Fama–MacBeth Regressions with Liquidity-Sorted Portfolios

Summary

The document asks how to estimate factor risk premia with the Fama–MacBeth procedure when liquidity is among the factors. It outlines the general setup of assets, factors, and time periods, then describes averaging the period-by-period factor price estimates to obtain average premia. It also asks whether studies using liquidity-sorted portfolios calculate average returns and factor exposures within each portfolio.

The text offers no answer to that portfolio-construction question and presents no empirical findings. It is best read as a statement of methodological uncertainties rather than a complete guide: it does not specify the regression equations, portfolio weighting, sorting procedure, standard errors, or treatment of time-varying exposures. Those details would need to be established from the relevant study or a fuller description of the Fama–MacBeth design.

Key ideas

• The Fama–MacBeth setup relates asset returns to factor exposures across multiple periods.
• Average period-specific factor price estimates are used to estimate average risk premia.
• Liquidity can be included as a factor whose premium is being tested.
• Liquidity-sorted portfolios raise questions about how portfolio returns and factor exposures are aggregated.

Tags

# Fama-Macbeth with Liquidity Sorted Portfolios


# Fama-Macbeth with Liquidity Sorted Portfolios












I'm currently working on a paper in which I'm trying to see whether the liquidity premium is an observable phenomena when taken into the context of computer games.

From my research online I've found a lot of conflicting answers to the question on how to run a Fama-Macbeth regression. If I understand correctly what needs to be done with N stocks, K factors (this should include the liquidity factor) and T periods:





Then in order to extract the risk-premium associated with every factor you simply average all of the Lambda's you have obtained in the second step and deduce your results from this.

However, since there is a lot of conflicting information on how to run this particular regression, I'm not quite sure I fully understand it. Additionally, in a lot of papers such as Ben-Raphael, Kadan and Wohl (2008) I see that they make use of liquidity-sorted portfolios to do their analysis. Is it right for me to assume that this means we are looking at average returns and average factors of all stocks within each of these liquidity-sorted portfolios?

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