Liquidity Risk and Expected Stock Returns

Lubos Pastor, Robert F. Stambaugh. "Liquidity risk and expected stock returns." The Journal of Political Economy; Jun 2003: 642-685. (Link)

In this paper, Pastor and Stambaugh analyze whether market wide liquidity should be considered in asset pricing models.  Intuitively, stocks that are more sensitive to changes in market wide liquidity will present greater risk during times of low liquidity.  Investors should demand a higher return from these high liquidity risk stocks to compensate for the additional risk.  The authors develop a measure of liquidity risk and use a sample from 1966 — 1999 to test their hypothesis.  

The measure of liquidity is based on the association between temporary changes in price and order flow.  The expectation is that stocks will experience greater price reversions on days following low liquidity.  This is based on Campbell, Grossman, and Wang (1993) and is backed by their empirical analysis.  The liquidity risk of stock i in month t is the ordinary least squares coefficient, $\gamma_{i,t}$, when excess stock returns of d+1 are regressed on daily dollar volume, signed by excess market returns, on day d.  

\[r_{i,d+1,t}^e = \theta_{i,t}r_{i,d,t}+\gamma_{i,t}\text{sign}(r_{i,d,t}^e)v_{i,d,t}+\epsilon_{i,d+1,t}\]

Where $r_{i,d,t}^e$ is the excess return of stock i on day d in month t, and $v_{i,d,t}$ is the dollar volume of stock i on day d in month t.  

If a stock makes a large reversal on day d+1 after small dollar volume and positive returns on day d, this implies poor liquidity on day d and hence a negative value of $\gamma_{i,t}$.

This regression is done for each month t and stock i in the period 1962 — 1999.  The monthly market wide liquidity is then calculated using an equal weighted average of each stock’s liquidity.  The series is scaled over time to account for increases in the dollar’s value.  This measure of liquidity is shown below.  

Many of the downward spikes in liquidity accompany market downturns, a feature that has been previously noted in the literature.  The largest of these spikes in Figure 1 occurs during the market crash of October 1987.  Other notable spikes include November 1973 during the mideast oil embargo and September 1998 after the collapse of LTCM.  The authors confirm these were times of low liquidity and so the graph provides a cursory check that the measure of market liquidity is reasonable.

Figure 1. Aggregate liquidity

Finally, the liquidity series is regressed on its lag and the residual is taken to be a measure of liquidity innovation in month t, $\mathcal{L}_t$.  The authors are interested in finding if this liquidity innovation can be used as a state variable in asset pricing since changes to market wide liquidity should have effects across all stocks.  

To assess the importance to asset pricing, the authors regress excess returns on liquidity innovation, along with the three Fama and French (1993) factors. 

\[r_{i,t} = \beta_{i}^0 + \beta_{i}^\mathcal{L}\mathcal{L}_{t}+\beta_{i}^\mathrm{M}\text{MKT}_{t}+\beta_{i}^\mathrm{S}\text{SMB}_{t}+\beta_{i}^\mathrm{H}\text{HML}_{t} + \epsilon_{i,t}\]

The slope of liquidity innovation is given by $\beta_{i}^\mathcal{L}$ and represents the liquidity beta of stock i.  Stocks are sorted into portfolios based on their liquidity betas, using only data available at the time of the sort, and the portfolio returns are tracked over the next 12 months.  Every 12 months the liquidity betas are re-calculated and stocks sorted into new portfolios using the new data available up to that point.  The 12 month returns for each decile are connected to form a return series for each decile across the entire sample period of 1966 — 1999.  

Note that in the regression, $\beta_i^\mathcal{L}$ only represents a measure of historical liquidity beta and is used to sort stocks into portfolios.  However, the authors show that it provides an accurate predictor of post-ranking liquidity beta over the following 12 month period when returns are measured.  Panel A of Figure 3 shows the post-ranking liquidity betas of portfolios ranked by historical liquidity betas.  

Table 3
Properties of Portfolios Sorted on Predicted Liquidity Betas

To show that market liquidity is indeed a priced factor, Pastor and Stambaugh show that there are different expected returns for the portfolios sorted by liquidity beta.  The alphas for each decile are computed with respect to the CAPM, Fama-French factors, and the 4-factors of Fama-French and momentum.  The 10-1 alpha spreads on equally weighted portfolios are all positive and significant as shown in the table below.  The results also hold across sub-periods and when the decile portfolio is value weighted.  

Table 4
Alphas of Value-Weighted Portfolios Sorted on Predicted Liquidity Betas

Pastor and Stambaugh find that portfolios with higher liquidity risk provide a positive risk premium which is not explained by the other common pricing factors.  This reflects the intuition that investors are averse to illiquid stocks, especially during market downturns, and thus will demand a higher return from them.  They also find that the returns associated with liquidity risk are not accounted for with the Fama-French three factors or momentum.  This evidence indicates that market wide liquidity is an important factor for asset pricing.