قیمت گذاری ریسک نقدینگی سیستماتیک: شواهد تجربی از بازار سهام ایالات متحده

In this study, we examine whether aggregate market liquidity risk is priced in the US stock market. We define a bivariate Garch (1,1)-in-mean specification for the market portfolio excess returns and the changes in the standardized number of shares in the S&P 500 Index, the aggregate market liquidity proxy. The findings, based on monthly data, suggest that systematic liquidity risk is priced in the US over the period January 1973–December 1997. The liquidity premium represents a non-negligible, negative and time-varying component of the total market risk premium whose magnitude is not influenced by the October’87 Crash.

Liquidity is a fundamental concept in finance which can, broadly speaking, be defined as the time and cost which are associated with the liquidation (or purchase) of a given quantity of financial securities. Liquidity thus refers to both the time and costs associated with the transformation of a given position into cash and vice versa. Typically, continuous-time arbitrage or equilibrium asset pricing models ignore liquidity since the cost and time required to transfer financial wealth into cash is assumed to be nil and since trading is often ruled out by these equilibrium asset pricing models. Yet, in practice, recent financial crises (such as in Asia or in Russia) and the debacle of the LTCM hedge fund suggest that at times of tight credit and market conditions, liquidity can decline and even temporarily dry out. This leads investors to aggressively bid for the safest, that is, the most liquid securities, which raises their price relative to the one of their less liquid counterparts. If market liquidity evolves randomly, securities or portfolios that covary more with liquidity, should offer a lower liquidity risk premium. We ask ourselves whether market liquidity risk is priced and whether the omission of stochastic market liquidity shocks may explain the market risk premium’s lack of significance reported in former empirical studies (see Table 1 in Scruggs (1998)). We attempt to test the latter conjecture and to further characterize the importance, magnitude and variations of the systematic liquidity premium as a component of the total expected excess market rate of return. We focus on a broader definition of systematic liquidity in order to examine whether long term – in our case, monthly – random movements in market liquidity affect stock prices to the extend that their returns covary with changes in market liquidity. Such a relationship is often implicitly assumed. For instance, when used to explain the small firms effect, or to justify the higher expected returns of less liquid financial instruments such as hedge funds. Recently, a number of studies have examined the presence of commonality in individual stocks’ liquidity measures. Hasbrouck and Seppi (1999) look at the 30 constituent stocks from the Dow Jones Industrial Index and conclude, on the basis of principal component and canonical correlation analyses, that the source of commonality in intra-daily liquidity measures for these stocks is rather small. Chordia et al. (2000) reach a distinct conclusion however after examining the sources of commonality in the changes of several daily liquidity measures for 1169 US stocks during the year 1992. Using a market model for liquidity, they find that common market and industry influences on individual stock’s liquidity measures such as their quoted spreads or depth are significant and material. In particular, they find that a stock’s bid and ask spread is negatively related to the aggregate level of market trading. They interpret this result as being consistent with a diminution in inventory risk resulting from greater market trading. Their findings are however less supportive of common factors driving asymmetric information based stock trading. Thus, their results can explain common liquidity factors influence on stocks’ expected returns through increased average trading costs. Huberman and Halka (1999) also explore the commonality in liquidity, using the depth as well as the bid–ask spread as proxies for the liquidity of 240 US traded stocks. Their findings are similar to the results of Chordia et al. (2000), and they attribute commonality in stocks’ liquidity to the presence of noise traders. These studies have left open the question as to whether illiquidity is a systematic risk factor, in which case stocks that are more sensitive to unexpected market illiquidity shocks, should offer higher expected returns. An exception is to be found in Pastor and Stambaugh (2001) who introduce a market-wide liquidity measure and show that cross-sectional expected stock returns are related to fluctuations in aggregate liquidity. Along the same lines, the recent study by Amihud (2002) introduces a new measure of illiquidity defined as the ratio of a stock’s absolute daily return over its daily trading volume (in dollars) and applies it to NYSE stocks traded during the period 1964–1997. He tests whether expected market liquidity has a positive effect on ex ante stock excess returns and whether unexpected market illiquidity has a negative effect on contemporaneous stock returns. The empirical results support the conjectured hypotheses. By examining whether aggregate market liquidity risk is priced in a time-series framework, we intend to complement the latter stream of recent literature on commonality in stocks’ liquidity risk measures. For that purpose, we examine the significance and magnitude of systematic liquidity risk pricing for an actively traded well-diversified US stock portfolio, that is the S&P 500 stock market index. Two important difficulties are related with the concept of aggregate market liquidity risk. First, one needs to define a proxy for the state variable describing aggregate market liquidity and second to specify a joint stochastic process for the latter and the excess returns of the market portfolio. While several candidate variables have emerged in the market microstructure literature to measure liquidity (for instance, Kyle’s lambda (1985), the bid–ask spread, the effective spread or the market depth), they are essentially intended as proxies of the liquidity of individual stocks. Furthermore, these measures are primarily suited to study the cross-sectional and time-series determinants of liquidity over short-term horizons. We need a proxy for longer horizons market-wide liquidity shocks. For that purpose, we chose to define the market liquidity as the number of traded shares in the S&P 500 Index during a month. The changes in the state variable are represented by the monthly relative changes in the number of traded shares in the S&P 500 Index. Recent empirical evidence tends to support the choice of the latter liquidity risk proxy. Indeed, Chordia et al. (2000) findings suggest that the number of shares traded may be considered as a measure capturing the sources of commonality in market-wide liquidity arising from aggregate inventory risk. They also conclude that greater market-wide volume leads to reduced bid–ask spread measures. We further assume that the market excess returns and the liquidity state variable jointly follow a bivariate Garch (1,1)-in-mean process with possibly time-varying unitary market and liquidity risk premia in the general specification of the model. In the latter, the unitary liquidity and market risk premia are driven by a set of instrumental variables that capture business cycles effects on investors’ risk aversion. The model is tested in its general form and in various nested specifications over the period January 1973–December 1997. The structure of the paper is the following: Section 2 provides a heuristic justification for the sign of the liquidity risk premium coefficient. Section 3 further describes the methodology and the data used to conduct the empirical tests. Section 4 discusses the main empirical results on the pricing of liquidity risk in the S&P 500 excess returns both under a constant and a time-varying specification of the unitary liquidity risk premium coefficient. Section 5 examines the stability of the results and the role of the October’87 Crash on the pricing of systematic liquidity risk. Section 6 discusses the economic significance of the systematic liquidity risk premium. In Section 7, we conclude by emphasizing the main findings, limitations and research questions raised by this study.

In this study, we rely on a bivariate Garch (1,1)-in-mean specification for the stock market excess returns in order to examine whether systematic liquidity risk is priced and whether the sign of the unitary liquidity risk premium is negative. The bivariate Garch (1,1)-in-mean specification is tested on monthly excess market returns of the S&P 500 Index during the period January 1973–December 1997. We use the number of shares traded in the S&P 500 per month as a proxy measure for aggregate liquidity. Overall, the results suggest that liquidity risk is indeed priced during the entire as well as over sub-periods in the US. The sign of the liquidity risk premium is significantly negative and time-varying. Furthermore, according to these preliminary results, the unitary market risk premium becomes insignificant within the general bivariate Garch (1,1)-in-mean model with constant risk premia. According to our results, systematic liquidity risk dominates market risk and is insensitive to the introduction of extreme liquidity events such as the October’87 Crash. It is important to stay aware of the joint hypothesis testing implications of this preliminary investigation into systematic liquidity risk pricing on the US stock market. Indeed, our results are clearly influenced by the specification of the excess market return generating model and of the time-varying unitary liquidity risk premium retained and ultimately by the systematic liquidity proxy variable chosen. It is interesting to mention that using a different market “illiquidity” risk measure, Amihud (2002) finds a positive relationship between expected market illiquidity and expected stock returns. The latter is consistent with our findings given our specific proxy for systematic “liquidity”. The theoretical implications of these results are also worth exploring since they raise questions about the potential biases in traditional asset pricing models that ignore systematic liquidity risk. As pointed out by Chordia et al. (2000), commonality in liquidity risk is still an emerging stream of theoretical and empirical literature. The empirical results found in this study should be extended along several dimensions to deepen our understanding of the origins, the time-series properties and the international cross-effects of systematic liquidity risk pricing. Finally, these empirical results emphasize the need to develop inter-temporal asset pricing models that endogeneize agents’ need to hedge against inter-temporal systematic liquidity shocks. This would allow us to reconsider and perhaps explain some empirical anomalies within a rational asset pricing framework that accounts for the pricing of systematic liquidity risk.