The authors declare that they have no conflicts of interest.
This study did not require formal ethics approval.
Data sharing is not applicable to this article.
The authors received no specific funding for this work.
The study inspects the size and liquidity pattern in Pakistan equity market. Sample size contains 278 non-financial firm's monthly data listed on Pakistan Stock Exchange (PSX) from 2001 to 2012. This study uses three asset pricing models (eq.5), (eq.6) and (eq.7). Four factors asset pricing model estimates that momentum factor is positively and negatively linked with winner and loser stocks, both in size and liquidity patterns. Although it is observed that the presence of size and liquidity does not affect the coefficient results but average value of momentum premium in larger in liquidity than size pattern. Further, the study reveals high average stock returns on momentum strategy in liquidity pattern than size that is 8.05% Vs 6.67%, respectively. Results of this study contradicts Fama and French (2012) who concluded that size pattern in momentum factor outperform the equity market. But this study conclude that liquidity pattern outperforms the size pattern in momentum factor. This study raises the question that should investors and academicians consider size or liquidity pattern in momentum factor for high returns and future research?
Banz (
The sample size consists of monthly data of 278 non-financial firms listed at Pakistan Stock Exchange for the period of 2001 to 2012. The data of share prices and trading volume are collected from PSX website (www.psx.com.pk) and business recorder (www.brecorder.com.pk). Liquidity is measured by trading volume of stock. KSE-100 index data is collected from yahoo finance for the measurement of market returns. The Treasury bill rates are used as a proxy for the measurement of risk free return, its data is collected from the website of State Bank of Pakistan. Market value of equity and book-to- market equity ratio is use as a proxy for the measurement of size and value factor. For this purpose, data of outstanding shares and book equity is obtained from the financial reports of firms.
Portfolio approach is used to explore the relationship amongst the strategies sorted portfolio returns and four several risk factors i.e., market, size, value and momentum premium. This study follows methodology of Fama & French (
We construct six equal weighted portfolios for value factor from the intersection of two size and three value factors. These are S/V, S/N, S/G, B/V, B/N and B/G, where V, N and G represent value, neutral and growth respectively and S and B represent small and big stocks. Further six equally weighted portfolios were momentum factor from the intersection of two size and three momentum factors. These are S/W, S/N, S/L, B/W, B/N and B/L, where W, N and L represent winner, neutral and loser respectively, while S and B represent small and big stocks. At last addition to Fama & French (
For the measurement of size factor, the firms are rank and divided by 50:50 on the base of high and low market equity. The firms with low market equity are small (S) firms and the firms with high market equity are big (B) firms. To measure the market equity for single time, the closing price of share at June t is multiplied by the outstanding shares of specific firms at the end of June t. For the measurement of value factor, the firms are rank and divided as 30:40:30 on the base of book to market equity ratio. The firms with the top 30% (value) B/M ratio are consider high value stocks, middle 40% are consider neutral and last 30% (growth) are consider low value stocks. For the measurement of B/M ratio, the book value of equity at the end of June "t" was divided by the market value of equity at the of June "t" for each period. For the measurement of momentum factor, the firms are rank and divided into 30:40:30 on the base of previous year return from t-10 to t-1. Top 30% firms from previous year returns (t-10 to t-1) were considered winner stocks, middle 40% were neutral and last 30% were loser stocks. At last to measure the liquidity factor, the firms are rank and divided into 50:50 on the base of share turnover of each month at the end of June t. The firms with the top 50% were considered highly liquid stocks and last 50% was considered low liquid stocks.
This study uses the CAPM, F-F (1993) three factor and Carhart (
The size (SMB) factor is the difference of equal-weighted average returns on three (2 x 3) small stocks base on size and B/M ratio and equal-weighted average returns on three (2 x 3) big stocks base on size and B/M ratio.
SMB = (S/V + S/N + S/G)/3 - (B/V + B/N + B/G)/3 (1)
The value (HML) factor is the equal weighted average of value premium for small stocks HMLs and value premium for big stocks HMLb.
HML = (HMLs + HMLb)/ 2 (2).
HMLs = S/V - S/G (2.a)
HMLb = B/V - B/G (2.b)
The momentum (WML) factor is the equal weighted average of momentum premium for small stocks WMLs and momentum premium for big stocks WMLb.
WML = (WMLs + WMLb)/ 2 (3).
WMLs = S/W - S/L (3.a).
WMLb = B/W - B/L (3.b).
We also constructed the momentum factor with intersection of liquidity factor that is the equal- weighted average of momentum premium for illiquid stocks WMLi and momentum premium for liquid stocks WMLl.
WML = (WMLi + WMLl)/ 2 (4).
WMLi = I/W - I/L (4.a).
WMLl = l/W - l/L (4.b).
This study considers the eight-extreme excess portfolio returns on Pakistan Treasury bill rate on B/M ratio and momentum factor for small and big stocks. Also examine the extreme four excess portfolio returns for momentum on illiquid and liquid stocks by replacing momentum factor for small and big stocks.
We use three different step-wise asset pricing model to examine the portfolio returns in relation to given risk factors for monthly time series data. The first step is to estimate the capital asset pricing model (Sharpe,
Rpi,t − Rft = αi + bi(Rmt - Rft) + ℮i,t (5)
Rpi,t − Rft = αi + bi(Rmt - Rft) + si(SMBt) + hi(HMLt) + ℮i,t (6)
Rpi,t − Rft = αi + bi(Rmt - Rft) + si(SMBt) + hi(HMLt) + wi(WMLt) + ℮i,t (7)
Where Rpi,t present the return on portfolio i for month t, Rf is risk free rate for month t, Rm is market return for month t, (Rm-Rf) is the excess return on market to risk free rate known as market premium, 'α' is intercept that measures abnormal profit and 'b' is the coefficient of market factor. SMB is the difference between portfolio returns on base of small and big stocks known as size premium, HML is the difference between portfolio returns on base of high (value) and low (growth) B/M ratio known as value premium and WML is the difference between portfolio returns on base of previous high returns (winner) and previous low returns (loser) known as momentum premium. Where si, hi and wi are the coefficient of SMB, HML and WML respectively.
Capital asset pricing model assumes that the value of intercept ('α') must be equal to zero that is fully explained by market factor. If the value of intercept is significant and not equal to zero, it shows that CAPM failed to fully explain the portfolio returns and it encourages the investors to look for other CAPM anomalies. This study use OLS Newey-West standard errors with maximum lags to consider autocorrelation and heteroskedasticity issue in time series data.
Table 1 reports the mean, standard deviation and p-value of explanatory factor that is market premium (Rm-Rf) which is excess market return to 6 months Treasury bill rate. Further it reports portfolio returns of Small (S) and Big (B) firms as well as size premium (SMB). The result shows that market premium is positive and different from zero (p-value 0.016), it is followed by the risk aversion assumption. The monthly effect of market premium for given period is 1.118%. The monthly mean value of portfolio returns of S and B shows that B firms outperform the S firms. Recent literature argue that the behavior of small firm's is not consistent over various time period, sometime the effect of size anomalies vanishes and even behave reverse (Fama and French
| Mean | 0.011178151 | -0.00364 | 0.000891 | 0.004532 |
| Standard Deviation | 0.090872234 | 0.048129 | 0.074004 | 0.067765 |
| P-value at 95%. | 0.015646705 | 0.008287 | 0.012742 | 0.011668 |
The table 1 reports the monthly mean, standard deviation and p-value (95% confidence level) of market premium (Rm-Rf), size premium (SMB), Small (S) and Big (B) firms on the basis of market value. Market premium (Rm-Rf) presents the difference of returns on KSE-100 index and 6-month Pakistan T-bill rate. Small (S) presents the portfolio returns of small stocks (low market value). Big (B) presents the portfolio returns of big stocks (high market value). Size premium (SMB) presents the difference between the portfolio returns of Small and Big firms.
Table 2 reports the monthly mean, standard deviation and p-value of value premium (HML), value factor for small (HMLs) and big firm's stocks (HMLb) and the difference between HMLs and HMLb that is HMLs-b. The result shows that the mean value of value premium for small stocks are high than the mean value of value premium for big stocks and statistically significant. The mean value of HMLs-b indicates that the value premium for small stocks significantly outperform the value premium for big stocks by 1.06% per month. Fama & French (
Mean | 0.002812 | -0.00782 | -0.00251 | 0.010636 |
Standard Deviation | 0.058948 | 0.062174 | 0.047479 | 0.07526 |
P-value at 95%. | 0.01015 | 0.010705 | 0.008175 | 0.012959 |
The table 2 reports the monthly mean, standard deviation and p-value (95% confidence level) of value premium (HML), value premium for small stocks (HMLs) and value premium for large stocks (HMLb). It also reports the difference between HMLs and HMLb that is HMLs-b. HML factor is constructed by following the procedure of Fama and French (
Table 3 reports the monthly mean, standard deviation and p-value of momentum premium (WML), as well as the momentum factor for small (WMLs) and big firm's stocks (WMLb) and the difference between WMLs and WMLb that is WMLs-b. The result shows that the mean value of momentum premium for small stocks are bit higher than the mean value of momentum premium for big stocks and statistically significant. The mean value of WMLs-b indicates that the momentum premium for small stocks significantly outperform the value premium for big stocks by 0.4894% per month. The mean value of momentum premium (WML) is positively (6.67% per month) and statistically significant. Which is robust with Chui, Titman and Wei (2010) and Cakici N. et al (2013).
| Mean | 0.069199 | 0.0643053 | 0.066752 | 0.004894 |
| Standard Deviation | 0.105614 | 0.0947656 | 0.091106 | 0.084075 |
| P-value at 95%. | 0.018185 | 0.0163171 | 0.015687 | 0.014476 |
The table 3 reports the monthly mean returns, standard deviation and p-value (95% confidence level) of momentum premium (WML), momentum premium for small stocks (WMLs) and momentum premium for large stocks (WMLb). It also report the difference between WMLs and WMLb that is WMLs-b. WML factor is constructed by following the procedure of Fama and French (
Table 4 reports the monthly mean, standard deviation and p-value momentum premium (WML), as well as the momentum factor for illiquid (WMLi) and momentum factor for liquid firm's stocks (WMLl) and the difference between WMLi and WMLl that is WMLi-l. The result shows that the mean value of momentum premium for illiquid stocks are bit lower than the mean value of momentum premium for liquid stocks and statistically significant. The mean value of WMLi-l indicates that the momentum premium for liquid stocks significantly outperform the momentum premium for illiquid stocks. The mean value of momentum premium (WML) is positive (8.05% per month) and statistically significant.
| Mean | 0.079288 | 0.081772 | 0.08053 | -0.00248 |
| Standard Deviation | 0.097678 | 0.104554 | 0.088487 | 0.098109 |
| P-value at 95%. | 0.016819 | 0.018003 | 0.015236 | 0.016893 |
The table 4 reports the monthly mean returns, standard deviation and p-value (95% confidence level) of momentum premium (WML), momentum premium for illiquid stocks (WMLi) and momentum premium for liquid stocks (WMLl). It also report the difference between WMLi and WMLl that is WMLi-l. WML factor is constructed by following the procedure of Fama and French (
Table 5 result shows that the firm with high book to market equity ratio for small stocks outperform the firm with high book to market equity ratio for big stocks, while the firm with low book to market equity ratio for big stocks outperform the firm with low book to market equity ratio for small stocks.
| Mean | 0.0037 | 0.0009 | -0.0020 | -0.0004 | 0.0074 | 0.0066 |
| Standard Deviation | 0.0826 | 0.0972 | 0.0650 | 0.0860 | 0.0644 | 0.0712 |
| P-value at 95%. | 0.0142 | 0.0167 | 0.0112 | 0.0148 | 0.0111 | 0.0123 |
The table 5 reports the monthly mean returns, standard deviation and p-value (95% confidence level) of value and growth stocks of small firms (low market equity) and big firms (high market equity). S/G presents the intersection of small firms with the firms with low book to market equity ratio. S/N presents the intersection of small firms with the firms with neutral book to market equity ratio. S/V presents the intersection of small firms with the firms with high book to market equity ratio. B/G presents the intersection of big firms with the firms with low book to market equity ratio. B/N presents the intersection of big firms with the firms with neutral book to market equity ratio. B/V presents the intersection of big firms with the firms with high book to market equity ratio.
Table 6 result shows that the firm high returns in last year for small stocks outperform the firm with high returns in last year for big stocks, while the firm with the low returns in last year for big stocks are larger than the firm with the low returns in last year for small stocks although both are negative.
| Rural | 0.039 | 0.001 | -0.030 | 0.037 | 0.003 | -0.027 |
| Rural | 0.094 | 0.074 | 0.097 | 0.082 | 0.065 | 0.085 |
| Rural | 0.016 | 0.013 | 0.017 | 0.014 | 0.011 | 0.015 |
The table 6 reports the monthly mean returns, standard deviation and p-value (95% confidence level) of winner stocks and loser stocks of small firms (low market equity) and big firms (high market equity). S/W presents the intersection of small firms with the high returns (winner) in last year. S/M presents the intersection of small firms with the medium returns in last year. S/L presents the intersection of small firms with the low returns (loser) in last year. B/W presents the intersection of big firms with the high returns (winner) in last year. B/M presents the intersection of big firms with the medium returns in last year. B/L presents the intersection of big firms with the low returns (loser) in last year.
Table 7 result shows that the firm high returns in last year for illiquid stocks slightly outperform (almost equal) the firm with high returns in last year for liquid stocks, while the firm with the low returns in last year for liquid stocks are bit larger (almost equal) than the firm with the low returns in last year for illiquid stocks.
Mean | 0.0452 | 0.0029 | -0.0341 | 0.0445 | 0.0022 | -0.0372 |
Standard Deviation | 0.0828 | 0.0561 | 0.0787 | 0.0905 | 0.0836 | 0.1066 |
P-value at 95%. | 0.0143 | 0.0097 | 0.0135 | 0.0156 | 0.0144 | 0.0184 |
The table 7 reports the monthly mean returns, standard deviation and p-value (95% confidence level) of winner stocks and loser stocks of illiquid firms (low turnover) and liquid firms (high turnover). I/W presents the intersection of illiquid firms with the high returns (winner) in last year. I/M presents the intersection of illiquid firms with the medium returns in last year. I/L presents the intersection of illiquid firms with the low returns (loser) in last year. L/W presents the intersection of liquid firms with the high returns (winner) in last year. L/M presents the intersection of liquid firms with the medium returns in last year. L/L presents the intersection of liquid firms with the low returns (loser) in last year.
Table 8 reports the correlation between the given risk factors in Pakistan equity market for monthly time period from 2001 to 2012. It allows investors to design a portfolio among market, size, value and momentum strategies. The momentum factor is negatively correlated with all other risk factors which indicates that momentum perform well when other perform badly and vice versa. The same result is reported in table 9 also.
Rm-Rf | SMB | HML | WML | |
| Rm-Rf | 1 | |||
| SMB | -.329** | 1 | ||
| HML | 0.096 | -0.072 | 1 | |
| WML | -0.134 | -0.101 | -0.148 | 1 |
Table 8 reports the Pearson pair-wise correlation of explanatory four factors for monthly time series over. These four factors are excess market return (MKT), size premium (SMB), value premium (HML) and momentum premium (WML) on base of size.
Rm-Rf | SMB | HML | WML | |
| Rm-Rf | 1 | |||
| SMB | -.329** | 1 | ||
| HML | 0.096 | -0.072 | 1 | |
| WML | -0.122 | -0.077 | -0.154 | 1 |
Table 9 reports the Pearson pair-wise correlation of explanatory four factors for monthly time series over. These four factors are excess market return (MKT), size premium (SMB), value premium (HML) and momentum premium (WML) on base of liquidity.
Table 10 report the alpha and beta estimation of standard CAPM for time period of 2001 to 2012. The study used OLS through Newey-West standard errors with 6 lags to consider autocorrelation and heteroskedasticity in the returns. The result shows that alpha for value excess returns to T-bill is negatively insignificant while for loser excess returns to T-bill stocks the alpha is negatively significant at 95% confidence level. It is interesting to find that alpha for all winner stocks excess returns, both intersect with size and liquidity are positively and highly significant. The beta value of the market premium is positive and statistically significant for each given portfolio. The value of F-Statistics indicates that the overall model is statistically significant.
F-Stat (P-value) | |||
| S/G-Rf | -0.0108 | 0.3885 | 27.47 (0) |
| t-Stat | -1.3600 | 5.2400 | |
| S/V-Rf | -0.0074 | 0.3397 | 30.32 (0) |
| t-Stat | -0.9200 | 5.5100 | |
| B/G-Rf | -0.0047 | 0.4289 | 30.32 (0) |
| t-Stat | -1.0800 | 8.4800 | |
| B/V-Rf | -0.0142 | 0.5779 | 38.85 (0) |
| t-Stat | -2.3400 | 6.2300 | |
| S/W-Rf | 0.0280 | 0.3153 | 27.08 (0) |
| t-Stat | 3.4700 | 5.2000 | |
| S/L-Rf | -0.0426 | 0.4436 | 11.48 (0) |
| t-Stat | -4.6400 | 3.3900 | |
| B/W-Rf | 0.0252 | 0.3796 | 31.41 (0) |
| t-Stat | 3.0800 | 5.6000 | |
| B/L-Rf | -0.0406 | 0.5195 | 26.1 (0) |
| t-Stat | -5.3800 | 5.1100 | |
| I/W-Rf | 0.0354 | 0.2211 | 14.7 (0.0002) |
| t-Stat | 4.8500 | 3.8300 | |
| I/L-Rf | -0.0442 | 0.2493 | 6.47 (0.0121) |
| t-Stat | -6.2300 | 2.5400 | |
| L/W-Rf | 0.0325 | 0.4202 | 19.39 (0) |
| t-Stat | 4.1400 | 4.4000 | |
| L/L-Rf | -0.0516 | 0.6298 | 31.16 (0) |
| t-Stat | -6.2100 | 5.5800 |
Table 10, reports the alpha coefficient and beta estimates of capital asset pricing model (CAPM), where a i present the alpha for each given portfolios and b i present coefficient of market premium (MKT). The models are estimated using OLS Newey-West standard errors with six lags. The value in parentheses below the coefficient estimate present t-statistics.
Table 11 report the alpha and beta estimation of Fama & French (
| F-Stat (P-value) | |||||
| S/G-Rf | -0.009 | 0.649 | 1.403 | -0.334 | 30.09 (0) |
| t-Stat | -1.690 | 7.300 | 8.730 | -1.930 | |
| S/V-Rf | -0.004 | 0.501 | 1.110 | 0.628 | 64.65 (0) |
| t-Stat | -0.800 | 8.290 | 7.810 | 4.360 | |
| B/G-Rf | -0.006 | 0.423 | -0.134 | -0.348 | 30.52 (0) |
| t-Stat | -1.400 | 6.860 | -1.100 | -2.170 | |
| B/V-Rf | -0.012 | 0.571 | 0.160 | 0.690 | 44.3 (0) |
| t-Stat | -2.160 | 6.280 | 1.110 | 3.610 | |
| S/W-Rf | 0.029 | 0.491 | 0.989 | -0.064 | 11.77 (0) |
| t-Stat | 3.680 | 5.940 | 4.140 | -0.260 | |
| S/L-Rf | -0.040 | 0.635 | 1.178 | 0.278 | 17.68 (0) |
| t-Stat | -6.470 | 4.960 | 6.530 | 1.560 | |
| B/W-Rf | 0.025 | 0.381 | 0.015 | 0.033 | 13.96 (0) |
| t-Stat | 3.010 | 3.900 | 0.070 | 0.120 | |
| B/L-Rf | -0.039 | 0.589 | 0.467 | 0.241 | 21.63 (0) |
| t-Stat | -6.550 | 6.890 | 1.690 | 1.770 | |
| I/W-Rf | 0.037 | 0.361 | 0.817 | 0.046 | 9.54 (0) |
| t-Stat | 5.490 | 4.970 | 4.800 | 0.220 | |
| I/L-Rf | -0.042 | 0.388 | 0.827 | 0.114 | 14.83 (0) |
| t-Stat | -7.510 | 4.960 | 3.770 | 0.790 | |
| L/W-Rf | 0.032 | 0.481 | 0.301 | -0.164 | 6.53 (0) |
| t-Stat | 4.170 | 4.260 | 1.360 | -0.650 | |
| L/L-Rf | -0.049 | 0.753 | 0.800 | 0.326 | 29.01 (0) |
| t-Stat | -8.280 | 6.930 | 2.820 | 1.770 | |
Table 11 reports the alpha and beta estimates of Fama and French (
Table 12 reports the results of four factor model in which momentum factor is augmented with the Fama & French (
| F-Stat (P-value) | ||||||
| S/G-Rf | -0.017 | 0.668 | 1.437 | -0.305 | 0.106 | 24.71 (0) |
| t-Stat | -3.18 | 7.12 | 9.14 | -1.86 | 1.36 | |
| S/V-Rf | -0.007 | 0.51035 | 1.12605 | 0.64259 | 0.05134 | 52.02 (0) |
| t-Stat | -1.44 | 8.04 | 7.92 | 4.58 | 0.79 | |
| B/G-Rf | -0.0095 | 0.43217 | -0.117 | -0.3335 | 0.05182 | 22.07 (0) |
| t-Stat | -2 | 6.66 | -0.95 | -2.15 | 0.76 | |
| B/V-Rf | -0.019 | 0.58995 | 0.19429 | 0.71928 | 0.10659 | 30.05 (0) |
| t-Stat | -3.64 | 6.1 | 1.36 | 3.95 | 1.3 | |
| S/W-Rf | -0.014 | 0.605 | 1.197 | 0.114 | 0.649 | 53.89 (0) |
| t-Stat | -2.26 | 8.54 | 10.41 | 0.84 | 9.03 | |
| S/L-Rf | -0.011 | 0.559 | 1.041 | 0.160 | -0.428 | 62.84 (0) |
| t-Stat | -2.52 | 5.45 | 7.69 | 0.87 | -5.95 | |
| B/W-Rf | -0.007 | 0.466 | 0.171 | 0.166 | 0.486 | 11.45 (0) |
| t-Stat | -1.13 | 5.18 | 0.97 | 0.79 | 4.14 | |
| B/L-Rf | -0.010 | 0.512 | 0.326 | 0.121 | -0.438 | 43.9 (0) |
| t-Stat | -1.28 | 7.08 | 2.23 | 0.91 | -3.78 | |
Table 12 reports the alpha and beta estimates of four factor asset pricing model that is Fama and French (
Table 13 reports the four factor model but this time momentum factor is constructed by intersection with liquidity instead of size. The coefficient (wi) value for momentum premium predicts the positive significant association for winner sorted stocks for both liquid and illiquid stocks, while negative significant association with loser sorted stocks for both liquid and illiquid stocks.
| F-Stat (P-value) | ||||||
| S/G-Rf | -0.014 | 0.658 | 1.417 | -0.319 | 0.055 | 34.76 (0) |
| t-Stat | -2.98 | 7.12 | 8.36 | -1.85 | 0.72 | |
| S/V-Rf | -0.005 | 0.503 | 1.113 | 0.632 | 0.012 | 55.55 (0) |
| t-Stat | -0.85 | 7.83 | 7.41 | 4.37 | 0.18 | |
| B/G-Rf | -0.006 | 0.424 | -0.132 | -0.346 | 0.005 | 22.87 (0) |
| t-Stat | -1.25 | 6.54 | -1.03 | -2.15 | 0.08 | |
| B/V-Rf | -0.016 | 0.578 | 0.172 | 0.703 | 0.048 | 34.42 (0) |
| t-Stat | -3.21 | 6.13 | 1.13 | 3.68 | 0.63 | |
| I/W-Rf | -0.004 | 0.437 | 0.947 | 0.189 | 0.512 | 27.27 (0) |
| t-Stat | -0.6 | 6.17 | 7.02 | 1.55 | 6.25 | |
| I/L-Rf | -0.003 | 0.315 | 0.703 | -0.022 | -0.487 | 105.29 (0) |
| t-Stat | -0.67 | 4.43 | 5.56 | -0.19 | -6.87 | |
| L/W-Rf | -0.008 | 0.555 | 0.428 | -0.025 | 0.499 | 10.99 (0) |
| t-Stat | -1.2 | 5.21 | 2.42 | -0.13 | 4.77 | |
| L/L-Rf | -0.009 | 0.678 | 0.672 | 0.186 | -0.503 | 35.97 (0) |
| t-Stat | -1.17 | 6.7 | 4.24 | 0.9 | -5.18 | |
Table 13 reports the alpha and beta estimates of four factor asset pricing model that is Fama and French (
Some empirical studies conducted in emerging equity markets including Asia and many studies conducted in developed equity markets to identify the facts regarding size, value and momentum effects. The Karachi Stock Exchange (KSE) is one of the popular emerging equity market of Asia but we lack empirical literature in this context. Emerging equity markets are in large number of today population of the world and attract lot of significance. It is among the pioneer studies in Pakistan equity market which consider the size and liquidity pattern in momentum factor.
This study has three key findings, firstly we identified the size pattern in value and momentum effect; secondly, we identify the liquidity pattern in momentum effect. Thirdly we constructed excess portfolio base on size and value, size and momentum and lastly liquidity and momentum and regress by using CAPM, Fama & French (
We found market premium is positive and different from zero. The average portfolio returns of big firms are larger than the small firms and the mean value of size premium is negative and statically significant. The results are robust with Cakici and Tan (
The CAPM (5) result shows that the beta value of the market premium is positively significant for each given portfolio and the alpha for all winner stocks excess returns, both intersect with size and liquidity are positively significant. The Fama & French three factor model (6) shows that coefficient value for value stocks and growth stocks are positively and negatively respectively statistically significant. The Carhart four factor model shows that the market and size factor is positively significant. The coefficient value for value premium is positive and but only statistically significant for value stocks both small and big. While the coefficient value for momentum premium is positive for winner and negative with loser stocks both are highly significant. On other hand liquidity patterns in momentum factor by using four factor models predict that the coefficient value for momentum premium predicts the positive significant association for winner stocks and negative significant association with loser stocks.
It has been noticed that the inclusion of size and liquidity pattern did not influence the coefficient results, but the mean value for momentum is larger in liquidity pattern than size pattern.
The authors declare that they have no conflicts of interest.
This study did not require formal ethics approval.
Data sharing is not applicable to this article.