5. Empirical results 1. Risk-adjusted returns
5.3. 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
5.3.2. Additional robustness analyses
We conduct additional analyses to ensure that the results reported in column (1), Table 10 are robust. First, we employ alternatively constructed factors, as reported in columns (2-5),
24 The process to estimate the average conditional price of a liquidity factor is discussed in Appendix 3, and is similar to the approach applied in Litzenberger and Ramaswamy (1979) and Amihud and Noh (2020b).
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Table 10. Second, we utilise alternative value-weighted FF’s two-way and three-way sorted portfolios as test assets. Third, we conduct Fama-MacBeth’s two-stage procedure over two sub-periods of markedly different economic conditions, 1987-2009 and 2010-2019. Fourth, we construct equally weighted test assets and equally weighted liquidity risk factors. Finally, we employ inverse trading volume (instead of Amihud’s measure) to create liquidity factors. For reasons of brevity, the following discussion focuses on the key results of a few robustness tests.
The results of untabulated analyses are available upon request.
a. Alternative test assets
Table 11 reports the mean beta coefficients using alternative test assets. We use the same alternative test assets as in Table 8 when we estimate the prices of the unconditional liquidity factors. Both SDLSRK and SDCORR are constructed as value weighted, 11m-1m- 12m factors, as in the baseline specification.
TABLE 11 ABOUT HERE
As shown in Panel A, the estimates using alternative test assets (columns 2-6) are generally consistent with the estimates of the baseline specification (column 1). The mean beta coefficients for the interaction term between the liquidity volatility factor SDLRSK and lagged TED spread (ˆSDLRSK_TED) are positive in most specifications (except one in column 4), and statistically significant in most models in columns (2-3, 5-6).
For the interaction term between the correlation factor SDCORR and lagged TED spread, the mean beta coefficients reported in Panel B (ˆSDCORR TED_ ) have varying signs across specifications. However, except for column 5 where FF’s 32 three-way sorted portfolios are used as the test asset, the average beta coefficients for the interaction term, where statistically significant, have negative signs. This is consistent with the main specification (column 1).
Overall, the results in Panel A of Table 11 are generally consistent with those in Table 10, suggesting that the liquidity volatility factor SDLRSK is more positively priced during
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market downturns. On the other hand, the results in Panel B of Table 11 present weak evidence to support the findings in Table 10 that the correlation factor SDCORR is more negatively priced during market turmoil.
b. Sub-periods
Table 12 reports the mean beta coefficients over the two sub-periods where lagged TED spread data is available: 1987-2009 (column 2) and 2010-2019 (column 3). In all specifications, the test asset is FF’s 25 value-weighted portfolios sorted by SMB and HML.
Both SDLSRK and SDCORR are constructed as value weighted, 11m-1m-12m factors. The results of the full sample period February 1986-2019 are presented in column 1 of this Table.
TABLE 12 ABOUT HERE
Panel A presents some interesting results. Over the period of market crash and GFC 1987-2019 (column 2), the liquidity volatility factor SDLRSK is strongly priced. The average beta coefficients for both SDLRSK,ˆSDLRSK, and its interaction term ,ˆSDLRSK_TED, are positive and statistically significant at the 5% level. The results for this sub-period are consistent with the results for the full period February 1986-2019 (column 1) and support our hypothesis.
However, over the period of economic recovery and soaring equity prices 2010-2019 (column 3), SDLRSK is not as strongly priced as during the volatile period 1987-2009. The mean beta coefficients ˆSDLRSK are statistically insignificant though positive. For the interaction term
ˆ _
SDLRSK TED
, the average beta coefficients are negative, statistically insignificant and markedly smaller (column 3 vs. column 2). This is not too surprising as investors have counter-cyclical risk aversion in our theoretical model (high risk aversion during poor economic states and low risk aversion during good economic states). If liquidity volatility is a risk that investors care about, investors will require a greater risk premium during a period of funding distress. Over the period 2010-2019, funding liquidity, proxied by TED spread, was relatively stable (Figure
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2), and investors’ risk aversion is low. Thus, investors may just require a very small liquidity volatility risk premium.
Using the estimates for the baseline FF’s five-factor model in Panel A and employing the process outlined in Appendix 3 to compute the mean conditional price of a factor, we find that SDLRSK is positively priced at 0.27% per month for the sub-period 1987-2009 (column 2) but negatively priced at -0.06% per month for the sub-period 2010-2019 (column 3), compared to 0.18% for the full period February 1986 - December 2019 (column 1). These average conditional prices for SDLRSK (untabulated) are statistically significant at the 1%
level in both sub-periods.
As presented in Panel B, the mean beta coefficients for the interaction term between SDCORR and lagged TED spread, ˆSDCORR TED_ , are negative in both sub-periods but only statistically significant during 1987-2009 (column 2). Using the estimates for the baseline FF’s five-factor model in Panel B, we find that the average conditional prices of SDCORR are more negative in both sub-periods, at -1.26% per month in 1987-2009 and -0.64% per month in 2010- 2019, compared to -0.46% in the full period February 1986 - December 2019. However, none of these mean conditional prices for SDCORR (untabulated) are statistically significant.
Overall, we find consistent evidence of a statistically significant positive (negative) relation between liquidity volatility (correlation) risk premium and TED spread during the period of market crash and economic crisis, 1987-2009. The result for the liquidity volatility factor supports our hypothesis that in times of liquidity dry-up, investors require a greater risk premium to hold stocks whose liquidity is more volatile.
c. Equally weighted test assets and equally weighted liquidity factors
We estimate the risk premia of equally weighted liquidity factors using three different equally weighted test assets, namely FF’s 25 portfolio sorted by SMB and HML, FF’s 200 two- way sorted portfolios, and FF’s 96 three-way sorted portfolios. The untabulated mean slope
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coefficients for the interaction terms between the liquidity volatility factor SDLRSK and lagged TED spread, ˆSDLRSK_TED, are positive in all FFC’s four-factor/ FF’s five-factor models, and statistically significant when the test asset is 200 (96) equally weighted two-way (three-way) sorted portfolios. This is consistent with the results in Table 10 and supports our hypothesis. In contrast, the untabulated mean beta coefficients for the interaction terms between the correlation factor SDCORR and lagged TED spread,ˆSDCORR TED_ , are all insignificant.
d. Alternative illiquidity measure: Inverse trading volume
We employ FF’s 25 value-weighted portfolios sorted by SMB and HML as the test asset and use inverse trading volume to create triple sorted, value-weighted, 11m-1m-12m SDLRSK and SDCORR factors. For SDLRSK and its interaction term, we consistently observe positive ˆSDLRSK, and statistically significant (at the 1% level) and positive ˆSDLRSK_TEDacross all three models (untabulated). For SDCORR and its interaction term, the results are less consistent; however, we find a negative ˆSDCORR, and a statistically significant (at the 5% level) and negative ˆSDCORR TED_ in the FF’s five-factor model (untabulated).
In summary, the results discussed above confirm our hypothesis for the liquidity volatility factor SDLRSK. The risk premium of SDLRSK increases significantly in times of funding distress, particularly during the period of market crash and GFC, 1987-2009. Our finding is robust to a battery of tests. For the correlation factor SDCORR, we find that its conditional pricing is either negative, economically small or statistically insignificant, which is not in line with the implication of our theoretical model. The pricing result for SDCORR may be explained in light of Simon’s (1955) suggestion that humans do not act in accordance to perfect economic rationality. It is hard for humans to detect and adapt to extreme realisations (D’Acremont and Bossaerts, 2016; Payzan-LeNestour and Woodford, 2020), and extreme realisations strongly influence correlation. Ungeheuer and Weber’s (2021, p. 799) stress that
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investors “do not understand dependence in extreme returns and diversify less when dependence increases in moderate returns, even if correlation decreases due to decreasing dependence in extreme returns. Thus, their behavior is exactly the opposite of what one would expect according to Markowitz (1952) in combination with observed return correlations.”25