Evidence to Support the Four-Factor Pricing Model from the Canadian Stock Market

Int.Fin.Markets,Inst.and Money14(2004)313–328Evidence to support the four-factor pricing model from the Canadian stock marketJean-François L’Her a,∗,Tarek Masmoudi b,1,Jean-Marc Suret c,2a Research-Risk Management and Depositors’Accounts Management,La Caisse de dépˆo t et placement duQuébec,Centre CDP Capital,1000Place Jean-Paul-Riopelle,Montréal,Qué.,Canada H2Z2B3 bÉcole des HautesÉtudes Commerciales,3000Chemin de la Cˆo te-Sainte-Catherine,Montréal,Qué.,Canada H3T2A7c School of Accountancy,Facultéd’Administration,UniversitéLaval,Québec,Qué.,Canada G1K7P4Accepted26September2003Available online9April2004AbstractThis paper tests the Fama-French three-factor pricing model augmented by a momentum factor on the Canadian stock ing Fama-French’s methodology to construct the risk factors,the average annual premium obtained for the market,size,book-to-market and momentum risk factors are, respectively,equal to4.52,5.08,5.09and16.07%,over the July1960–April2001period.The results relative to the three zero-investment portfolios are in line with those obtained by Liew and Vassalou [Journal of Financial Economics57(2000)221]for the1976–1996period,even though the authors use sequential sorts to construct the risk factors.The main evidence of regularities in factors’behavior are as follows:the size factor returns are substantially greater in January than in other months,whereas the momentum factor returns are always significant,except in January.Book-to-market factor returns are positive(negative)and highly(barely)significant in down-markets(up-markets).Lastly,regarding conditioning on the monetary policy environment,wefind that the SMB and HML premiums are only significant in an expansive environment.©2004Elsevier B.V.All rights reserved.JEL classification:G12Keywords:Four-factor pricing model;Canadian stock market∗Corresponding author.Tel.:+1-514-847-2601;fax:+1-514-847-5443.E-mail addresses:jlher@cdp.ca(J.-F.L’Her),tarek.masmoudi@hec.ca(T.Masmoudi),jean-marc.suret@fsa.ulaval.ca(J.-M.Suret).1Tel.:+1-514-340-6000;fax:+1-514-340-6411.2Tel.:+1-418-848-3021;fax:+1-418-656-7746.1042-4431/$–see front matter©2004Elsevier B.V.All rights reserved.doi:10.1016/j.intfin.2003.09.001314J.-F.L’Her et al./Int.Fin.Markets,Inst.and Money14(2004)313–3281.IntroductionSince1992,Fama and French have outlined the importance of three factors in explaining security returns.These factors are the market premium(market excess return),the size premium(difference in returns between portfolios of small capitalizationfirms and big capitalizationfirms;small minus big(SMB))and the book-to-market premium(difference in returns between portfolios of high book-to-market and small book-to-marketfirms;high minus low(HML)).The last two factors are designed to mimic“two underlying risk factors or state variables of special hedging concern to investors”(Fama and French,1996,p.57).Fama and French argue that this pricing is rational and conjecture that the book-to-market premium is associated with a relative distress factor,as did Chan and Chen(1991).In other words, value stocks that have high book-to-market ratios(or earnings-to-price cashflow-to-price; see Lakonishok et al.,1994or Fama and French,1996)have,on average,higher returns than growth stocks or glamour stocks,that is stocks that have low book-to-market ratios(or earnings to price or cashflow to price).The Fama and French three-factor pricing model captures most market anomalies(Fama and French,1996),except the momentum anomaly.A number of studies initiated by Jegadeesh and Titman(1993)show that strategies that involve taking a long(short)po-sition in well(poorly)performing stocks on the basis of past performance over the previous 3–12months tend to produce significantly positive abnormal returns of about1%per month for the following year.These return continuation strategies(momentum return in individual stocks),motivated by the positive correlation between past and future stock returns,have been tested extensively.The results,which are corroborated by Fama and French(1996) and Jegadeesh and Titman(2001)for the United States,apply equally well to developed markets(see Rouwenhorst(1998),Chui et al.(2000)for Asian markets)and emerging markets(Rouwenhorst,1999).Grundy and Martin(2001)conclude that“assuming that the anomaly(profitability of momentum strategies)endures,then,quite appropriately,it will enter the lexicon offinance as a‘factor’whose economics are as well understood as the SMB and HML factors:if it remains a fact,it becomes a factor(p.72).”Few studies have augmented the Fama and French three-factor model with a momentum factor winners minus losers(WML).Following Carhart(1997),Brav et al.(2000),Eckbo et al.(2000),Jegadeesh (2000),and Liew and Vassalou(2000),we use a four-factor pricing model(FFPM).The magnitude of the size and book-to-market premiums cast some doubts on the CAPM, but also created skepticism among thefinancial management and academic communities:first,in1999–2000,growth stocks in the US have experienced an unprecedented extraor-dinary good performance;second,“if small,high B/M stock earn such high returns,how come investment professionals have a hard time beating the S&P500—an index of large, low B/Mfirms?”(Loughran,1997,p.250).This study provides another out-of-sample test of the Fama-French TFPM and the momentum factor in the Canadian stock market,and sheds some light on this debate.To our knowledge,only three studies have reported results obtained on two or three zero-investment portfolios in Canada over a long period.All these studies consist of in-ternational research in which Canadian results are not the main focus.Arshanapalli et al. (1998a,b)report results on18international equity markets,over the1975–1996period. Theyfind positive HML premiums in13out of18markets and positive SMB premiums inJ.-F.L’Her et al./Int.Fin.Markets,Inst.and Money14(2004)313–328315 10out of18markets.Both results pertaining to Canada are significantly positive.Bauman et al.(1998)use four valuation ratios to define value stocks and growth stocks in19coun-tries.Over the1985–1996period,theyfind a positive HML premium in11out of19markets (including Canada),and a strongfirm-size effect.Only Liew and Vassalou(2000)have ex-amined the returns from SMB,HML and WML in Canada.In a study of10major markets, the authorsfind significant local SMB premiums for four out of ten markets,significant local HML premiums for nine out ten markets and significant local WML premiums for eight out of10markets.3All results pertaining to Canada are significantly different from zero over the1978–1996period.The main differences between Liew and Vassalou(2000)and this study are as follows. Liew and Vassalou focus on the predictability of economic growth through book-to-market, size and momentum risk factors in10major markets,whereas this study focuses on the risk factors’returns in Canada and examines the regularities in the factors’behavior that are associated with the turn-of-the-year,with up-and down-market conditions,as well as restrictive and expansive monetary policies.Liew and Vassalou examine the1978–1996 period and their sample of Canadianfirms comprises274on average,whereas the period analyzed in this study is much longer(the1960–2001period)and the average number of firms is298.Finally,the portfolio construction procedure to calculate SMB,HML and WML is based on three sequential sorts in Liew and Vassalou,whereas the one used here is based on three independent sorts,followed by an orthogonalization of HML and WML with SMB(Fama-French methodology).The main results are presented below.First,the average annual returns on SMB and HML are,respectively,equal to5.08and 5.09%,with standard deviations of10.97and12.72%.The SMB premium is slightly larger and less volatile than the one observed by Fama and French in the US,however,the HML premium is lower and as volatile as the premium found by Fama and French in US.WML premium is by far the largest premium observed in the Canadian stock market:1.34%per month.This premium is comparable to the one observed in the US by Jegadeesh and Titman (2001)over the1965–1998period(1.23%per month,t-statistic=6.43).4These results are also consistent with those obtained by Liew and Vassalou(2000)over the1978–1996period. Second,it documents in the Canadian stock market the very pronounced January effect documented by Loughran(1997),Davis(1994),and Davis et al.(2000)in the US.Average returns in January are significantly different from0at the1%level for the market,SMB and HML premiums.They are still significantly different from0for the other months,but to a much lesser extent.We alsofind that up-and down-markets influence the SMB and HML premiums as reported by Chan et al.(1998)in the US,the UK and Japan.During periods of up-markets,the SMB and HML premiums are not significantly different from zero,whereas in periods of down-markets the size premium,and particularly the book-to-market premiums are positive and very large.Finally,following Jensen et al.(1997),we also examine the influence of the monetary environment over the SMB,HML and WML premiums.We find that the stratification between periods of restrictive expansive monetary policy has 3These reported results hold for quarterly rebalancing frequencies,which yield higher returns than portfolios rebalanced on semi-annual or annual frequencies.4Jegadeesh and Titman(2001)used10momentum portfolios and the numbers reported hold for the hedge portfolio:the top10%minus the bottom10%.316J.-F.L’Her et al./Int.Fin.Markets,Inst.and Money14(2004)313–328no significant impact on the WML premium,whereas,consistently with JJM,the SMB and HML premiums are not significant in a restrictive monetary environment,and highly significant in an expansive monetary environment.The remainder of the paper is organized as follows.In Section2,we present the FFPM, the data and the methodology used to construct the factors.In Section3,we present the results on the risk factors,then on the regularities in the factors’behavior in the Canadian stock market.Section4presents concluding remarks.2.Data and methodologyThis section describes the data followed by the methodology used to calculate the four risk factors.2.1.DataWe examine the monthly returns from the four factors:R M−R F,SMB,HML and WML on the Canadian stock market over the July1960–April2001period.Data rela-tive tofinancial statements come from the Financial Post database(from1959to1986; 1992version)and from Research Insight Compustat(from1987to2000;2001version).5 Monthly stock returns andfirms’market equity(ME:number of shares outstanding times the stock price)come from the TSE-Western tape(from July1959to December1986; 1998version)and from Research Insight Compustat(from January1987to April2001; 2001version).The market return is a value-weighted return computed from the sample.6 Returns from the risk-free asset are estimated from the Scotia Capital91-day Canadian Treasury Bills series.Book equity(BE)is computed as the book value of stockholders’equity,plus balance sheet deferred taxes and investment tax credit(if available),minus the book value of preferred stock(see Fama and French,1992).All observations with a negative BE are excluded from the sample.Thefinal sample includes12,526observa-tions(firm/year).The average annual number offirms is298.However,the average num-ber is122for the1960s,233for1970s,272for the1980s and520for the1990s.For the sake of comparison,the average numbers offirms for the Canada are,respectively, 274in Liew and Vassalou(2000)for the1978–1996period,101in Arshanapalli et al. (1998a)for the1975–1996period,and113in Bauman et al.(1998)for the1986–1996 period.2.2.Construction of the four factorsThe four-factor pricing model states that the excess return of a security is explained by the market portfolio and three factors designed to mimic risk variables related to size,5To avoid a look-ahead bias,the book equity corresponding to the end of thefiscal year y is assumed to be available in June from year y+1.Consequently,as in Fama and French,returns from factors are measured from July of year y+1to June of year y+2.6The correlation between our sample market return and the TSE300index is more than96%.J.-F.L’Her et al./Int.Fin.Markets,Inst.and Money14(2004)313–328317 book-to-market(BM)and momentum.According to the FFPM,stocks’excess returns are equal to:E(R it)−R ft=b i×(E(R mt)−R ft)+s i×E(SMB t)+h i×E(HML t)+w i×E(WML t)(1) where the factor loadings are,respectively,b i,s i,h i and w i.We have constructed SMB and HML in keeping with Fama and French(1993),and WML is constructed as up minus down(UMD)on Kenneth French’s Website.For each month t from July of year y−1to June of year y,we rank the stocks based on their size and book-to-market ratio of June y−1.We then use these two rankings to calculate a 50%breakpoint for size,and30and70%breakpoints for book-to-market.The stocks are subsequently sorted into two size groups and three book-to-market groups based on these breakpoints.In addition,the stocks above the50%size breakpoint are designated B(for big)and the remaining50%are designated S(for small).In addition,the stocks above the 70%book-to-market breakpoint are designated H(for high),the middle40%are designated N(for neutral)and thefirms below the30%book-to-market breakpoint are designated L (for low).We form six value-weighted portfolios,S/L,S/N,S/H,B/L,B/N and B/H as the intersection of size and book-to-market groups.Note that the number offirms in each of the six portfolios varies.SMB is the equally-weighted average of the returns on the small stock portfolios minus the returns on the big stock portfolios:SMB=((S/L)−(B/L))+((S/N)−(B/N))+((S/H)−(B/H))3(2)Similarly,HML is the equally-weighted average of the returns on the value stock port-folios minus the returns on the growth stock portfolios:HML=((S/H)−(S/L))+((B/H)−(B/L))2(3)For each month t from July of year y−1(beginning in July1990)to June of year y,werank the stocks based on their size in June y−1and their performance between t−12and t −2.7We proceed for the momentum factor as for the book-to-market factor.Stocks above the70%prior performance breakpoint are designated W(for winner),the middle40%aredesignated N(for neutral)and thefirms below the30%prior performance breakpoint aredesignated L(for loser).We form six value-weighted portfolios,S/L,S/N,S/W,B/L,B/N andB/W,as the intersection of size and prior performance groups.WML is the equally-weightedaverage of the returns on the winner stock portfolios minus the returns on the loser stockportfolios:8WML=((S/W)−(S/L))+((B/W)−(B/L))2(4)7The portfolio ranking is in t−2and not t−1,for the bid-ask bounce can attenuate the continuation effect (see Rouwenhorst,1998or Jegadeesh and Titman,2001).8Liew and Vassalou(2000)used three sequential sorts,Carhart(1997)did not construct size-neutral momentum portfolios and Brav et al.(2000)used50%breakpoints for momentum.318J.-F.L’Her et al./Int.Fin.Markets,Inst.and Money14(2004)313–328We also determine the market risk premium,which is the capitalization-weighted returnof all the securities considered in excess of the realized monthly return on91-day CanadianTreasury Bills(R m−R f).Using data from July1960to April2001,we derive the time-series of the market,size,book-to-market,and momentum premiums,which are described in thenext sections.3.ResultsWefirst present summary statistics on the distribution of the four factors:market excessreturns,SMB,HML and WML.Then,we discuss the portfolio returns obtained from strate-gies based on market equity alone,book-to-market-equity alone,and strategies based onstly,we examine the regularities in the factors’behavior.3.1.Summary statisticsTo our knowledge,the only researches that have examined the factor returns in theCanadian stock market over a long period are the international studies by Liew and Vassalou(2000),Arshanapalli et al.(1998a,b),and Bauman et al.(1998).9Liew and Vassalou usedthree sequential sorts instead of the Fama-French methodology.Even if the results are notdirectly comparable,they found three significant positive SMB,HML and WML premiumsin Canada for quarterly,semi-annual and annual rebalancing.The SMB and HML premiumsare stable,respectively,within the intervals of[7.44%,8.56%]and[4.85%,6.02%].TheWML premium is not significantly different from zero for annual rebalancing(3.32%),but very important for quarterly and semi-annual rebalancing(14.50and10.52%).ACDSexamine the robustness of the value investing strategy over the1975–1996period for18equity markets.They compute the SMB and HML factors in the same way as BARRA.They report an annualized mean of0.68%for SMB and3.43%for HML.BCM use fourvaluation ratios to define value stocks and growth stocks in21countries.Assigning stocksto quartile groups(equally-weighted portfolios),theyfind that the spread between valueand growth stocks is positive in11out of the19markets considered;the HML averagegeometric return is1.2%.Table1presents a summary of the main results obtained by thesestudies in the Canadian stock market as well as the main results obtained in the US.Table2,panel A presents summary statistics on the distribution of the four factors inCanada.The average annual market premium is4.52%,which is lower than the historicalpremium observed in the United States.The market premium annualized standard deviationis15.23%,so we can reject the null hypothesis(t(mean)=1.89)at the95%confidencelevel.Over the1960–2001period,the average monthly return on the SMB factor is0.42%,corresponding to5.08%annually.This size premium is considerable,and we must rejectthe null hypothesis(t(mean)=3.96)at the99%confidence level.The annualized SMB9Ikenberry et al.(2000)also reports significant SMB and HML premiums over the July1990–March1998 period,but this study focused on examining the excess performance of stock repurchase programs measured relative to the Fama and French(1993)three-factor model using BARRA’s methodology.J.-F.L’Her et al./Int.Fin.Markets,Inst.and Money14(2004)313–328319 standard deviation(10.97%)is almost30%lower than the market premium standard devi-ation(15.23%).Therefore,this portfolio is much less risky than the market excess return. For the42-year period examined in the study,the average annual return on the HML factor is equal to the average annual return on the SMB factor.The annualized HML standard de-viation(12.72%)is between the market premium and SMB standard deviations.However, we still reject the null hypothesis at the99%confidence level(t(mean)=2.55).The SMB premium is slightly larger and less volatile than the one observed by Fama and French in the United States(4.92and15.44%;1996,Table1,1964–1993period).However,the HMLTable1Summary of main results obtained by comparable studies in Canada(panel A)or in the US(panel B)Period R m−R f SMB HML WML Panel A:CanadaLiew and Vassalou(2000)a1978–1996Mean(%) 4.857.4414.50 Standard deviation(%)10.7111.0614.80 t-statistic 2.01 2.98 4.34 Arshanapalli et al.(1998a,b)b1975–1996Mean(%)0.68 3.43Standard deviation(%)7.6010.44t-statistic0.40 1.47Bauman et al.(1998)July1986–June1996Mean(%) 5.40 1.20Standard deviation(%)t-statisticPanel B:the United StatesFama and French(1996)July1964–June1993Mean(%) 5.94 4.92 6.33Standard deviation(%)16.3315.4413.11t-statistic 1.96 1.72 2.60Davis et al.(2000)c July1929–June1997Mean(%)8.34 2.43 5.66Standard deviation(%)19.9211.2910.77t-statistic 3.43 1.76 4.30 Jegadeesh and Titman(2001)d1965–1998Mean(%)15.80 Standard deviation(%)13.32 t-statistic 6.81a Liew and Vassalou(2000)calculated factor returns for quarterly,semi-annual,and annual rebalancing fre-quencies.We report factor returns calculated on a quarterly rebalancing frequency.b We compute t-statistics of Arshanappalli,Coggin,Doukas and Shea on the basis on annualized means and standard deviations reported in Appendix A,p.20.c We annualize the means and standard deviations reported by Davis et al.(2000)and calculate the t-statistics on68years.d We annualize the means and standard deviations reported by Jegadeesh and Titman(2001)and calculate the t-statistics on34years.The WML factor is the difference between P1and P10.P1(P10)are the equally-weighted portfolio of10%of the stocks with the highest(lowest)returns over the previous6months.320J.-F.L’Her et al./Int.Fin.Markets,Inst.and Money14(2004)313–328Table2Summary statistics and correlations between the four factors monthly returns(R m−R f,SMB,HML and WML) on the July1960–April2001period(N=490)R m−R f SMB HML WML Panel AMean(%)0.380.420.42 1.34 Standard deviation(%) 4.40 3.17 3.67 4.45 t(mean) 1.89 2.96 2.55 6.66 Minimum(%)−23.27−14.12−21.92−19.09 Maximum(%)17.1015.5217.4017.50 Compounded mean return(%)0.230.310.30 1.03 Panel BR m−R f 1.00SMB0.12∗∗ 1.00HML−0.36∗∗−0.39∗∗ 1.00WML0.070.15∗∗−0.13∗∗ 1.00 R m stands for the value-weighted market return obtained from thefirms considered in the sample.R f represents the return on a portfolio of Canadian Treasury Bills of expiry91days(source:Scotia Capital).SMB is the return from a hedged portfolio for which the securities whose stock exchange capitalization is small are bought and the securities for which the stock exchange capitalization is large are shorted.HML is the return from a hedged portfolio for which the securities for which the ratio book-to-market is high are bought and the securities for which the ratio book-to-market is low are stly,WML represents the return of a hedged portfolio for which securities with the best prior performance over the previous period(t−12with t−2)are bought and securities with the worst performance during the same period are shorted.t(mean)is the mean return divided by its standard error(standard deviation/4890.5).∗∗Significant at a95%confidence level.premium is lower and as volatile as the premium found by Fama and French in United States (6.33and13.11%;1996,Table1,1964–1993period).The annual HML premium is compa-rable to the HML premiums obtained by Fama and French(1998)in other developed markets (US:6.79%;Hong-Kong:7.16%;France:7.64%;Sweden:8.02%;Table3,p.1981).10 The WML premium is very large,16.07%per year.11The annualized standard deviation is the largest,slightly higher than the market premium(15.41%).The null hypothesis cannot be rejected at the99%confidence level(t(mean)=6.66).The WML premium is by far the largest premium observed in the Canadian market:1.34%per month.This premium is comparable to the one observed in the US by Jegadeesh and Titman(2001)over the 1965–1998period(1.23%per month,t-statistic=6.43),even if over the1926–1995 period,Grundy and Martin(2001)reported a much lower premium(0.44%per month, t-statistic=1.83).1210Fama and French(1998)use data from MSCI in13developed markets(United States and EAFE)and16 emerging markets.Because MSCIfirms are large,Fama and French could not test for the size effect and comparison is impossible.11On the TSE100,over the period1978–1992,Foerster et al.(1994)obtained for the top10%and bottom10% an annualized return of41.2and10.9%respectively.They rank stocks based on the weighted average of their past four quarters of price changes and repeat the procedure each quarter.12This low average return is mainly due to the negative performance of the momentum strategy during the 1926–1945period(−0.91%per month,t-statistic=−1.36).J.-F.L’Her et al./Int.Fin.Markets,Inst.and Money14(2004)313–328321 Table3Summary statistics per month on the four factor returns:R m−R f,SMB,HML and WML returns(July1960–April 2001)Month Statistics R m−R f SMB HML WML January Mean(%) 1.95 2.56−0.05−0.49Standard deviation(%) 4.99 4.07 4.10 5.62t(mean) 2.51 4.03−0.08−0.55 February Mean(%)0.12 1.280.94 1.49Standard deviation(%) 3.62 3.59 5.53 4.50t(mean)0.21 2.27 1.09 2.12 March Mean(%)0.310.57 1.37 1.01Standard deviation(%) 4.16 3.37 3.18 4.49t(mean)0.48 1.09 2.76 1.44 April Mean(%)0.33−0.09 1.45 1.10Standard deviation(%) 4.30 3.53 2.66 4.14t(mean)0.50−0.15 3.50 1.70 May Mean(%)−0.100.51−0.06 1.13Standard deviation(%) 3.54 2.60 3.30 3.21t(mean)−0.19 1.25−0.11 2.25 June Mean(%)−0.36−0.270.59 2.18Standard deviation(%) 4.10 2.80 3.38 4.67t(mean)−0.56−0.62 1.11 2.99 July Mean(%)0.520.250.09 1.80Standard deviation(%) 3.71 2.53 2.14 3.99t(mean)0.900.620.26 2.89 August Mean(%)0.470.12−0.320.77Standard deviation(%) 5.39 2.53 2.74 4.40t(mean)0.560.29−0.74 1.13 September Mean(%)−1.250.310.550.78Standard deviation(%) 4.04 2.29 3.25 4.11t(mean)−1.980.87 1.09 1.22 October Mean(%)−0.94−0.560.79 1.54Standard deviation(%) 5.78 3.11 4.02 4.57t(mean)−1.04−1.15 1.27 2.15 November Mean(%) 1.080.32−0.50 2.50Standard deviation(%) 4.31 3.31 5.04 4.73t(mean) 1.600.62−0.64 3.38 December Mean(%) 2.350.070.23 2.28Standard deviation(%) 3.21 2.97 3.15 4.32t(mean) 4.690.150.46 3.38 Months other than january Mean(%)0.230.230.47 1.51Standard deviation(%) 4.32 3.00 3.63 4.30t(mean) 1.14 1.61 2.727.43 Ratio January to other months8.4111.24−0.11−0.32 R m−R f,SMB,HML and WML monthly excess returns are partitioned relatively to months to examine seasonality in returns.t(mean)is the mean return divided by its standard error(standard deviation/4890.5).322J.-F.L’Her et al./Int.Fin.Markets,Inst.and Money14(2004)313–328The results obtained on the SMB,HML and WML premiums are in line with thosereported by Liew and Vassalou(2000)over the1978–1996period.The HML premiumreported by Arshanapalli et al.(1998a)over the1975–1996period is approximately thesame as the HML premium we report.13However,the SMB premiums differ significantly.Table2,panel B presents the correlations between the factors.The correlation coeffi-cients are low,which is consistent with the way factors are constructed:orthogonalizationof SMB and HML or SMB and WML.However,they are all significant at the95%confi-dence level(one exception between R m−R f and WML).The highest absolute values are observed between HML and R m−R f and between HML and SMB.The HMB factor is negatively correlated with all factors.By comparison,(Davis et al.,2000,p.392)report a13%correlation between SMB and HML over the July1929–June1997.3.2.Regularities in the factors’behaviorBelow,we document regularities in the factors’behavior that are associated with theturn-of-the-year and with up-and down-market conditions,as well as restrictive and expan-sive monetary policies.3.2.1.Turn-of-the-year effectChan et al.(1998)report a very marked January effect for the SMB and HML factors.14Loughran(1997)contends that Fama and French’s empiricalfindings are driven by a Jan-uary seasonal effect in the book-to-market effect and low returns on small newly-listedgrowth stocks outside of January.Davis(1994)documents that book-to-market does notexplain cross-sectional variation in returns once January is excluded from the sample.Overthe July1929–June1997period,Davis et al.(2000)report a market premium of0.67%permonth(t-statistic=3.34),0.46%per month(t-statistic=4.24)for the book-to-marketpremium and0.20%(t-statistic=1.78)for the size premium.Jegadeesh and Titman(2001)report a strong January effect in momentum profits.Over the1965–1998period,returns from winners and losers are,respectively,3.40and4.95%(t-statistic=−1.87for the hedge portfolio)in January versus1.49and0.01%in other months(t-statistic=7.89).The seasonal effects of the four factors are shown in Table3.Market excess returns arepositive in2out of3months.However,they are only significantly different from zero atthe1%level in January(1.95%)and December(2.35%).The SMB returns are positive for3out of4months,and significantly different from zeroat the1%level in January(2.56%)and February(1.28%).The SMB return is positive butnot significant for the non-January months.The SMB effect is mostly driven by January:theratio of the average return in January to the average return observed in non-January monthsis equal to11.24.This result is consistent with the turn-of-the-year effect documented by13The HML premium of10.73%reported by Arshanapalli et al.(1998b)for Canada over the1975–1995period significantly differs from the those reported by Arshanapalli et al.(1998a),Liew and Vassalou(2000)and us. 14Usingfive portfolios,theyfind that the return spread between large and smallfirms in January is−8.45% on average in January,and that the return spread between high book-to-market and low book-to-marketfirms is 6.46%.。