We hypothesize that (1) expected stock returns are positively related to idiosyncratic (and aggregate) liquidity cost volatility since risk-averse investors do not have fully diversified portfolios; (2) expected stock returns are positively correlated with the correlation between stock liquidity costs and market liquidity costs, as strong and positive correlation means weaker liquidity hedging ability; and (3) the expected return of a stock is positively related to its conditional exposure to liquidity volatility and correlation factors during periods of liquidity drying and worsening market depth. Furthermore, the expected return of a stock is positively related to its conditional exposure to the liquidity volatility factor σi during market downturns. We show that both liquidity volatility and correlation are important factors for the stochastic discount factor.
Second, we provide insights into the pricing of liquidity volatility and contribute to the debate on its pricing. Third, our study extends the literature by demonstrating, both within our theoretical model and empirical analyses, that the price of liquidity volatility is conditional on the state of market funding liquidity. In particular, the liquidity volatility factor σi is estimated more positively during periods of liquidity drying up and worsening market depth.
Our empirical findings that the liquidity volatility factor is positively priced and more positive during market turbulence is consistent with the implication of our theoretical model. Equation (2.5) suggests that liquidity volatility matters—only to the extent that the correlation of liquidity with consumption growth is nonzero (see the derivation in Appendix 1).
Empirical method 1. Measuring (il)liquidity
- Building return factors
- Sorting procedures a. Simple (mono) sorting
- Factor construction strategies
- Abnormal returns of liquidity factors
- The pricing of liquidity risk factors
- The pricing of liquidity factors conditional on market funding liquidity state In our theoretical model, liquidity cost shocks are not directly correlated with the
- Samples
- Statistics: Unadjusted factors returns
- Cumulative unadjusted factors returns
Because market liquidity costs closely follow business cycles (as measured by real consumption growth) (NÆS et al., 2011), we therefore examine the correlation between equity liquidity and market liquidity in subsequent empirical analyses. The LRSK (LRSK4) return factor is the return differential between the stocks in the portfolios with the highest and lowest decile (quartile) liquidity volatility. These two factors are our main factors used in the subsequent two-stage procedure of Fama-MacBeth.
We estimate the five-factor Fama-French (FF) model (Fama and French to determine whether the risk-adjusted return 𝛼 obtained from investing in the liquidity volatility factor σi. For robustness checks, we also estimate and report the results of an extended FF three-factor model and the extended FFC four-factor model (Carhart, 1997) in the following empirical analyses. In the second stage of the Fama-MacBeth procedure, we estimate the following cross-sectional extended regression for each month t.
Second, the cumulative return from investing in the correlation factor CORR (Panel A), CORR4 (Panel B), SDCORR (Panel C) (solid line) is significantly less than that obtained by investing in the corresponding liquidity volatility factor (dashed line) . At the end of the study period, investors who invested in the liquidity volatility factor LRSK (Panel A), LRSK4 (Panel B), SDLRSK (Panel C), compared to those who invested in the corresponding correlation factor, would be better off by approx. 77, 21 and 15 fold respectively (without tables).
Empirical results 1. Risk-adjusted returns
- Main analysis: Value-weighted 11m-1m-12m risk-adjusted returns
- Robustness analyses
- The pricing of liquidity risk factors
- Main analysis
- Robustness analyses
- The pricing of liquidity factors conditional on the state of market funding Our theoretical model in section 2 suggests that investors demand a higher illiquidity
- Analyses with various factor construction strategies
- Additional robustness analyses
Third, we use equal weighted returns (versus value weighted returns) for the full sample over the period 1964-2019. Consistent with the baseline and robustness results using Amihud's measure, we find statistically significant positive returns for the triple-sorted, value-weighted 11m-1m- 12m liquidity volatility factor SDLRSK, and negative returns for the correlation factor SDCORR in all FFs/FFC's models ( untabulated). For our main analysis, the test asset is FF's 25 value-weighted portfolios sorted by size (SMB) and book-to-market (HML).
We find that the average slope coefficients for the liquidity volatility factor SDLRSK (ˆSDLRSK) are positive and statistically significant at the 1% level in all three models, with a magnitude of per month (panel A). In contrast, the average slope coefficients for the correlation factor SDCORR (ˆSDCORR) are negative with a magnitude of between -0.27%. In all specifications, the test asset is FF's 25 value-weighted portfolios sorted by SMB and HML.
For the analysis where the test asset is FF's 25 equally weighted portfolios sorted by SMB and HML, the SDLRSK Untabulated Mean Beta Coefficients (SDCORR) are positive (negative) for three models. We argue that the mean slope coefficients for the interaction terms between SDLRSK or SDCORR and delayed TED spread, derived from the cross-sectional extended regression of Fama-MacBeth (Equation 3.8), are positive and statistically significant. As in the previous section, the test asset for the base specification consists of FF's 25 value-weighted portfolios, sorted by SMB and HML, and both SDLRSK and SDCORR are constructed as value-weighted, 11m-1m-12m factors.
Using the estimates for the five-factor model of the basic FF (column 1), we find that the mean contingent price of SDLRSK is 0.18% per month (2.16% per annum) and is statistically significant at the level of 1% (t=11.16). Using the estimates for the five-factor model of the base FF (column 1), we find that SDCORR's average conditional price is -0.46% per month and is not statistically significant (t= -0.02). The mean beta coefficients for the interaction term between the liquidity volatility factor SDLRSK and the lagged TED spread (ˆSDLRSK_TED) are positive in most specifications (except one in column 4) and statistically significant in most models in the columns (2-3, 5- 6).
For the interaction term between the SDCORR correlation factor and the lagged TED spacing, the mean beta coefficients reported in Panel B (ˆSDCORR TED_ ) have different signs across specifications. In all specifications, the test asset is 25 value-weighted FF portfolios sorted by SMB and HML. As presented in Panel B, the mean beta coefficients for the interaction term between SDCORR and lagged TED spacing, ˆSDCORR TED_, are negative in both subperiods but only statistically significant in column 2).
In contrast, the untabulated mean beta coefficients for the interaction terms between the correlation factor SDCORR and the delayed TED spread, ˆSDCORR TED_, are all insignificant. In summary, the results discussed above confirm our hypothesis for the liquidity volatility factor SDLRSK.
Conclusion
Panel C contains the results of the three-factor model of FF, augmented by Carhart's (1997) moment factor (the four-factor model of FFC). This table presents the results of the robustness analyzes for the liquidity volatility value-weighted returns and the correlation factors derived from triple ranking (columns 1, 3) and extended triple ranking (columns 2, 4) using alternative strategies of building factors. This table displays the results of the robustness analysis for the 11-1m-12m value-weighted returns of liquidity volatility and correlation factors derived from triple ranking (columns 1, 3) and extended triple ranking (columns 2, 4 ) during the three sub-periods of different economic conditions.
The test asset is FF's 25 value-weighted portfolios sorted by size (SMB) and book-to-market (HML). This table presents the results of the Fama-MacBeth monthly cross-sectional regressions, where monthly excess returns rj,t of the test asset j over the risk-free asset rf,t are regressed on the beta loadings obtained from the first stage time series regressions. This table reports the means of the slope coefficients for the liquidity volatility factor SDLRSK (panel A) and the correlation factor SDCORR (panel B) obtained by estimating Fama-MacBeth monthly cross-sectional regressions, where monthly excess returns of the test asset are regressed over the risk-free assets on the beta loadings from the first-stage time series regressions.
For ease of comparison, the means of the slope coefficients for value-weighted SDLRSK and SDCORR of 11m-1m-12m reported in Table 6 are presented in column 1, Panels A and B of this Table, respectively. This table reports the average of the slope coefficient for the value-weighted, 11m-1m-12m liquidity volatility factor SDLRSK (Panel A) and correlation factor SDCORR (Panel B), obtained by estimating the monthly cross-sectional regressions of Fama-MacBeth, where the monthly excess The returns of the test asset relative to the risk-free asset are regressed based on the beta loads from the time series regressions of the first stage. Column 2/Column 3 reports the averages of the slope coefficients where the test asset is FF's 25 value-weighted portfolios, sorted by size (SMB) investment (CMA)/size (SMB) momentum (MOM).
Column (5) presents the averages of the slope coefficients where the test asset is FF's 32 value-weighted portfolios sorted by size (SMB) - book-to-market (HML) - operating profitability (RMW). For ease of comparison, the averages of the slope coefficients for the value-weighted, 11m-1m-12m SDLRSK and SDCORR where the test asset is the 25 value-weighted portfolios of FF sorted by SMB and HML, as reported in Table 6, are shown in column 1, respectively panels A and B of this Table. For ease of comparison, the averages of the slope coefficients for the weighted values, 11m-1m-12m SDLRSK and SDCORR using the same test asset over the entire study period as reported in Table 6, are shown in column 1, panels A and B. of this Table, respectively.
This table lists the averages of the slope coefficients for the value-weighted, 11m-1m-12m liquidity volatility factor SDLRSK (Panel A)/correlation factor SDCORR (Panel B) and the lagged TED spread interaction term. Column 2/Column 3 reports the averages of the slope coefficients where the test asset is FF's 25 value-weighted portfolios, sorted by size (SMB) investment (CMA)/size (SMB) momentum (MOM). Column (5) presents the averages of the slope coefficients where the test assets are FF's 32 value-weighted portfolios, sorted by size (SMB)-book-to-market (HML)-operating profitability (RMW).
For ease of comparison, the averages of the slope coefficients for the weighted value, 11m- 1m-12m SDLRSK/ SDCORR where the test asset is the 25 value-weighted portfolios of FF sorted by SMB and HML, as reported in column 1 of table 10, are presented in column 1, respectively panels A and B of this Table. For ease of comparison, averages of slope coefficients for 11m-1m-12m SDLRSK and value-weighted SDCORR over the full period February 1986-December 2019 when TED propagation data are available are shown, as reported in column 1 of the table 10. in column 1, respectively panels A and B of this Table.
