In this paper published in the Journal of Political Economy, Prof. Pastor and Stambaugh explore the presence of a priced systematic liquidity factor in equity returns and whether the stocks with the largest exposure to the liquidity factor command a higher return.

They build their liquidity factor by estimating for each stock i and in each month t, the regression of daily excess stock return over the market on a constant, the previous day return and the dollar volume in the previous day multiplied by the sign of the previous day return. Each regression uses all the days of the given month.

The regression coefficient of the return on the signed volume is the measure of the individual stock liquidity. The signed volume is a proxy for the previous day order flow. If for instance there is a large buy order, the order will increase the stock price if the stock is not very liquid, the increase will then revert in the following day.

The market wide liquidity is simply the cross-sectional average of the individual stock liquidity coefficients. The authors weight this market liquidity by the market total dollar value to reflect that liquidity cost of a given size trade was higher in the earlier period. The innovation of the market liquidity is then the liquidity factor. A stock with a high liquidity beta will have a large comovement with this liquidity factor.

They compare this liquidity factor with some other measures and find that theirs seems to be the most plausible. They then test if liquidity risk is priced by using the liquidity factor along the Fama and French factors and the Momentum factor. They use both predicted liquidity betas (with firm characteristics) and simple historical betas. Curiously, they find that low liquidity beta portfolios are in fact less liquid.

They rank portfolios according to their liquidity betas and find that indeed, the portfolios have different average alpha returns, portfolios with higher betas have higher alphas. They can estimate the liquidity premium using ten portfolios sorted based on their liquidity exposures. From Jan 1966 to Dec 1999, the contribution of liquidity risk to the difference in returns between the illiquid portfolio (upper ten decile) and the liquid portfolio (lower ten decide) is 9.63% using value-weighted portfolios.

Pastor, Lubos and with Robert F. Stambaugh, 2003, Liquidity risk and expected stock returns, Journal of Political Economy 111, 642—685, available at __http://faculty.chicagogsb.edu/lubos.pastor/research/liquidity.pdf__

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