Trading costs, fat-tailed liquidity risk, and expected returns

This paper examines the effect of liquidity cokurtosis(or fat-tailed liquidity) risk on asset prices using a utility function with investor wealth and trading costs considered simultaneously. This study develops a model that includes liquidity cokurtosis risk, or fat-tailed liquidity risk, which is captured by the covariance between stock i’s liquidity and the cubed market liquidity, or {(Cᵢ, C³m)} Conceptually, this refers to an individual stock’s contribution to a diversified portfolio’s liquidity kurtosis. Investors would regard a portfolio as less desirable when a stock is added to a portfolio that changes the portfolio’s liquidity distribution to a more fat-tailed shape. In the presence of a leptokurtic distribution in liquidity, the expected return is related to the systematic liquidity kurtosis, and investors require a higher premium for bearing the systematic liquidity kurtosis risks. Using factor model analysis, I find the systematic liquidity kurtosis is priced, and, according to the Hansen-Jagannathan(HJ) distance, systematic liquidity kurtosis reduces the pricing error.