms’ systematic return.

In light of the common market determinants of systematic liquidity and systematic return, we conjecture that the divergence in liquidity commonality would translate to similar divergence in return commonality. Indeed, we show that return commonality exhibits a similar divergence: the systematic risk of different size groups estimated by using a market model of stock returns exhibit similar time trends to their respective systematic liquidity. We also find that time variations in systematic risk are significantly (positively) related to time variations in systematic liquidity. This relation is significantly stronger for large firms than for small firms.

Our results about systematic risk complement the work of Campbell, Lettau, Malkiel, and Xu (2001) that shows an increasing trend in idiosyncratic return volatility over the period 1962–1997. There are two main differences. First, focusing on the cross-section of firms, we show different size groups can have different patterns of systematic risk. Second, while Campbell, Lettau, Malkiel, and Xu (2001) essentially assume a beta of one for all stocks, we allow beta to vary across firms and over time, e.g., we use a market model for stock returns. This enables us to discuss time patterns in systematic risk (beta) as well as the idiosyncratic component. We find that idiosyncratic risk has increased for the small firms but has declined for the large firms. Most importantly, we show that the patterns of systematic risk that we have uncovered in the cross-section are highly related to systematic liquidity.

The increased divergence of liquidity in the cross-section of firms has important implications for the ability to diversify return volatility and aggregate liquidity shocks across firms. We find that the ability to diversify risk and liquidity shocks by holding relatively liquid, large-cap stocks has declined over the sample period of 1963–2005, both in absolute terms and relative to the diversification benefits of small-cap stocks. Our evidence suggests that the ability to diversify risk and liquidity shocks by holding an otherwise well-diversified, value-weighted portfolio has declined over time. In contrast, we find that the ability to diversify risk and liquidity shocks by holding shares of small firms has improved over time. This is particularly noteworthy because of the “flight to quality” in turbulent times from small-cap stocks to large-cap stocks.⁶ We also show that liquidity sensitivity to extreme market illiquidity events has diverged over time across large and small firms. This suggests that the fragility of the US equity market to unanticipated events has increased over the past few decades.

There are several additional reasons why the evolution of systematic liquidity across firms is an interesting topic of financial research. First, the evolution of liquidity across firms has implications for the efficient functioning of financial markets: Amihud, Mendelson, and Wood (1990) find that sudden unanticipated declines in liquidity have played a key role in the stock market crash of October 1987. Second, variations in (systematic and total) liquidity volatility affect the ability of arbitrageurs and derivative traders to exploit and eliminate “mispricing” (see, e.g., Kamara, 1988, Amihud and Mendelson, 1991, Pontiff, 1996, Mitchell and Pulvino, 2001; Lesmond, Schill, and Zhou, 2004; Korajczyk and Sadka, 2004, Sadka and Scherbina, 2007). Third, Longstaff, 2001, Longstaff, 2005 shows that asset illiquidity has a significant effect on the optimal portfolio choices of investors, leading them to abandon diversification as a strategy. Thus, our results are also imperative for active investment managers who rebalance their portfolios frequently. Last, since liquidity is associated with the price discovery process and, can thus affect the systematic and idiosyncratic volatility of stock returns (O’Hara, 2003), our study may also have implications for the recently documented pricing of idiosyncratic return volatility (Goyal and Santa-Clara, 2003; Ghysels, Santa-Clara, and Valkanov, 2006; Ang, Hodrick, Xing, and Zhang, 2006).

The remainder of the paper is organized as follows. Section 2 describes the data. Section 3 describes the evolution of systematic liquidity over the sample period of 1963–2005. In particular, Section 3.2 investigates the evolution of systematic liquidity for firms in the smallest and largest size quintiles. We then discuss some explanations for, and implications of, the cross-sectional divergence of systematic liquidity. In Section 4 we investigate the relation between institutional ownership of a firm's equity and its exposure to systematic liquidity. In Section 5 we study the relation between time variations in systematic liquidity and time variations in systematic risk. Section 6 analyzes the implications for the ability to diversify liquidity risk using small and large stocks. In Section 7 we examine the robustness of our results. Section 8 concludes.