The Liquidity-Augmented CAPM: Empirical Evidence from the JSE

Christo Auret and David McClelland

Presentation Outline

o Background and Literature

o Motivation

o Augmenting Liquidity and CAPM: Liu’s Two-Factor Model

o Preliminary Analysis and Results

o Still to be Investigated

Background Empirical failings of the CAPM

Attempts to address these failings:

Empirical approach Theoretical approachAddress the empirical Address the limitations oflimitation by CAPM’s simplifyingincluding variables that assumptionsdirectly capture documentedanomalies

Background The assumption of frictionless capital markets has

particularly severe implications for cross-sectional homogeneity with respect to trading costs, volumes, speeds and depth

The degree to which assets or a market resemble this frictionless state can be seen as their level of liquidity

“The ability to trade large quantities quickly at low cost with small price impact”

Furthermore, illiquidity seems to severely affects market Beta estimation

Literature Review Trading Cost (Bid-Ask Spreads)

Amihud and Mendelson (1986)

Trading Quantity (Turnover) Datar et al. (1998)

Price Impact of Trading Amihud (2002) Pastor and Stambaugh (2003)

Trading Speed Liu (2006)

Motivation Gap in the current South African literature for

tests of asset pricing models that include a comprehensive liquidity factor

Test the international robustness of Liu’s 2-factor model

Possibly provide a comprehensive asset pricing solution that can be used for the smaller less liquid stocks that are abundant on the JSE

Augmenting Liquidity and CAPM: Liu (2006) Two-Factor ModelThe liquidity measure (LM12) is constructed as follows:

LM12 = [number of zero daily volumes in prior 12 months + ]

x

Where NoTD is the total number of trading days over the past 12 months and the Deflator is chosen such that:

Benefit of this measure: Shown to be highly significant internationally Required data is easily available

Preliminary Analysis

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

-0.4-0.2

1.11022302462516E-160.20.40.60.8

11.21.41.6

Low

8

6

4

2

Beta across liquidity portfolios

Preliminary Analysis

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Liquidity premium

ALSI

Prob > |t| = 0.0425Test of Ho: alsi and liq are independent

Spearman's rho = 0.6485 Number of obs = 10

. spearman alsi liq, stats(rho p)

Preliminary Results

Standard: _consInstruments for level equation GMM-type: L(2/.).returnInstruments for differenced equation _cons -.2609358 .1100519 -2.37 0.018 -.4766336 -.045238 liquidity .4622064 .1049511 4.40 0.000 .2565061 .6679067 return Coef. Std. Err. z P>|z| [95% Conf. Interval] One-step results Prob > chi2 = 0.0000Number of instruments = 37 Wald chi2(1) = 19.40

max = 10 avg = 10 Obs per group: min = 10Time variable: dateGroup variable: id Number of groups = 10Dynamic panel-data estimation Number of obs = 100

. xtdpd return liquidity, dgmmiv(return) artests(2)

Liquidity sort into deciles

0.0000 0.0000 0.0000 liquidity -0.5257* 0.7299* -0.7737* 1.0000 0.0000 0.0000 beta 0.5939* -0.6273* 1.0000 0.0000 nbm -0.5046* 1.0000 size 1.0000 size nbm beta liquid~y

Sig. level rho Key

(obs=100). spearman size nbm beta liquidity, stats(rho p) print(0.10) star(0.05)

0.0000 0.0000 0.0000 liquidity -0.5257* 0.7299* -0.7737* 1.0000 0.0000 0.0000 beta 0.5939* -0.6273* 1.0000 0.0000 nbm -0.5046* 1.0000 size 1.0000 size nbm beta liquid~y

Sig. level rho Key

(obs=100). spearman size nbm beta liquidity, stats(rho p) print(0.10) star(0.05)

Preliminary Results Size sort into deciles

Standard: _consInstruments for level equation GMM-type: L(2/.).abnormalInstruments for differenced equation _cons .8030142 .2813407 2.85 0.004 .2515966 1.354432 size -.1782887 .0783694 -2.27 0.023 -.3318898 -.0246875 abnormal Coef. Std. Err. z P>|z| [95% Conf. Interval] One-step results Prob > chi2 = 0.0229Number of instruments = 37 Wald chi2(1) = 5.18

max = 10 avg = 10 Obs per group: min = 10Time variable: dateGroup variable: id Number of groups = 10Dynamic panel-data estimation Number of obs = 100

. xtdpd abnormal size, dgmmiv(abnormal) artests(2)

Standard: _consInstruments for level equation GMM-type: L(2/.).abnormalInstruments for differenced equation _cons -.2245964 .1262375 -1.78 0.075 -.4720173 .0228245 liquidity .0053606 .0016614 3.23 0.001 .0021043 .0086169 abnormal Coef. Std. Err. z P>|z| [95% Conf. Interval] One-step results Prob > chi2 = 0.0013Number of instruments = 37 Wald chi2(1) = 10.41

max = 10 avg = 10 Obs per group: min = 10Time variable: dateGroup variable: id Number of groups = 10Dynamic panel-data estimation Number of obs = 100

. xtdpd abnormal liquidity, dgmmiv(abnormal) artests(2)

Standard: _consInstruments for level equation GMM-type: L(2/.).abnormalInstruments for differenced equation _cons .3299638 .3191942 1.03 0.301 -.2956453 .9555729 size -.1451349 .0762466 -1.90 0.057 -.2945754 .0043057 liquidity .0048448 .0017376 2.79 0.005 .0014392 .0082505 abnormal Coef. Std. Err. z P>|z| [95% Conf. Interval] One-step results Prob > chi2 = 0.0012Number of instruments = 37 Wald chi2(2) = 13.38

max = 10 avg = 10 Obs per group: min = 10Time variable: dateGroup variable: id Number of groups = 10Dynamic panel-data estimation Number of obs = 100

. xtdpd abnormal liquidity size, dgmmiv(abnormal) artests(2)

Preliminary Results B/M sort into deciles

Standard: _consInstruments for level equation GMM-type: L(2/.).abnormalInstruments for differenced equation _cons -.0461563 .0722086 -0.64 0.523 -.1876826 .0953699 nbm .1894826 .058062 3.26 0.001 .0756832 .3032821 abnormal Coef. Std. Err. z P>|z| [95% Conf. Interval] One-step results Prob > chi2 = 0.0011Number of instruments = 37 Wald chi2(1) = 10.65

max = 10 avg = 10 Obs per group: min = 10Time variable: dateGroup variable: id Number of groups = 10Dynamic panel-data estimation Number of obs = 100

. xtdpd abnormal nbm, dgmmiv(abnormal) artests(2)

Standard: _consInstruments for level equation GMM-type: L(2/.).abnormalInstruments for differenced equation _cons -.1743846 .1024858 -1.70 0.089 -.375253 .0264838 liquidity .0046806 .0013432 3.48 0.000 .002048 .0073133 abnormal Coef. Std. Err. z P>|z| [95% Conf. Interval] One-step results Prob > chi2 = 0.0005Number of instruments = 37 Wald chi2(1) = 12.14

max = 10 avg = 10 Obs per group: min = 10Time variable: dateGroup variable: id Number of groups = 10Dynamic panel-data estimation Number of obs = 100

. xtdpd abnormal liquidity, dgmmiv(abnormal) artests(2)

Standard: _consInstruments for level equation GMM-type: L(2/.).abnormalInstruments for differenced equation _cons -.1707729 .1029378 -1.66 0.097 -.3725273 .0309814 liquidity .0029237 .0017887 1.63 0.102 -.0005821 .0064294 nbm .1103026 .0737534 1.50 0.135 -.0342515 .2548566 abnormal Coef. Std. Err. z P>|z| [95% Conf. Interval] One-step results Prob > chi2 = 0.0008Number of instruments = 37 Wald chi2(2) = 14.28

max = 10 avg = 10 Obs per group: min = 10Time variable: dateGroup variable: id Number of groups = 10Dynamic panel-data estimation Number of obs = 100

. xtdpd abnormal nbm liquidity, dgmmiv(abnormal) artests(2)

Preliminary Results Dual sort into 9 portfolios

Standard: _consInstruments for level equation GMM-type: L(2/.).abnormalInstruments for differenced equation _cons .7689085 .2394674 3.21 0.001 .2995609 1.238256 size -.1680981 .0669543 -2.51 0.012 -.2993261 -.0368701 abnormal Coef. Std. Err. z P>|z| [95% Conf. Interval] One-step results Prob > chi2 = 0.0121Number of instruments = 37 Wald chi2(1) = 6.30

max = 10 avg = 10 Obs per group: min = 10Time variable: dateGroup variable: id Number of groups = 9Dynamic panel-data estimation Number of obs = 90

. xtdpd abnormal size, dgmmiv(abnormal) artests(2)

Standard: _consInstruments for level equation GMM-type: L(2/.).abnormalInstruments for differenced equation _cons -.2081826 .0937164 -2.22 0.026 -.3918634 -.0245019 nbm .4090686 .0939893 4.35 0.000 .2248529 .5932842 abnormal Coef. Std. Err. z P>|z| [95% Conf. Interval] One-step results Prob > chi2 = 0.0000Number of instruments = 37 Wald chi2(1) = 18.94

max = 10 avg = 10 Obs per group: min = 10Time variable: dateGroup variable: id Number of groups = 9Dynamic panel-data estimation Number of obs = 90

. xtdpd abnormal nbm, dgmmiv(abnormal) artests(2)

Standard: _consInstruments for level equation GMM-type: L(2/.).abnormalInstruments for differenced equation _cons -.1037579 .1161205 -0.89 0.372 -.3313499 .1238342 liquidity .003766 .0015081 2.50 0.013 .0008102 .0067217 abnormal Coef. Std. Err. z P>|z| [95% Conf. Interval] One-step results Prob > chi2 = 0.0125Number of instruments = 37 Wald chi2(1) = 6.24

max = 10 avg = 10 Obs per group: min = 10Time variable: dateGroup variable: id Number of groups = 9Dynamic panel-data estimation Number of obs = 90

. xtdpd abnormal liquidity, dgmmiv(abnormal) artests(2)

Preliminary Results Dual sort into 9 portfolios

Standard: _consInstruments for level equation GMM-type: L(2/.).abnormalInstruments for differenced equation _cons .20468 .270484 0.76 0.449 -.3254588 .7348188 nbm .3694293 .0973767 3.79 0.000 .1785744 .5602842 size -.1062041 .0652412 -1.63 0.104 -.2340744 .0216662 abnormal Coef. Std. Err. z P>|z| [95% Conf. Interval] One-step results Prob > chi2 = 0.0000Number of instruments = 37 Wald chi2(2) = 21.47

max = 10 avg = 10 Obs per group: min = 10Time variable: dateGroup variable: id Number of groups = 9Dynamic panel-data estimation Number of obs = 90

. xtdpd abnormal size nbm, dgmmiv(abnormal) artests(2)

Standard: _consInstruments for level equation GMM-type: L(2/.).abnormalInstruments for differenced equation _cons .1723088 .2868691 0.60 0.548 -.3899443 .7345619 size -.1047271 .0655875 -1.60 0.110 -.2332763 .0238221 liquidity .0005975 .0017179 0.35 0.728 -.0027695 .0039644 nbm .3513114 .1107108 3.17 0.002 .1343223 .5683005 abnormal Coef. Std. Err. z P>|z| [95% Conf. Interval] One-step results Prob > chi2 = 0.0001Number of instruments = 37 Wald chi2(3) = 21.46

max = 10 avg = 10 Obs per group: min = 10Time variable: dateGroup variable: id Number of groups = 9Dynamic panel-data estimation Number of obs = 90

. xtdpd abnormal nbm liquidity size, dgmmiv(abnormal) artests(2)

Still to be Investigated Analyse Liu’s 2-Factor model compared to FF 3

Factor model and the CAPM in explaining excess returns as sorted according to value and size criteria

Compare the mimicking liquidity factor to an innovations based liquidity risk

Compare and contrast results of different holding period returns

Expand sample backwards, pre-1997, and forward to the end of 2011

Questions?

Thank you!