Four Factors Model in Asset Pricing: Fama&French Three Factors Model is Combined With Liquidity in the Stock Exchange of Vietnam

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1 Proceedngs Book of ICEFMO, 2013, Malaysa Handbook on the Economc, Fnance and Management Outlooks ISBN: Four Factors Model n Asset Prcng: Fama&French Three Factors Model s Combned Wth Lqudty n the Stock Exchange of Vetnam Tran Vet Hoang PhD, Natonal Unversty Ho Ch Mnh Cty, Lnh Trung Ward, Thu Duc Dstrct, Ho Ch Mnh Cty, Vet Nam. E-mal: tranvethoangvnu@yahoo.com Nguyen Ngoc Huy PhD, Head of Faculty of Fnance and Bankng, Unversty of Economcs and Law, Natonal Unversty Ho Ch Mnh Cty, Lnh Xuan Ward, Thu Duc Dstrct, Ho Ch Mnh Cty, Vet Nam E-mal: nnhuy@uel.edu.vn Nguyen Anh Phong PhD Canddate, Faculty of Fnance and Bankng, Unversty of Economcs and Law, Natonal Unversty Ho Ch Mnh Cty, Lnh Xuan Ward, Thu Duc Dstrct, Ho Ch Mnh Cty, Vet Nam E-mal: phongna@uel.edu.vn Abstract Ths paper ams to assess the applcaton of Fama and French three factors models n Vetnam's stock market from January 2007 to December The selected lstng companes must contnuously had been lsted for at least 2 years and non-stop tradng or moved to the other exchange. Accordng that, n 2007 the author selected 162 companes, and n 2008, 2009, 2010 and 2011, there were 204, 308, 382, 382 lsted companes were selected n turn. The author also dvded them nto 6 groups: B/H, B/M, B/L; S/H, S/M and S/L. In whch, portfolos B and S are to evaluate the effects of sze and rsk scale to the proftablty rate (sze measured by captalzaton of the stock market) and portfolos H, M and L are measurng the effects of book to market value. The result are appearng that Fama and French three factor models explanng the relatonshp between rate of return and rsk n superor to CAPM. Ths research also evaluates the mpacts of lqudty and rsk of lqudty to stock returns whch were lsted n 28

2 Tran Vet Hoang; Nguyen Ngoc Huy; Nguyen Anh Phong Vetnamese stock market. Accordng to ths research, lqudty rato s the porton between number of share traded and number of share outstandng (ths called Lq2) as same as Amhud and Mendelson s research (1986), Datar-Nak and Radclffe s research (1998), and Wang and Ioro s research (2007). Moreover, the authors also use the alternatve approaches to evaluate lqudty: the average of traded value n a month (ths called Lq1). Contrary to prevous researches, ths research shows that correlatons between ndcators Lq1 and Lq2 and stock returns are postvely correlatons. Fnally, we evaluates four factor model by combng the FF3 and lqudty. The result are appearng ths models explanng the relatonshp between rate of returns and rsk n superor to CAPM and FF3. So we suggest the four factor model: FF3 combned wth lqudty n evaluatng stocks exchange of Vet Nam. Keywords: FF3, CAPM, GMM, Lqudty, rsk and returns, asset prcng, cross-secton. 1. Introducton Captal Assest Prcng Model whch was ntroduced by Sharpe (1964), Lntner (1965) consders the relatonshp between expected return of an asset and t s systematc rsk (measured by beta (β)). Ths model s more controversal today because of the lmtatons of t such as the perfect market assumpton, the dffcult of choosng the representatve portfolo, values need to be assgned to the rsk-free rate of return, the return on the market or the equty rsk premum (ERP),... The paper conducted by Fama and MacBeth (1973) whch ntroduced the method to verfy the emprcal valdaton of the CAPM, after that, put a cornerstone for a number of researches testng the approprateness of the CAPM model n the emergng stock market such as the study handled by Therou Chatzoglou, Madtnos and Aggelds (2003) n the Greek stock market, the study of Wang and Ioro (2007) n the Chnese stock market... In the Vetnam stock market, the research by Nguyen Anh Phong (2012) also ponted out that the lack of emprcal results of the CAPM model and the desre for an alternatve quanttatve method wth more approprateness. Therefore, besdes the market rsk represented by the CAPM, the need for dscover the other rsks affectng stocks yeld lsted on the Vetnam stock market s more essental. 2. Overvew of the researches Banz (1981) Ths s the frst emprcal study on the relatonshp between the rate of return wth the market prce of the stocks lsted on NYSE. Ths study s the premse for the subsequent others evaluatng the effect of the rsk scale to the rate of return rather than the market rsk (beta) n the CAPM model. The result showed that the rsk adjusted rate of return of small companes had been hgher than the ones of the large companes. Ths s ndcated that the effect of sze had exsted at least 40 years and ths s evdence that the CAPM s no longer sutable. The result showed that the exstence of the non-lnear relatonshp between the sze wth the expected rate of return: on average, the ncome of small companes s 0.4% hgher than the ncome of large companes. There was a negatve correlaton between beta and rate of return. Banz concluded that company sze may represent rsk to the CAPM. Basu (1983) Hs study measured the relatonshp between earnngs prce ratos (E/P), frms sze wth rate of return. The result showed that the stocks wth hgh E / P ratos earned hgher average yeld than the others wth low E/P ratos, and the small frms tended to have a hgher average yeld than the large ones. The stocks wth small sze yelded hgher average rate of return than the others wth large sze: the average yeld earned by the small stocks s 1.38% per month, whle the large frms only produced 0.59% per month. Smlarly, the stocks wth hgh E/P ratos had hgher average rate of return than the group wth low E/P: average yeld come from the group wth hgh E/P s 1.38% per month whle only 0.72% per month earned by the stocks wth low E/P. 29

3 Handbook on the Economc, Fnance and Management Outlooks Fama and French (1992), Fama and French (1993) The study (1992) evaluatng the effects of beta, sze and BE/ME (book to market equty) to rate of return showed the relatonshp between beta wth yeld s blurrng even when only beta was ndvdually consdered wthout any other varables puttng nto the model, meanwhle the sze and BE/ME varables are closely correlated to rate of return. The research (1993) dentfed fve rsk factors affectng the rate of return of stocks and bonds, n whch, there were three market rsks of the stocks: the general market factor, the factor related to sze and a factor related to the book to market prce (B/M). The two rest factors were belonged to the bond market: the term factor and the rsk of default. It s mportant to note that there was a sgnfcant relatonshp between these fve factors and the rate of return of the stocks and bonds. In the reasonable market, the change n proft n the short term had fantly affected the stock prce and the BE/ME rato. The relatonshp between BE/ME wth the proft dfferrences s only sgnfcant n the long-term. Those companes had the hgh BE/ME ratos (market prce low relatve to book value) tend to prolong the recesson. By contrast, the ones wth low BE/ME ratos (market prce hgh relatve to book value) tend to mantan strongly proftablty. Combnng wth BE/ME, the small stocks tend to be less proftable than large stocks. There were two questons rased up by thst result: (1) What s the potental varables of economc condton whch create the relatonshp between the change n earnngs and profts wth the sze and the BE/ME ratos? (2) whether the condton varables whch are not aware, make a change n consumpton and wealth whch wll not be recognzed by an overall market factor or not and whether there s any relaton exstng between the rsk premum wth the sze and BE/ME or not? Keth S.K. Lam (2002) The study consdered the relatonshp between rate of return wth beta, sze, fnancal leverage, BE/ME, E/P n the Hong Kong stock market by the Fama-French method (1992). Lke many prevous studes n Hong Kong and U.S. stock market, ths study ndcated that beta s not wellexplaned the monthly average rate of return n the Hong Kong stock market from 7/1980 to 6/1997; three varables: sze, BE/ME and E/P, however, seems to be better n explanng the monthly average rate of return. Pn Huang Chou, Robn K.Chou, and Jane Sue Wang (2004) They consder the strength n explanng the effect of the sze, the book to market (BM) rato to the rate of return. The research result showed that n general, the forecast ablty of the sze and the BM factors decreased over the and perod respectvely. The sze varable remaned sgnfcant level n explanaton n January. The relatonshp between the rate of return wth the ln(me) s nverse (negatve correlaton), whle the relatonshp between the rate of return wth the ln(be/me) s postvely assocated (postve correlaton) Yuenan Wang and Amala D Ioro (2007) In ths study, the authors used a market value of equty representng for the sze, n addton, the study also examned the mpact of other factors to the rate of return of stocks such as lqudty, the B/M rato (Book to market rato), E/P, sze... Accordng to Fama and MacBeth (1973), the result showed that the effects of sze and B/M are sgnfcant at 95%, the effect of sze s %/month and the effect of the B/M rato s %/month, whle the effect of lqudty s %/month. However, the effect of lqudty s qute fant, the sgnfcance level s not convncng. Nopbhanon Homsud, Jatuphon Wasunsakul, Srna Phuangnark, Jtwatthana Joongpong (2009) Ths study measured the valdaton of the Fama and French three factor model n the Thaland stock market from June 2002 to May The research result showed that the three factors model explanng the effect of the rsk factor to the rate of return of stock s better than the tradtonal CAPM model. Nguyen Anh Phong (2012), Research show that lqudty s relatonshp wth rate of return when Beta coeffcent s brought nto research model. The results also show that the combnaton between lqudty and Beta coeffcent explan the result of rate of return clearly (because constants are close tozero). Moreover, ths result also shows that correlaton between Beta coeffcent and lqudty ndcators are postvely correlatons and correlaton coeffcent s so small. Those prove that usng CAPM to forecast rate of return n Vetnamese stock market s not approprate, but lqudty ndcators explan the results of rate of return and rsk of stocks whch were posted better. 30

4 Tran Vet Hoang; Nguyen Ngoc Huy; Nguyen Anh Phong 3.The research method a. Data The research data s calculated based on the data of companes announced n Hano and HCM Cty Stock Exchange from January 2007 to Decembe 2011, the rate of return data are based on the closng prce of last month and early month. The rate of return of the ndvdual stocks s calculated by the formula: R t = ln(p t /P t-1 ), rsk-free rate s the 1 year government bond rate. (calculate average per month) The study used the lstng companes whch contnuously had been lsted for at least 2 years and non - stop tradng or moved to the other exchange. Accordng that, n 2007 the author selected 162 companes, and n 2008, 2009, 2010 and 2011, there were 204, 308, 382, 382 lsted companes were selected n turn. All of the stocks are dvded nto the groups by market value of equty (ME), then there are 5% of stocks n hghest and lowest values cleaned out n order to avod the dstorton of data. Market value of equty s calculated based on the number of shares outstandng the prevous year (t-1) multple wth the current last month tradng prce. Every month all the companes are dvded nto 2 groups: Group wth ME above the ntersect pont (mean value) s the group of large companes (B), group wth ME below the ntersect pont s called the small corporate group (S). BE/ME rato s dvded nto 3 groups: group wth hghest BE/ME (30%) s called the group H, group wth medum BE/ME referred to as the group M and the last one wth lowest BE/ME s known as the group L. Fnally, these groups are combned and then dvded nto 6 groups: S/L, S/M, S/H, B/L, B/M and B/H. For example, the group S/L ncludes the small company compared wth the company wth lowest BE/ME rato. Group SMB (Small mnus Bg) represents the rsk scale, SMB s the dfference each month between the average rate of return of a small group (S/L, S/M and S/H) compared wth the average rate of return of a large group (B/ L, B/M and B/H) SMB = 1/3 (S/H + S/M + S/L) - 1/3 (B/H + B/M + B/L) Group HML (Hgh mnus Low) represent rsk of the BE/ME rato. HML s the dfference each month between the average rate of return of the two portfolos wth hgh BE/ME (S/H and B/H) compared wth the average rate of return of the two groups wth low BE/ME (S/L and B/L) HML = ½ (S/ H + B/H) - ½ (S/L + B/L) Accordng to ths research, we use two proxy to represent lqudty. Lq1 s the average of traded value n a month; Lq2 s the porton between number of share traded and number of share outstandng. We devde each lqudty nto two porfolos: portfolo wth hgh lqudty and low lqudty. After that we calculate average returns two ths portfolos. Average return of hgh lqudty s called H, and average return of low lqudty s called L. LHLq s equal average return of low lqudty s called L mnus average return of hg lqudty s called L. So we have LHLq1, LHLq2 portfolos. Our target to fnd the rsk premum of lqudty n each case. b.method The authors use the model of Fama and French (1993) and applyng the method of Fama and French (1996). We use four models: Model 1: Model 2: ( r r RF ) a b ( r M r RF ) s ( r SMB ) h ( r HML ) e ( r rrf ) a b ( rm rrf ) s ( rsmb ) h ( rhml ) l1 ( r LHLq1 ) e 31

5 Handbook on the Economc, Fnance and Management Outlooks Model 3: Model 4: ( r rrf ) a b ( rm rrf ) s ( rsmb ) h ( rhml ) l2 ( r LHLq2 ) e ( r rrf ) a b ( rm rrf ) s ( rsmb ) h ( rhml ) l1 ( r LHLq1 ) l2 ( r LHLq2 ) e where: r : the average rate of return of the group r M RF : the average market rate of return r : the rsk-free rate ( the 1 year government bond rate converted nto a monthly bass) r r SMB HML : the average rate of return of the portfolo wth small mnus bg : the average rate of return of the portfolo wth hgh BE/ME mnus low BE/ME r LHLq1: the average rate of return of the portfolo wth low Lq1 mnus hgh Lq1 r LHLq2 : the average rate of return of the portfolo wth low Lq2 mnus hgh Lq2 a : the ntercept coeffcent of the group b, s, h, l 1, l 2 : the slope coeffcents of the groups e : random error 4. The result Table 1 descrbes the sample data from 1/2007 to 12/2011 categorzed by 8 portfolos. In 2007 and 2008 the volaton of average rate of return s slghtly hgh, the dfference between the hghest rate of return wth the lowest rate of return also appears as a bg gap. For example, n 2007 the hghest average rate of return of the group B/H s 54,81% whle the lowest average rate of return belongs to the group B/L (-20,58%). The average rate of return of the groups n 2008 and 2011 are below 0 because before 2008 the stock market strongly grow up, after that the crss comng from US n 2008 makes the market dramatcally fall n the downturn. In 2011 because of the affect of the crss, the hgh nflaton rate, the goverment conducted a tgh monetary polcy; these factors, after that, contrbuted nto the recesson of the stock market. The volaton n 2011, however, s not hgh, the standard devaton s below 8%/month, the hghest volaton s only 7.61%/month. Because of standard devaton s too hgh and ftful, so we use GMM (General Momentum Method) to evaluate the data nstead of usng tradtonal methods. GMM overcome some problems n solvng data such as: heteroscedastc, condtonally heteroscedastc, multcollnerrty, Table 2 presents the regresson results of 8 portfolos appled the CAPM model; the Fama & French model and FF3 combned wth lqudty. The CAPM regresson results n sx portfolos showed the relatve hgh Adj R 2 coeffcence rangng from 62.78% to 87.23% (the average s 75.24%), the statstcal sgnfcance level of the slope coeffcent reached 99% for all portfolos. The regresson results on sx portfolos accordng to FF3 also showed the hgh Adj R 2 coeffcence rangng from 84.34% to 93.88% (the average s 89.86%). The sgnfcance level of the slope coeffcent, however, s not stable, the nfluence on the BE/ME rato n portfolos B/M, B/H and B/L s not statstcally sgnfcant (the pro coeffcents are 0.49 and 0.75 respectvely for examble). FF3 combned lqudty regresson results n sx portfolos showed hgher Adj R 2 than CAPM and FF3. However, all the ntercept coeffcent n FF3 combned wth lqudty models s whole lower than CAPM and FF3, so ths models explanng the relatonshp between rate of returns and rsk n superor to CAPM and FF3. The average ntercept coeffcent (constant) of 6 portfolos followng the CAPM model s , average ntercept coeffcent 32

6 Tran Vet Hoang; Nguyen Ngoc Huy; Nguyen Anh Phong of 6 portfolos applyng the Fama and French model s , whle the average ntercept coeffcent of 6 portfolos applyng the Fama and French combned lq1 and lq2 model are and The smaller ntercept coeffcents n the Fama and French combned lqudty model, the more sgnfcance level of the varables puttng nto the model compared wth the CAPM and FF3. Table-1. Descrpton data (returns per month) S/L S/M S/H B/L B/M B/H Rm LHLq1 LHLq2 Year-2007 (1944 Obs) Mn Max Average S.D Year-2008 (2448 Obs) Mn Max Average S.D Year-2009 (3696 Obs) Mn Max Average S.D Year-2010 (4584 Obs) Mn Max Average S.D Year-2011 (4584 Obs) Mn Max Average S.D Table 2 show the coeffcent of L1 and L2 are negatve, so returns of low lqudty stock s hgher than returns of hgh lqudty stock. Those results are opposte researches whch are executed n foregn stock market as same as Datar, Nak and Radclffe s research (1988), Chan and Faff s research (2005), Wang and Ioro s research (2007). Thus, ths research wants to prove followed problems: Frstly, Vetnamese nvestors only expect to have hgh rate of return of stocks whch have hgh lqudty, because the stocks whch have hgh lqudty n Vetnamese stock market s Blue-chp stock, they are wllng to accept hgher rsk to get hgher rate of return. Secondly, Vetnamese nvestors nvest together, they buy stocks whch are hgh captalzaton, easy to trade followng the bg nvestor s control and they do not care the rsks when ndex of stock marketfall down or havng some bad news. For example, on March 33

7 Handbook on the Economc, Fnance and Management Outlooks 2012, some stocks whch are warned as same as SAM, NTB stll ncrease ther celng prces. And fnally, the nvestors who nvest to Vetnamese stock market often have short-nvestment (ths called surfng nvestment). Therefore, they focus to nvest to the stocks whch have hgh lqudty (blue-chp stock) expectedhgh rate of return (f ndex of stock market grow up), and they also accept hgh rsk (f ndex of stock market fall down because the stock market s leaded by those stocks). Table-2. Regresson of CAPM; Fama and French Three factors Model and FF3 combned wth Lqudty sorted by portfolos: from Jan 2007 to Dec 2011 (usng GMM regresson) a b s h l1 l2 Adj.R 2 CAPM S/L (0.14) 1.06(0.00) S/M (0.19) 1.01(0.00) S/H (0.04) (0.00) B/L (0.00) (0.00) B/M 0.006(0.50) (0.00) B/H (0.00) (0.00) Fama&French (FF3) S/L (0.00) (0.00) (0.00) *(0.00) S/M (0.05) (0.00) (0.00) (0.39) S/H (0.00) 1.02(0.00) (0.00) (0.00) B/L (0.00) (0.00) (0.24) (0.43) B/M (0.51) (0.00) (0.11) (0.75) B/H (0.00) (0.00) (0.49) (0.00) Fama&French combned Lq1 S/L (0.06) (0.00) (0.00) (0.01) *(0.02) S/M (0.09) (0.00) (0.00) (0.33) (0.64) S/H (0.01) (0.00) (0.00) (0.00) (0.09) B/L (0.00) (0.00) (0.00) (0.25) (0.04) B/M (0.22) (0.00) (0.31) (0.93) (0.51) B/H (0.01) (0.00) (0.00) (0.00) (0.00) Fama&French combned Lq2 S/L (0.55) (0.00) (0.00) (0.00) (0.03) S/M (0.63) (0.00) (0.00) (0.57) (0.31) S/H (0.65) (0.00) (0.00) (0.00) (0.00) B/L (0.67) (0.00) (0.08) (0.03) (0.00) B/M (0.86) (0.00) (0.40) (0.66) (0.67) B/H (0.48) (0.00) (0.03) (0.00) (0.00) Number n parentheseses s sgnfcant (Sg) Sgnfcant at 95% confdence nterval f Sg <=0.05 Sgnfcant at 99% confdence nterval f Sg <= 0.01 Sgnfcant at 90% confdence nterval f Sg <= Concluson Ths paper resarch propose two mportant results: Frstly, lq1 rato s the the average of traded value n a month and lq2 s the porton between number of share traded and number of share outstandng are relatve to the stock returns. But the correlatons between ndcators LHLq1 and LHLq2 and stock returns are negatve correlatons. Ths mples that returns of low lqudty stock s hgher than returns of 34

8 Tran Vet Hoang; Nguyen Ngoc Huy; Nguyen Anh Phong hgh lqudty stock. Those results are opposte researches whch are executed n others stock market. Fnally, we evaluates four factors model by combng the FF3 and lqudty. The result are appearng ths models explanng the relatonshp between rate of returns and rsk n superor to CAPM and FF3. So we suggest the four factors model: FF3 combned wth lqudty n evaluatng stocks exchange of Vet Nam. References Banz, R. W. (1981). The relatonshp between return and market value of common stocks. Journal of Fnancal Economcs, 9, Chan, H. W. and R. W. Faff (2005), Asset prcng and the llqudty premum. The Fnancal Revew 40, Fama, E. F. and J. D. MacBeth (1973), Rsk, return and equlbrum: Emprcal tests. Journal of Poltcal Economy 81, Fama, E. F. and K. R. French (1992), The cross-secton of expected stock returns. Journal of Fnance 47, Fama, E. F. and K. R. French (1993), Common rsk factors n the returns on stocks and bonds. Journal of Fnancal Economcs 33, Keth S.K. Lam (2002), The relatonshp between sze, book-to-marketequty rato, earnngs prce rato, and return for the Hong Kong stock market Global Fnance Journal, Jagannathan, R., and Wang, Z. (1996), "The condtonal CAPM and the cross-secton of expected returns". Journal of Fnance 51, Longstaff, F. A. (1995), "How much can marketablty affect securty values?". Journal of Fnance 50, Nguyen Anh Phong (2012), The sutablty of the CAPM n the Vetnam Securtes Market, Bakng Technology Revew 73, pp Nguyen Anh Phong (2012), Lqudty and Expected Stock Returns Lsted on Vetnamese Stock Market, European Journal of Economcs, Fnance and Admnstratve Scences 48, pp Nguyen Anh Phong and Tran Vet Hoang (2012), Applyng Fama and French Three Factors Model and Captal Asset Prcng Model n the Stock Exchange of Vetnam, Internatonal Research Journal of Fnance and Economcs, Issue 95, pp Pn-Huang Chou, Robn K. Chou and Jane-Sue Wang (2004), On the Cross secton of Expected Stock Returns: Fama-French Ten Years Later, Fnance Letters, 2004, 2 (1), Shanken, J. (1992), "On estmaton of beta-prcng models", Revew of Fnancal Studes 5, Sharpe, W. (1964), "Captal asset prces: A theory of market equlbrum under condtons of rsk". Journal of Fnance 19, Yuenan Wang, Amala D Ioro (2007), The cross secton of expected stock returns n the Chnese A- share market, Global Fnance Journal 17 (2007)