4.6 Are Liquidity Spillovers Related to Correlated Funda-
4.6.4 Does Style Investing Contribute to Liquidity Spillovers?
Findings in the previous sections do not support the Learning hypothesis nor the Substitution Hypothesis. In this section, we investigate whether the observed pattern of liquidity spillovers is related to style investing.
Barberis and Shleifer (2003) shows that trading based on style induces higher com- monality of returns within a given style and lower commonality across different styles.
Recently, an implication of style investing on trading volume has been investigated by Huang (2005) and Nagel (2005). For size and book-to-market sorted portfolios, Huang (2005) found trading volume tend to comove within styles more than it does in different styles. Nagel (2005) argues that transitions of styles based on the changes in stock characteristics induces trading volume. An important implication of style investing for this paper is that it may explain liquidity spillovers.
I employ size and book-to-market portfolios in this section. Before we go further, it is logical to investigate whether we observe spillovers in returns or liquidity according to size and book-to-market style following Huang (2005). To do so, I sorted stocks into one of nine portfolios based on their market capitalization and book-to-market value at the end of previous year. In portfolio sorting, NYSE breakpoints are used for both size and book-to-market (independent sorting). Equal-weighted portfolios are used as test assets. Based on the results in Table A.27, I focus only on weekly frequency analysis with lag of 1 week in the joint estimation of the following system
of equations.
Y = ΓB+ǫ (4.13)
where, Y =
V DQS1 ... GDQS1 ... V RET1 ... GRET1 ... V V OL1 ... GV OL1 ′
. Y is a 6T ×1 vector each of whose six component has T ×1 dimension. The prefix V (G) is used to denote the variable is from value or high book-to-market(growth or low book-to-market) portfolios. As in the previous case, a suffix of 1 is used to denote the small stock portfolio, while that of 3 is used for the large stock portfolio. Γ is a block diagonal matrix with the matrix X located in the diagonal blocks.
X =
1 ... DQS−1 ... RET−1 ... V OL−1
where,
DQS−1 =
V DQS1−1 ... V DQS3−1 ... GDQS1−1 ... GDQS3−1 RET−1 =
V RET1−1 ... V RET3−1 ... GRET1−1 ... GRET3−1
V OL−1 =
V V OL1−1 ... V V OL3−1 ... GV OL1−1 ... GV OL3−1
1 is aT ×1 vector of ones andV DQS1−1 is aT ×1 vector of one-week lagged DQS of small-value portfolio. (−1) is used in the notation to denote lag of one-week. Since the matrix X has dimension of T ×13, dimension of the block diagonal matrix Γ is 6T ×(13×6). B is a 72×1 parameter vector andǫ is a vector of error terms.
Table A.28 shows the estimation results. We see some evidence that the style in- vesting is related to returns and liquidity spillovers. We find that lagged comovement
is stronger among value stocks for liquidity (coefficient ofDQS3(V alue) is 0.111 with p-value of 0.011) and among growth stocks for returns (coefficient ofRET3(Growth) is 0.143 with p-value of 0.082). However, spillovers across different styles are statisti- cally insignificant.
I now turn into the main question of whether style investing can explain the fact that liquidity spillovers are stronger across industries than within industry. To achieve this goal, I sort stocks into three size groups within a given industry. Further, in a given size-industry group, I sort stocks into three book-to-market groups. This dependent sorting prevents the problem of thin groups, where only a few or no stocks are included in some industry-size-B/M group. I jointly estimate the following system
of equations.
V DQS1i,t=αV DQS+ XK k=1
DQSi,t−kΘV DQSk + XK k=1
ΘV DQSk j6=iDQS3j6=i,t−k
+ XK k=1
RETi,t−kΘV RETk + XK
k=1
V OLi,t−kΘV V OLk +ǫV DQSi,t (4.14) GDQS1i,t=αGDQS+
XK k=1
DQSi,t−kΘGDQSk + XK
k=1
ΘGDQSk j6=iDQS3j6=i,t−k
+ XK k=1
RETi,t−kΘGRETk + XK k=1
V OLi,t−kΘGV OLk +ǫGDQSi,t (4.15) V RET1i,t=ξV RET +
XK k=1
RETi,t−kΓV RETk + XK k=1
ΓV RETk j6=iRET3j6=i,t−k +
XK k=1
DQSi,t−kΓV DQSk + XK
k=1
V OLi,t−kΓV V OLk +ηi,tV RET (4.16) GRET1i,t=ξGRET +
XK k=1
RETi,t−kΓGRETk + XK k=1
ΓGRETk j6=iRET3j6=i,t−k
+ XK k=1
DQSi,t−kΓGDQSk + XK k=1
V OLi,t−kΓGV OLk +ηGRETi,t (4.17) V V OL1i,t=ζV V OL+
XK k=1
V OLi,t−kΦV V OLk + XK k=1
ΦV V OLk j6=iV OL3j6=i,t−k
+ XK k=1
DQSi,t−kΦV DQSk + XK
k=1
RETi,t−kΦV RETk +νi,tV V OL (4.18) GV OL1i,t=ζGV OL+
XK k=1
V OLi,t−kΦGV OLk + XK k=1
ΦGV OLk j6=iV OL3j6=i,t−k
+ XK
k=1
DQSi,t−kΦGDQSk + XK k=1
RETi,t−kΦGRETk +νi,tGV OL (4.19)
where,
DQSi,t−k = V DQS1i,t−k V DQS3i,t−k GDQS1i,t−k GDQS3i,t−k
RETi,t−k = V RET1i,t−k V RET3i,t−k GRET1i,t−k GRET3i,t−k
V OLi,t−k = V V OL1i,t−k V V OL3i,t−k GV OL1i,t−k GV OL3i,t−k
DQS3j6=i,t−k = V DQS3j6=i,t−k GDQS3j6=i,t−k
RET3j6=i,t−k = V RET3j6=i,t−k GRET3j6=i,t−k V OL3j6=i,t−k = V V OL3j6=i,t−k GV OL3j6=i,t−k
.
Subscript i (i = 1,2, ...,12) denotes industry i and j 6= i denotes that the portfolio is obtained by excluding stocks in industry i. Suffixes 1 and 3 indicate small and large stock portfolios, respectively and prefixes V (G) are used to distinguish value (growth) stock portfolios.
Parameter vectors in the liquidity equations (equation 4.14 and 4.15) are as fol- lows.
ΘV DQSk = θVk−V DQS1 θVk−V DQS3 θVk−GDQS1 θVk−GDQS3 ′
ΘGDQSk = θG−V DQS1k θkG−V DQS3 θkG−GDQS1 θG−GDQS3k ′
ΓV DQSk = γkV−V DQS1 γkV−V DQS3 γkV−GDQS1 γkV−GDQS3 ′
ΓGDQSk = γkG−V DQS1 γkG−V DQS3 γkG−GDQS1 γkG−GDQS3 ′
ΦV DQSk = φVk−V DQS1 φVk−V DQS3 φVk−GDQS1 φVk−GDQS3 ′
ΦGDQSk = φG−V DQS1k φG−V DQS3k φG−GDQS1k φG−GDQS3k ′
ΘV DQSk j6=i =
θkV−V DQS3j6=i θkV−GDQS3j6=i ′
ΘGDQSk j6=i =
θkG−V DQS3j6=i θkG−GDQS3j6=i ′
ΓV DQSk j6=i =
γkV−V DQS3j6=i γkV−GDQS3j6=i ′
ΓGDQSk j6=i =
γkG−V DQS3j6=i γG−GDQS3k j6=i ′
ΦV DQSk j6=i =
φVk−V DQS3j6=i φVk−GDQS3j6=i ′
ΦGDQSk j6=i =
φG−V DQS3k j6=i φG−GDQS3k j6=i ′
Parameter vectors in the return equations (equation 4.16 and 4.17) are as follows.
ΘV RETk = θVk−V RET1 θkV−V RET3 θkV−GRET1 θkV−GRET3 ′
ΘGRETk = θG−V RETk 1 θG−V RETk 3 θkG−GRET1 θG−GRETk 3 ′
ΓV RETk = γkV−V RET1 γkV−V RET3 γkV−GRET1 γkV−GRET3 ′
ΓGRETk = γkG−V RET1 γkG−V RET3 γkG−GRET1 γkG−GRET3 ′
ΦV RETk = φVk−V RET1 φVk−V RET3 φVk−GRET1 φVk−GRET3 ′
ΦGRETk = φG−V RETk 1 φG−V RETk 3 φG−GRETk 1 φG−GRET3k ′
ΘV RETk j6=i =
θkV−V RET3j6=i θkV−GRET3j6=i ′
ΘGRETk j6=i =
θkG−V RET3j6=i θG−GRETk 3j6=i ′
ΓV RETk j6=i =
γkV−V RET3j6=i γVk−GRET3j6=i ′
ΓGRETk j6=i =
γkG−V RET3j6=i γkG−GRET3j6=i ′
ΦV RETk j6=i =
φVk−V RET3j6=i φVk−GRET3j6=i ′
ΦGRETk j6=i =
φG−V RETk 3j6=i φG−GRET3k j6=i ′
Parameter vectors in the volatility equations (equation 4.18 and 4.19) are also defined similarly.
ΘV V OLk = θkV−V V OL1 θkV−V V OL3 θkV−GV OL1 θkV−GV OL3 ′
ΘGV OLk = θkG−V V OL1 θG−V V OL3k θkG−GV OL1 θkG−GV OL3 ′
ΓV V OLk = γkV−V V OL1 γVk−V V OL3 γkV−GV OL1 γkV−GV OL3 ′
ΓGV OLk = γkG−V V OL1 γkG−V V OL3 γkG−GV OL1 γkG−GV OL3 ′
ΦV V OLk = φVk−V V OL1 φVk−V V OL3 φVk−GV OL1 φVk−GV OL3 ′
ΦGV OLk = φG−V V OL1k φG−V V OL3k φG−GV OL1k φG−GV OL3k ′
ΘV V OLk j6=i =
θVk−V V OL3j6=i θVk−GV OL3j6=i ′
ΘGV OLk j6=i =
θG−V V OL3k j6=i θG−GV OL3k j6=i ′
ΓV V OLk j6=i =
γkV−V V OL3j6=i γkV−GV OL3j6=i ′
ΓGV OLk j6=i =
γkG−V V OL3j6=i γkG−GV OL3j6=i ′
ΦV V OLk j6=i =
φVk−V V OL3j6=i φVk−GV OL3j6=i ′
ΦGV OLk j6=i =
φG−V V OL3k j6=i φG−GV OL3k j6=i. ′
Note that the parameters are restricted to be the same across different industries (i.e., subscript i is not used).
Table A.29 shows the results in separate panels according to different restrictions imposed on the estimation. Panel A shows the basic result where the coefficients are not restricted to be the same by style nor by industry. The first four numeric rows are for liquidity spillovers while the next four rows are for returns spillovers in panel A. First, we see that our previous finding of stronger spillovers in liquid- ity across industries than within a given industry is also supported when we further
decompose liquidity based on book-to-market values. One week lagged changes of liq- uidity of large-value stocks from all industries except for a given industry,θG−V DQS3k j6=i (DQS3(V alue, other) in the table), have a coefficient of 0.35 with a p-value of 0.003 when the dependent variable is GDQS1. This effect seems to be the driving force of stronger spillovers from other industries in the previous section. However, we see some evidence that within-industry liquidity spillovers are statistically signifi- cant. On the right-side of panel A, we see that V DQS3 andGDQS3 (DQS3(V alue) and DQS3(Growth), respectively in the table) have significant effect on the changes of liquidity of small-value or/and small-growth portfolios. The offsetting signs of DQS3(V alue) to DQS1(Growth) (negative) and to DQS1(V alue) (positive) seem to mitigate the overall effect of within-industry liquidity spillovers. In addition, we see that, in a given industry, within-industry liquidity spillovers are positive and sig- nificant (coefficients of 0.168 (with ap-value of 0.001) for DQS3(Growth) and 0.075 (p-value of 0.025) for DQS3(V alue)). For returns, we see more significant cases.
Except for the effect of returns of the large-growth portfolio, GRET3, on the re- turns of the small-growth portfolio,GRET1, all estimated coefficients of returns are significant, though the signs vary according to style or industry.
With strong evidence that there are spillovers in returns and liquidity by styles and by industries, I now test for the relative importance of style and industry classi- fications. In panel B, we restrict the coefficients of value-large and value-small stocks formed by excluding a given industry to be the same in both equations of small- large and small-growth liquidity (ie, DQS3(V alue, other) for DQS1(Growth) = DQS3(Growth, other) for DQS1 (Growth) =DQS3(V alue, other) for DQS1 (Value)
= DQS3(Growth, other) for DQS1 (Value)). This restriction is true if style effects
are negligible while the industry classification matters. If the estimated coefficient of DQS3 from other industries are significantly different from that of DQS3 from a given industry, I interpret that as supporting the notion that industry classification has significant impact on liquidity spillovers. However, the F-test statistic, which tests whether the two estimated coefficients of -0.049 and -0.015 are statistically the same or not, of one with a p-value of 0.318 shows that it is not the case. For re- turns, theF-statistic of 13.55 (p-value less than 0.01) shows supporting evidence that within-industry spillovers in returns are stronger than across-industry spillovers and that this pattern is not related to style investing.
In panel C, I restrict the coefficients to be the same for a given style but different for
different industries. That is,DQS3(V alue, other) =DQS3(V alue) (DQS3(Growth, other) = DQS3(Growth)) in both equations when the dependent variables are growth-small
or growth-large stocks. I perform this test to assess impact of style investing by excluding industry effect. Liquidity spillovers from value stocks are negative while those from growth stocks are positive and these are statistically different each other (F-statistics of 18.04 with ap-value less than 0.01). In the case of returns, we do not see a significant difference betweenV RET3 andGRET3 (F-statistic is 0.51 with its p-value of 0.48).