Sell-order liquidity and the cross-section of expected stock returns

Abstract

We estimate buy- and sell-order illiquidity measures (lambdas) for a comprehensive sample of NYSE stocks. We show that sell-order liquidity is priced more strongly than buy-order liquidity in the cross-section of equity returns. Indeed, our analysis indicates that the liquidity premium in equities emanates predominantly from the sell-order side. We also find that the average difference between sell and buy lambdas is generally positive throughout our sample period. Both buy and sell lambdas are significantly positively correlated with measures of funding liquidity such as the TED spread as well option implied volatility.

Introduction

The liquidity of an asset market refers to the ability of investors to buy and sell significant quantities of the asset, quickly, at low cost, and without a major price concession. A series of market crises that were associated with major decreases in liquidity, including the crash of 1987, the Asian crisis of 1998, and the credit crisis of 2008, has focused the attention of market participants, regulators and researchers on liquidity in financial markets. A major question is whether investors demand higher returns from less liquid securities. Amihud and Mendelson (1986), Brennan and Subrahmanyam (1996), Brennan, Chordia, and Subrahmanyam (1998), Jones (2002), and Amihud (2002) all provide evidence that liquidity is an important determinant of expected returns. More recently, following the finding of commonality in liquidity by Chordia, Roll, and Subrahmanyam (2000), Pastor and Stambaugh (2003) and Acharya and Pedersen (2005) relate systematic liquidity risk to expected stock returns.

An important issue that arises in studies relating liquidity to asset prices and returns is the empirical proxy that is used for illiquidity. The simplest proxy is the bid-ask spread, which is the difference between the price effects of a zero size buy and a zero size sell. Other proxies relate the size of the trade to the size of the price movement (i.e., they measure the price impact of trades), while assuming that the price effects of buys and sells are symmetric. This price impact approach finds theoretical support in the classic Kyle (1985) model, which predicts a linear relation between the net order flow and the price change. Amihud (2002) proposes the ratio of absolute return to dollar trading volume as a measure of illiquidity. In an alternative approach, Brennan and Subrahmanyam (1996) suggest measuring illiquidity by the relation between price changes and order flows, based on the analysis of Glosten and Harris (1988). Pastor and Stambaugh (2003) measure illiquidity by the extent to which returns reverse after high trading volume, an approach based on the notion that such a reversal captures the impact of price pressures due to demand for immediacy. Hasbrouck (2009) provides a comprehensive set of estimates of these and other measures of illiquidity, including the Roll (1984) measure.

All these measures presume a symmetric relation between order flow and price change. In contrast, we allow for an asymmetric relation and estimate separate buy and sell measures of illiquidity (“lambdas”) for a large cross-section of stocks over a 26-year period, using a modified version of the Brennan and Subrahmanyam (1996) approach, which assumes that price responses are linear, and is an adaptation of the Glosten and Harris (1988) method. Any differences in buy- and sell-order illiquidity measures and their associated return premia may cast light on the mixed results in studies of the relation between liquidity and the cross-section of expected stock returns. For example, Brennan and Subrahmanyam (1996) find a negative relation between the bid-ask spread and expected returns, and Spiegel and Wang (2005) find no significant relation between expected returns and either bid-ask spreads or Amihud's (2002) measure of liquidity, after controlling for trading activity measures such as share volume and turnover. Thus, we look for evidence on the pricing of the buy- and sell-order illiquidity measures in the cross-section of expected stock returns.

We find that sell-order illiquidity is priced more strongly in the cross-section of expected stock returns than is buy-order illiquidity. This result continues to obtain after controlling for other known determinants of expected returns such as firm size, book-to-market ratio, momentum, and share turnover. The finding is robust to the Fama and French (1993) risk factors as well as to the estimation of factor loadings conditional on macroeconomic variables and firm characteristics such as size and book-to-market ratio. Finally, the pricing of sell-order illiquidity is also economically significant. A one-standard-deviation change in the sell lambda results in an annual premium that ranges from 2.9% to 3.7%.

We also study the time-series behavior of buy and sell lambdas and examine their cross-sectional determinants. We find reliable evidence that sell lambdas exceed buy lambdas.¹ Market-wide averages of buy and sell lambdas are significantly positively correlated with the TED spread (the spread between London Interbank Offer Rate (LIBOR) and U.S. Treasury bills) as well as with the implied market volatility measure, VIX, both of which have been used as measures of funding liquidity by Asness, Moskowitz, and Pedersen (2009). Cross-sectional determinants of buy and sell lambdas accord with those established earlier in the literature, and the time-series average of the cross-sectional correlations between the estimated buy and sell lambdas of individual securities is about 0.72.

The remainder of the paper is organized as follows. Section 2 presents the method for estimating the lambdas and describes the data. Section 3 presents some time-series and cross-sectional characteristics of the estimated lambdas. Section 4 presents the average returns on portfolio sorts, while Section 5 describes the methodology and results of asset pricing regressions. Section 6 concludes.