How big is the stock liquidity premium and does it subsume other variables widely used to estimate future returns? In their December 2014 paper entitled “A Comparative Analysis of Liquidity Measures”, Yuping Huang and Vasilios Sogiakas investigate the relationships of excess (relative to the risk-free rate) stock returns to three pairs of monthly liquidity metrics:

- Transaction cost: (1) average daily absolute bid-ask spread; or, (2) relative spread (average daily absolute spread divided by stock price).
- Trading activity: (3) turnover ratio (shares traded divided by shares outstanding); or, (4) average daily dollar volume.
- Price impact: (5) average absolute daily return divided by dollar volume; or, (6) average daily ratio of absolute return divided by daily turnover ratio.

They also examine the interaction of these liquidity metrics with widely used risk factors (market capitalization or size, book-to-market ratio and momentum) and other predictive variables (price, earnings yield and dividend yield). They base some analyses on average gross returns of equally weighted portfolios reformed monthly by ranking stocks into fifths (quintiles) by prior-month liquidity metrics. Analyses exploring interaction of liquidity metrics with other factors/variables employ multivariate regressions. In grooming/processing data, they exclude stocks with extremely low and high prices, liquidity metrics, factors and predictive variables. Using daily bid-ask spreads during 1991 through 2011 and monthly values of other trading metrics and factors/variables as described above during 1962 through 2011 for a broad (but filtered) sample of U.S. stocks (an average of 2,050 stocks each month),* they find that:*

- Based on pairwise correlations with monthly data:
- Each pair of liquidity metrics [(1) with (2), (3) with (4), (5) with (6)] exhibits significantly positive correlations, confirming that they measure related aspects of liquidity.
- Trading activity metrics (3) and (4) relate negatively to transaction cost and price impact metrics, confirming that high friction means little trading.
- Turnover ratio [metric (3)] relates positively to gross return and share price.
- Relative spread [metric (2)] and average daily return divided by dollar volume [metric (5)] relate negatively to size, confirming that small stock gross returns tend to compensate for relatively low liquidities.

- Strongest indications from quintile portfolios are that average gross annualized excess returns tend to increase with liquidity metrics (2), (3) and (5). The average gross annualized excess return of a hedge portfolio that is each month long (short) the quintile of stocks with the highest (lowest) prior-month:
- Relative spreads is 1.2%
- Turnover ratios is 3.9%.
- Average absolute daily returns divided by dollar volumes is 1.6%.

- Strongest indications from multivariate regressions are that liquidity metrics mostly subsume the size effect but not the information in earnings yield or stock price.
- Metrics (1) and (2) subsume the value premium.
- Metric (5) subsumes the momentum effect.

In summary, *evidence suggests that stock liquidity, indicative of trading frictions, interacts materially with some widely used factors, thereby affecting materiality of the gross returns for these factors.*

Cautions regarding findings include:

- Reported returns are gross, not net. Including estimates of trading frictions and shorting costs would (by definition for some liquidity metrics) reduce or eliminate the liquidity premium. Shorting may not be feasible for some stocks in the short side of hedge portfolios.
- Especially early in the sample period:
- The cost of acquiring and processing stock liquidity data may be material relative to gross returns.
- Timely data acquisition may not be feasible.

- The study does not include multiple sorts to define portfolios that exploit more than one liquidity component.
- Filtering of source data and intermediate calculations suggests that results may not apply to stocks exhibiting extreme behaviors.
- Testing multiple variables on the same data introduces snooping bias, such that the strongest indications across liquidity metrics may overstate expectations.