Evidence to support the four-factor pricing model from the Canadian stock market

Jean-François L’Her Tarek Masmoudi Jean-Marc Suret

First version: June 2002

Last version: March 2003

Corresponding author: Jean-François L'Her, Caisse de dépôt et placement du Québec, Depositors’

Accounts Management, 1981, McGill College Avenue, Montreal (QC) H3A 3C7, Tel: (514) 847-2601, Fax:

(514) 847-5443, e-mail: jlher@cdp.ca. Tarek Masmoudi: doctoral student, École des Hautes Études

Commerciales, tarek.masmoudi@hec.ca. Jean-Marc Suret: CIRANO (Montréal) and Director, School of

Accountancy, Université Laval, e-mail: suretjm@fsa.ulaval.ca.

Evidence to support the four-factor pricing model from the Canadian stock market

Abstract: This paper tests the Fama-French three-factor pricing model augmented by a momentum factor on the Canadian stock market. Using 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 to 4.52%, 5.08%, 5.09% and 16.07%, over the July 1960-April 2001 period. The results relative to the three zero-investment portfolios are in line with those obtained by Liew and Vassalou (2000) for the 1976-1996 period, 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, we find that the SMB and HML premiums are only significant in an expansive environment.

JEL Classification: G12.

Keywords: Four-factor pricing model, Canadian stock market.

1

Evidence to support the four-factor pricing model from the Canadian stock market

1 Introduction

Since 1992, 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 capitalization firms and big capitalization firms; SMB, small minus big) and

the book-to-market premium (difference in returns between portfolios of high

book-to-market and small book-to-market firms; HML, high minus low). 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 or cash flow to price; see Lakonishok, Shleifer and Vishny,

1994 or 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 cash flow to price).

2

The Fama and French three-factor pricing model captures most market

anomalies (Fama and French, 1996; Asness, 1997), except the momentum

anomaly1. A number of studies initiated by Jegadeesh and Titman (1993) show

that strategies that involve taking a long (short) position in well (poorly)

performing stocks on the basis of past performance over the previous 3 to 12

months tend to produce significantly positive abnormal returns of about 1

percent 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), Chan, Jegadeesh and

Lakonishok (1999), and Jegadeesh and Titman (2001) for the United States, apply

equally well to developed markets (see Rouwenhorst (1998), i.e. European

markets, Chui, Titman and Wei (2000) for Asian markets with the exception of

Japan and Korea) 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 of finance 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 WML (Winners minus losers). Following Carhart (1997), Brav,

Geczy and Gompers (2000), Eckbo, Masulis and Norli (2000), Jegadeesh (2000),

and Liew and Vassalou (2000), we use a four-factor pricing model (FFPM).

3

The magnitude of the size and book-to-market premiums cast some doubts on

the CAPM, but also created skepticism among the financial management and

academic communities: first, in 1999-2000, growth stocks in the US have

experienced an unprecedented extraordinary good performance; second, “if

small, high B/M stock earn such high returns, how come investment

professionals have a hard time beating the S&P 500 -- an index of large, low B/M

firms?” (Loughran, p.250, 1997). This study provides another out-of-sample test

of the Fama-French TFPM and the momentum factor in the Canadian stock

market, and has shed 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 international research in which Canadian results are not the main

focus. Using data from MSCI (Morgan Stanley Capital International) and IAA

(Independence International Associates Inc.), Arshanapalli, Coggin, Doukas and

Shea (1998) report results on 18 international equity markets, over the 1975-1996

period. They find positive HML premiums in 13 out of 18 markets and positive

SMB premiums in 10 out of 18 markets. Both results pertaining to Canada are

significantly positive. Using data from the Compustat Global Vantage file over

the 1985-1996 period, Bauman, Conover and Miller (1998) use four valuation

ratios to define value stocks and growth stocks in 19 countries. They find a

positive HML premium in 11 out of 19 markets (including Canada), and a strong

4

firm-size effect. Using data from Datastream International, only Liew and

Vassalou (2000) have examined the returns from SMB, HML and WML in

Canada. In a study of 10 major markets, the authors find 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 of ten

markets.2 All results pertaining to Canada are significantly different from zero

over the 1978-1996 period.

The main differences between Liew and Vassalou (2000) and this study are as

follows. Liew and Vassalou (2000) focus on the predictability of economic

growth through book-to-market, size and momentum risk factors in 10 major

markets, whereas this study focuses on the risk factors’ returns in Canada and

examines the regularities in the factors’ behaviour 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 the 1978-1996

period and their sample of Canadian firms comprises 274 on average, whereas

the period analyzed in this study is much longer (the 1960-2001 period) and the

average number of firms is 298. 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.

5

First, the average annual returns on SMB and HML are respectively equal to

5.08% and 5.09%, with standard deviations of 10.97% and 12.72%. The SMB

premium is slightly larger and less volatile than the one observed by Fama and

French in the U.S., however, the HML premium is lower and as volatile as the

premium found by Fama and French in U.S. The 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 U.S. by Jegadeesh and Titman

(2001) over the 1965-1998 period (1.23% per month, t-statistic=6.43)3. These

results are also consistent with those obtained by Liew and Vassalou (2000) over

the 1978-1996 period.

Second, it documents in the Canadian stock market the very pronounced January effect

documented by Loughran (1997), Davis (1994), and Davis, Fama and French (2000) in

the U.S. Average returns in January are significantly different from 0 at the 1% level for

the market, SMB and HML premiums. They are still significantly different from 0 for

the other months, but to a much lesser extent. We also find that up- and down-markets

influence the SMB and HML premiums as reported by Chan, Karceski and Lakonishok

(1998) in the U.S., the U.K. 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, Johnson and Mercer (1997), we also examine

the influence of the monetary environment over the SMB, HML and WML premiums.

6

We find that the stratification between periods of restrictive expansive monetary policy

has no significant impact on the WML premium, whereas, consistently with Jensen,

Johnson and Mercer (1997), 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 Section II, we present the

FFPM, the data and the methodology used to construct the factors. In Section III,

we present the results on the risk factors, then on the regularities in the factors’

behavior in the Canadian stock market. Section IV presents concluding remarks.

2 Data and methodology

This section describes the data followed by the methodology used to calculate the four

risk factors.

2.1 DATA

We examine the monthly returns from the four factors: RM-RF, SMB, HML and

WML on the Canadian stock market over the July 1960-April 2001 period. Data

relative to financial statements come from the Financial Post database (from 1959

to 1986; 1992 version) and from Research Insight Compustat (from 1987 to 2000;

2001 version).4 Monthly stock returns and firms' market equity (ME: number of

7

shares outstanding times the stock price) come from the TSE-Western tape (from

July 1959 to December 1986; 1998 version) and from Research Insight Compustat

(from January 1987 to April 2001; 2001 version). The market return is a value-

weighted return computed from the sample.5 Returns from the risk-free asset are

estimated from the Scotia Capital 91-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. The final sample includes 12,526

observations (firm/year). The average annual number of firms is 298. However,

the average number is 122 for the 60’s, 233 for 70’s, 272 for the 80’s and 520 for

the 90’s. For the sake of comparison, the average numbers of firms for the

Canada are respectively 274 in Liew and Vassalou (2000) for the 1978-1996

period, 101 in Arshanapalli, Coggin, Doukas and Shea (1998) for the 1975-1996

period, and 113 in Bauman, Conover and Miller (1998) for the 1986-1996 period.

Summary statistics about the market capitalization, the book-to-market ratios

and the prior performance of firms are also presented on an annual basis in

Table 1.

[Insert Table 1]

8

2.2 CONSTRUCTION OF THE FOUR FACTORS

The four-factor pricing model (FFPM) 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, book-to-market (BM) and momentum. According to the FFPM, stocks'

excess returns are equal to:

E(Rit) - Rft = bi*(E(Rmt)-Rft) + si*E(SMBt) + hi*E(HMLt) + wi*E(WMLt) (1)

where the factor loadings are respectively bi, si, hi and wi.

We have constructed SMB and HML in keeping with Fama and French (1993),

and WML is constructed as UMD (Up minus Down) on Kenneth French’s Website.

For each month t from July of year y-1 to 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 percent breakpoint for size, and 30 percent and 70

percent 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 the 50 percent size breakpoint are designated B (for

big) and the remaining 50 percent are designated S (for small). In addition, the

stocks above the 70 percent book-to-market breakpoint are designated H (for

high), the middle 40 percent are designated N (for neutral) and the firms below

the 30 percent book-to-market breakpoint are designated L (for low).

9

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 of firms in

each of the six portfolios varies. SMB (Small minus Big) is the equal-weight

average of the returns on the small stock portfolios minus the returns on the big

stock portfolios:

B/H))/3S/HB/N)S/NB/L)S/LSMB −+−+−= (((( . (2)

Similarly, HML (High minus Low) is the equal-weight average of the returns on

the value stock portfolios minus the returns on the growth stock portfolios:

B/L))/2(B/HS/L)((S/HHML −+−= . (3)

For each month t from July of year y-1 (beginning in July 1990) to June of year y,

we rank the stocks based on their size in June y-1 and their performance between

t-12 and t-2.6 We then use these two rankings to calculate a 50 percent

breakpoint for size, and 30 percent and 70 percent breakpoints for prior

performance. The stocks are subsequently sorted into two size groups and three

prior performance groups based on these breakpoints. Moreover, the stocks

above the 50 percent size breakpoint are designated B (for big) and the

remaining 50 percent S (for small). Moreover, the stocks above the 70 percent

prior performance breakpoint are designated W (for winner), the middle 40

10

percent are designated N (for neutral) and the firms below the 30 percent prior

performance breakpoint are designated L (for loser).

As previously, we form six value-weight portfolios, S/L, S/N, S/W, B/L, B/N and

B/W, as the intersection of size and prior performance groups. WML (Winners

Minus Losers) is the equal-weight average of the returns on the winner stock

portfolios minus the returns on the loser stock portfolios: 7

B/L))/2B/WS/L)S/WWML −+−= ((( . (4)

We also determine the market risk premium, which is the capitalization-

weighted return of all the securities considered in excess of the realized monthly

return on 91-day Canadian Treasury Bills (Rm - Rf). Using data from July 1960 to

April 2001, we derive the time-series of the market, size, book-to-market, and

momentum premiums, which are described in the next sections.

3 Results

We first present summary statistics on the distribution of the four factors:

market excess returns, SMB, HML and WML. Then, we discuss the portfolio

returns obtained from strategies based on market equity alone, book-to-market-

equity alone, and strategies based on both. Lastly, we examine the regularities in

the factors’ behavior.

11

3.1 SUMMARY STATISTICS

To our knowledge, the only researches that have examined the factor returns in the

Canadian stock market over a long period are the international studies by Liew and

Vassalou (2000), Arshanapalli, Coggin, Doukas and Shea (1998), and Bauman, Conover

and Miller (1998).8 Using data from Datastream International over the 1978-1996 period,

Liew and Vassalou (2000) used three sequential sorts instead of the Fama-French

methodology. Even if the results are not directly comparable, they found three

significant positive SMB, HML and WML premiums in Canada for quarterly, semi-

annual and annual rebalancing. The SMB and HML premiums are stable, respectively

within the intervals of [7.44%, 8.56%] and [4.85%, 6.02%]. The WML premium is not

significantly different from zero for annual rebalancing (3.32%), but very important for

quarterly and semi-annual rebalancing (14.50% and 10.52%). Using data from MSCI and

IAA, Arshanapalli, Coggin, Doukas and Shea (1998) examine the robustness of the

value investing strategy over the 1975-1996 period for 18 equity markets. They compute

the SMB and HML factors in the same way as BARRA.9 They report an annualized

mean of 0.68% for SMB and 3.43% for HML. Using data from the Compustat Global

Vantage file over the 1985-1996 period, Bauman, Conover and Miller (1998) use four

valuation ratios to define value stocks and growth stocks in 21 countries. Assigning

stocks to quartile groups (equally-weighted portfolios), they find that the spread

between value and growth stocks is positive in 11 out of the 19 markets considered; the

HML average geometric return is 1.2%. Table 2 presents a summary of the main results

12

obtained by these studies in the Canadian stock market as well as the main results

obtained in the U.S.

[Insert Table 2]

Table 3, Panel A presents summary statistics on the distribution of the four factors in

Canada. The average annual market premium is 4.52%, which is lower than the

historical premium observed in the United States.10 The market premium annualized

standard deviation is 15.23%, so we can reject the null hypothesis (t(mean)=1.89) at the

95% confidence level.

Over the 1960-2001 period, the average monthly return on the SMB factor is 0.42%,

corresponding to 5.08% annually. This size premium is considerable, and we must reject

the null hypothesis (t(mean) = 3.96) at the 99% confidence level. The annualized SMB

standard deviation (10.97%) is almost 30% lower than the market premium standard

deviation (15.23%). Therefore, this portfolio is much less risky than the market excess

return. For the 42-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 deviation (12.72%) is between the market premium and SMB standard

deviations. However, we still reject the null hypothesis at the 99% confidence level

(t(mean)=2.55). The SMB premium is slightly larger and less volatile than the one

observed by FF in the United States (4.92% and 15.44%; 1996, Table 11, 1964-1993

period). However, the HML premium is lower and as volatile as the premium found by

13

FF in United States (6.33% and 13.11%; 1996, Table 11, 1964-1993 period). The annual

HML premium is comparable to the HML premiums obtained by Fama and French

(1998) in other developed markets (U.S.: 6.79%; Hong-Kong: 7.16%; France: 7.64%;

Sweden: 8.02%; Table III, p.1981).11

The WML premium is very large, 16.07% per year.12 The annualized standard

deviation is the largest, slightly higher than the market premium (15.41%). The

null hypothesis cannot be rejected at the 99% 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 U.S. by Jegadeesh and Titman (2001) over the 1965-1998 period (1.23% per

month, t-statistic=6.43), even if over the 1926-1995 period, Grundy and Martin

(2001) reported a much lower premium (0.44% per month, t-statistic=1.83).13

The results obtained on the SMB, HML and WML premiums are in line with

those reported by Liew and Vassalou (2000) over the 1978-1996 period. The HML

premium reported by Arshanapalli, Coggin, Doukas and Shea (1998) over the

1975-1996 period is approximately the same as the HML premium we report.14

However, the SMB premiums differ significantly.

Table 3 presents the correlations between the factors. The correlation coefficients

are low, which is consistent with the way factors are constructed:

14

orthogonalization of SMB and HML or SMB and WML. However, they are all

significant at the 95% confidence level (one exception between Rm-Rf and WML).

The highest absolute values are observed between HML and Rm-Rf and between

HML and SMB. The HMB factor is negatively correlated with all factors. By

comparison, Davis, Fama and French (2000, p.392) report a 13% correlation

between SMB and HML over the July 1929-June 1997.

[Insert Table 3]

Table 4 presents the average monthly returns and standard deviations for each

year from 1960 to 2001. It appears that each factor was at least positive in 3 out

of 4 years. Note that the percentage reaches 86% for the WML factor.

[Insert Table 4]

3.2 REGULARITIES IN THE FACTORS’ BEHAVIOR

Below, we document regularities in the factors’ behavior that are associated with

the turn-of-the-year and with up- and down-market conditions, as well as

restrictive and expansive monetary policies.

15

3.2.1 Turn-of-the-year effect

Chan, Karceski and Lakonishok (1998) report a very marked January effect for

the SMB and HML factors.15 Loughran (1997) contends that Fama and French’s

empirical findings are driven by a January seasonal effect in the book-to-market

effect and low returns on small newly-listed growth stocks outside of January.

Davis (1994) documents that book-to-market does not explain cross-sectional

variation in returns once January is excluded from the sample. Over the July

1929-June 1997 period, Davis, Fama and French (2000) report a market premium

of 0.67% per month (t-statistic=3.34), 0.46% per month (t-statistic=4.24) for the

book-to-market premium and 0.20% (t-statistic=1.78) for the size premium.

Jegadeesh and Titman (2001) report a strong January effect in momentum

profits. Over the 1965-1998 period, returns from winners and losers are

respectively 3.40% and 4.95% (t statistic=-1.87 for the hedge portfolio) in January

versus 1.49% and 0.01% in other months (t statistic=7.89).

The seasonal effects of the four factors are shown in Table 5. Market excess

returns are positive in 2 out of 3 months. However, they are only significantly

different from zero at the 1% level in January (1.95%) and December (2.35%).

The SMB returns are positive for 3 out of 4 months, and significantly different

from zero at the 1% level in January (2.56%) and February (1.28%). The SMB

return is positive but not significant for the non-January months. The SMB effect

16

is mostly driven by January: the ratio of the average return in January to the

average return observed in non-January months is equal to 11.24. This result is

consistent with the turn-of-the-year effect documented by Berges, McConnell

and Schlarbaum (1984), Calvet and Lefoll (1989), and Athanassakos (1992).

During the 1975-1984 period, the firm size premium16 estimated by Elfakhani,

Lockwood and Zaher (1998) is 2.08% in January, and 0.98% in non-January

months.

The HML returns are positive in 2 out of 3 cases, and significantly different from

zero at the 1% level in March (1.37%) and in April (1.45%). We report no January

effect for the HML factor. These results are not consistent with results reported

by Chan, Karceski and Lakonishok (1998), Loughran (1997) and Davis (1994).

The WML returns are positive for 11 out of 12 months, except January, which is

fully consistent with the results from Jegadeesh and Titman (2001). They are

significantly different from zero at the 1% level in 7 out of 12 months. The

largest monthly returns are observed in November (2.50%), December (2.28%)

and June (2.18%).

[Insert Table 5]

17

3.2.2 Market environment

This section examines whether up- and down-markets, as well as the monetary

environment influence the SMB, HML and WML returns.

Up- and down-markets: Pettengill, Sundaram and Mathur (1995) recognize the

impact of using realized returns as proxy for expected market returns in CAPM

tests. They find a negative (respectively positive) relationship between realized

returns and beta when realized market returns fall below (are superior to) the

risk-free rate. Explicitly, acknowledging periods of up- and down-markets yields

a consistent and highly significant relationship between portfolios returns and

beta. Chan, Karceski and Lakonishok (1998) condition on whether, during a

given month, the market return is above or below the Treasury bill rate. They

find that returns from SMB and HML are respectively lower and higher during

down-market months.17 Following Pettengill, Sundaram and Mathur (1995), we

measure periods of up- and down-markets by the sign of the market excess

return observed ex post and we condition SMB, HML and WML returns on this

variable.

Table 6 presents these conditional effects. Market excess returns are positive for

55% of the observations. The SMB and WML premiums are larger in up-markets,

they are always positive and significantly different from zero in both down- and

up-markets. The annual size premium is equal to 4.03% and 5.95% in down- and

up-markets respectively, while the annual WML premium is 12.63% and 18.88%.

18

The principal conditional effect appears to be the HML factor. In down-market

periods, the book-to-market premium is positive and by far the most important

(16.78% on an annual basis), whereas in up-market periods, it is negative and

not significantly different from zero. This finding is inconsistent with the

argument advanced by Chan and Chen (1991) and Fama and French (1992, 1996)

that the book-to-market premium stands for a relative distress factor18.

Fama and French (1992, 1996) contend that the size and book-to-market ratio

premiums represent rewards for the additional risk incurred. As small-

capitalization firms and high book-to-market firms are sensitive to adverse

economic conditions and have sustained periods of low profitability (relative

distress factor), higher risk premiums on these companies are required. Fama

and French (1993) and Fama (1998) maintain that these non-risk characteristics

proxy for the security’s loadings on priced factors. They compensate for risk in a

multifactor version of Merton’s (1973) intertemporal capital asset pricing model

(ICAPM) or Ross’s arbitrage pricing theory (APT, 1976). Fama and French (1992,

1996) advocate that relative distress could be a state-variable risk of special

concern to investors (human capital, for instance). However, one would expect a

positive relationship between high book-to-market equity firms and subsequent

realized returns, not higher returns during down-market periods. A natural

proxy for firm distress is bankruptcy risk. If bankruptcy risk is systematic, one

could also expect a positive relationship between bankruptcy risk and

19

subsequent realized returns. Dichev (1998) shows that there is no reward for

bankruptcy risk and that a distress factor is unlikely to account for the size and

book-to-market effects. A risk-based explanation cannot fully explain the

persistence of these size and book-to-market premiums.19

[Insert Table 6]

Monetary environment: Jensen, Johnson and Mercer (1996) suggest that as monetary

policy and business conditions change, investors’ perceptions of risk are modified, and

so are the required return levels. Considering a stabilization policy where monetary

authorities follow a restrictive (expansive) policy when the economy is strong (weak)

and interest rates are rising (falling), Jensen, Johnson and Mercer (1997) examine

whether the size and book-to-market effects depend on the monetary policy. They show

that “the small-firm and low price-to-book premiums are economically and statistically

significant only in expansive monetary policy periods, and are small, and in some

instances negative, in restrictive policy periods” (p.34). Jensen, Johnson and Mercer

(1996) classify monthly observations that followed an increase in the discount rate as

falling in a restrictive policy environment and observations that followed a decrease in

the discount rate as falling in an expansive policy environment. We stratify our sample

in two sub-samples: periods of restrictive and periods of expansive monetary policy on

the basis of the months when the Bank Rate is greater (lesser) than the previous 12

month trailing average.20 The stratification between periods of restrictive and expansive

20

monetary policies yields results consistent with Jensen, Johnson and Mercer (1997) (see

Table 7). The SMB and HML premiums are not significant in a restrictive monetary

environment (an average monthly return of 0.16% and t=0.75 for SMB, and an average

monthly return of 0.28% and t=1.18 for HML) whereas they are highly significant in an

expansive monetary environment (an average monthly return of 0.72% and t=4.08 for

SMB and average monthly return of 0.58% and t=3.40 for HML). The stratification has

little impact on the WML premium, except that contrarily to SMB and HML, the WML

premium is higher in restrictive monetary policy periods than in expansive monetary

policy periods.

[Insert Table 7]

4 Conclusion

Whereas the TFPM and momentum strategies are widely documented in the

U.S., there is little out-of-sample evidence to support the strategies. The only

pertinent studies are the international investigations of Fama and French (1998),

Arshanappalli, Doukas, Coggin and Shea (1998a), Bauman, Conover and Miller

(1998), and Liew and Vassalou (2000). Fama and French (1998) present results on

the HML premium in 13 developed markets (United States and EAFE) and 16

emerging markets, but they do not present results for the Canadian stock

market. In a study of 18 international equity markets over the 1975-1996 period,

Arshanapalli, Doukas, Coggin and Shea (1998) report significant premiums on

SMB and HML in Canada. In a study on 19 countries, over the 1985-1996 period,

21

Bauman, Conover and Miller (1998) also observe a positive HML premium and a

strong firm-size effect. The only authors to our knowledge that present results

pertaining to the four risk factors are Liew and Vassalou (2000). Their analysis of

10 major markets reveals positive and significant returns for the four risk factors

in Canada over the 1978-1996 period.

The main differences between the studies of Liew and Vassalou (2000) and ours

are the following. Liew and Vassalou (2000) focus more on the predictability of

economic growth through book-to-market, size and momentum risk factors.

They examine the 1978-1996 period and their sample of Canadian firms

comprises 274 of them on average. Their portfolio construction procedure to

calculate SMB, HML and WML is based on three sequential sorts. Our study

concentrates solely on the four risk factors in the Canadian stock market and

examines the regularities in the factors’ behavior: turn-of-the-year effect and

market environment (up- and down-markets, as well as restrictive and

expansive monetary policies monetary environment). The period examined is

much larger (the July 1960-April 2001 period) and the average number of firms

slightly larger (298 firms on average). In addition, the portfolio construction

procedure used to calculate SMB, HML and WML is that of Fama-French, namely

independent sorts, followed by an orthogonalization of HML and WML with

SMB.

22

The main results relative to the four Canadian risk factors are as follows. The

average annual premiums are 4.52%, 5.08%, 5.09% and 16.07% for the market,

SMB, HML and WML respectively. Whereas the first three premiums are almost

identical, at 5% per year, the last is by far the largest. The annualized WML

premium standard deviation is slightly larger than that of the market (15.41% vs.

15.23%). These results are consistent with those found by Liew and Vassalou

(2000) for the 1978-1996 period.

The turn-of-the-year effect is significant for the market premium (1.95%) and very

pronounced for the SMB premium (2.56%), as documented by Loughran (1997), and

Davis, Fama and French (2000) in the U.S. However, we do not find the documented

turn-of-the-year effect for the HML premium. Consistently with Jegadeesh and Titman

(2001), we also find a strong turn-of-year effect for the WML; this is the only month

where losers outperform winners. We also noted that up- and down-markets influence

the HML premium as reported by Chan, Karceski and Lakonishok (1998) in the U.S., the

U.K. and Japan. During up-market periods, the HML premium is negative but not

significantly different from zero, whereas in down-markets the HML is significantly

positive and very large (1.40% per month). However, contrarily to Chan, Karceski and

Lakonishok (1998), we do not observe very different SMB premiums conditioned by up-

and down-markets. Like the SMB premium, the WML premium is slightly higher in up-

markets than in down-markets. Following Jensen, Johnson and Mercer (1996, 1997), we

examined the influence of the monetary environment on the factors’ premiums. The

23

SMB and HML premiums are significant only in expansive monetary policy periods,

while the WML premium is still significantly positive, but lower than in restrictive

monetary policy periods.

24

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Journal of Finance 54, 1439-1464.

27

Year N Ri-Rf ME BE/ME Mom Year N Ri-Rf ME BE/ME Mom

1.07% 1.29E+08 0.85 -1.50% -2.64% 5.52E+08 0.88 -0.30%

7.62% 2.49E+08 0.60 1.75% 12.03% 2.88E+09 1.58 3.60%

2.41% 1.21E+08 0.94 1.28% -0.37% 5.94E+08 0.85 -4.14%

8.14% 2.49E+08 0.66 2.17% 14.67% 2.89E+09 0.80 4.02%

-0.15% 1.31E+08 0.93 0.28% 1.97% 5.87E+08 0.98 1.88%

8.32% 2.96E+08 0.65 2.34% 12.00% 3.65E+09 0.77 3.95%

1.18% 1.33E+08 0.91 0.62% -1.31% 7.66E+08 0.90 -0.63%

7.01% 3.00E+08 0.61 2.13% 10.11% 5.22E+09 0.86 3.21%

1.96% 1.29E+08 0.95 1.21% 1.78% 8.57E+08 0.89 0.04%

7.24% 2.76E+08 0.63 2.25% 10.87% 5.97E+09 0.99 3.19%

0.97% 1.49E+08 0.86 1.35% 0.33% 9.75E+08 0.87 0.49%

7.33% 3.18E+08 0.60 2.06% 11.70% 7.35E+09 0.99 3.80%

-0.42% 1.65E+08 0.78 -0.06% -0.01% 4.84E+08 0.83 0.95%

7.84% 3.47E+08 0.58 2.14% 18.95% 1.10E+09 1.05 4.61%

1.63% 1.57E+08 0.83 0.45% -0.66% 4.94E+08 0.85 -2.72%

8.70% 3.34E+08 0.69 2.81% 14.94% 1.12E+09 0.88 4.46%

1.88% 1.59E+08 0.85 0.49% 0.56% 5.20E+08 0.90 -1.19%

10.54% 3.60E+08 0.70 3.05% 19.83% 1.17E+09 0.81 4.38%

-0.68% 1.77E+08 0.75 0.86% -3.18% 5.78E+08 0.95 -2.36%

10.39% 3.86E+08 0.56 2.99% 18.57% 1.36E+09 1.02 4.63%

-0.73% 1.75E+08 0.73 -2.33% 1.57% 5.99E+08 1.17 -2.18%

11.05% 3.74E+08 0.55 2.81% 23.47% 1.47E+09 1.46 5.26%

0.82% 1.51E+08 0.91 0.52% 0.96% 5.94E+08 1.30 -0.52%

9.33% 3.55E+08 0.97 2.97% 21.61% 1.48E+09 1.88 5.32%

2.83% 1.41E+08 0.97 1.57% 4.27% 6.22E+08 1.64 1.16%

10.50% 3.57E+08 0.97 3.08% 21.04% 1.51E+09 14.17 5.77%

-0.31% 1.60E+08 0.83 0.79% -0.38% 6.63E+08 1.30 0.79%

11.22% 4.41E+08 0.67 3.02% 21.79% 1.54E+09 13.32 4.41%

-2.96% 1.70E+08 0.81 -1.77% 0.95% 6.29E+08 0.73 -0.89%

12.44% 4.55E+08 0.62 3.57% 17.55% 1.54E+09 0.68 4.20%

2.90% 1.68E+08 1.08 -1.04% 2.43% 5.80E+08 0.80 1.06%

14.91% 4.03E+08 0.90 3.38% 16.94% 1.56E+09 1.36 4.66%

0.95% 2.06E+08 1.30 0.61% 0.40% 6.62E+08 0.75 0.74%

9.96% 1.58E+09 0.95 2.75% 20.99% 1.88E+09 1.33 5.20%

1.95% 2.89E+08 1.33 0.17% -1.53% 8.17E+08 0.72 -1.88%

9.69% 2.41E+09 1.17 2.60% 20.42% 2.45E+09 0.80 5.85%

2.69% 3.11E+08 1.30 1.77% 1.71% 8.63E+08 1.01 -1.87%

11.65% 2.66E+09 1.30 2.91% 23.23% 2.92E+09 1.41 5.79%

2.53% 3.63E+08 1.12 2.20% 1.00% 1.01E+09 1.14 0.45%

11.41% 2.99E+09 1.13 2.81% 41.01% 6.06E+09 1.43 6.30%

2.28% 4.52E+08 1.02 1.57% 2.82% 1.23E+09 1.09 -2.29%

13.53% 3.00E+09 1.93 3.27% 24.81% 8.18E+09 1.43 6.33%

All 298 0.80% 445531532 0.97 -0.10%

252

N stands for the average number of firms per year for which returns, market equity, book-to-market and momentum are available. The firstline represents the average of the variable, whereas the second represents the standard deviation of the variable. Ri stands for the monthlyreturn on firm i, whereas Rf stands for the realized return on Canadian 91-day Treasury Bills (index series from Scotia Capital). ME stands forthe market equity of the firm which is measured in June of each year. BE/ME represents the book-to-market ratio which is computed bydividing the book equity (BE) from year t (assumed available in June of year t+1) by the market equity of year t+1 measured in June. BE isequal to stockholders' equity, plus differed taxes and investment tax credit, minus the liquidation value of preferred stocks if available. Allobservations corresponding to negative BE values are eliminated from the sample. The variable momentum stands for the prior performanceof the stock form t-12 to t-2 (compounded return). For the 1959 year, only the six last months are considered. For the 2001 year, only the firstfour months are considered.

Table 1: Summary statistics per year on the number of firms, excess returns, market equity, book-to-market ratios and momentum on the July 1960 - April 2001 period (N=490)

702

741

778

795

364

409

512

624

345

360

357

354

260

255

254

234

251

254

265

263

285

320

212

237

256

266

205

228

241

252

2001

44

95

105

116

125

133

141

148

1997

1998

1999

2000

1993

1994

1995

1996

1989

1990

1991

1992

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1975

1976

1977

1978

1971

1972

1973

1974

1967

1968

1969

1970

1960

152

161

177

1961

1962

1963

1964

1965

1966

28

Panel A: CanadaPeriod Rm-Rf SMB HML WML

Liew and Vassalou (2000) a 1978-1996mean 4.85% 7.44% 14.50%

standard deviation 10.71% 11.06% 14.80%t statistic 2.01 2.98 4.34

Arshanappalli, Coggin, Doukas and Shea (1998a) 1975-1996mean 0.68% 3.43%

standard deviation 7.60% 10.44%t statistic b 0.40 1.47

Bauman, Conover and Miller (1998) 7/1986-6/1996mean 5.40% 1.20%

standard deviationt statistic b

Panel B: the United StatesFama and French (1996) 7/1964-6/1993

mean 5.94% 4.92% 6.33%standard deviation 16.33% 15.44% 13.11%

t statistic 1.96 1.72 2.60Davis, Fama and French (2000) c 7/1929-6/1997

mean 8.34% 2.43% 5.66%standard deviation 19.92% 11.29% 10.77%

t statistic 3.43 1.76 4.30Jegadeesh and Titman (2001) d 1965-1998

mean 15.80%standard deviation 13.32%

t statistic 6.81

d We annualize the means and standard deviations reported by Jegadeesh and Titman (2001) and calculate the t-statistics on 34 years. The WML factor is the difference between P1 and P10. P1 (P10) are the equal-weighted portfolio of 10 percent of the stocks with the highest (lowest) returns over the previous six months.

Table 2: Summary of main results obtained by comparable studies in Canada (Panel A) or in the U.S. (Panel B)

a Liew and Vassalou (2000) calculated factor returns for quarterly, semi-annual, and annual rebalancing frequencies. We report factor returns calculated on a quarterly rebalancing frequency.b We compute t-statistics of Arshanappalli, Coggin, Doukas and Shea on the basis of annualized means and standard deviations reported in Appendix A, p.20c We annualize the means and standard deviations reported by Davis, Fama and French (2000) and calculate the t-statistics on 68 years

29

Panel A Rm-Rf SMB HML WMLmean 0.38% 0.42% 0.42% 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 17.10% 15.52% 17.40% 17.50%

compounded mean return 0.23% 0.31% 0.30% 1.03%Panel B Rm-Rf SMB HML WML

Rm-Rf 1.00SMB 0.12** 1.00HML -0.36** -0.39** 1.00WML 0.07 0.15** -0.13** 1.00

** significant at a 95% confidence level* significant at a 90% confidence level

Table 3: Summary statistics and correlations between the four factors monthly

returns (Rm-Rf, SMB, HML and WML) on the July 1960 - April 2001 period (N=490)Rm stands for the value-weighted market return obtained from the firms considered in the sample. Rfrepresents the return on a portfolio of Canadian Treasury bills of expiry 91 days (source: Scotia Capital).SMB is the return from a hedged portfolio for which the securities whose stock exchange capitalizationis 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 ishigh are bought and the securities for which the ratio book-to-market is low are shorted. Lastly, WMLrepresents the return of a hedged portfolio for which securities with the best prior performance over theprevious period (t-12 with t-2) are bought and securities with the worst performance during the sameperiod are shorted. t (mean) is the mean return divided by its standard error (standarddeviation/489^0.5).

30

Year Rm-Rf SMB HML WML Year Rm-Rf SMB HML WML1.35% -0.89% 0.16% -0.48% -2.31% -1.47% 1.35% -0.51%4.35% 2.40% 3.06% 5.64% 4.97% 2.82% 5.01% 2.81%2.15% 0.27% 0.63% -0.08% 1.14% 0.28% 0.94% 3.04%1.90% 2.49% 3.19% 3.59% 5.75% 2.68% 4.89% 5.53%-0.93% 0.20% 0.25% 0.49% 1.79% -0.36% 0.96% -0.15%3.89% 2.86% 2.38% 2.48% 3.59% 4.01% 5.76% 3.44%0.96% -0.08% 0.86% 0.65% -0.49% -0.62% 0.01% 1.28%2.95% 1.78% 1.58% 1.99% 4.20% 1.49% 2.22% 4.23%1.64% 0.22% 1.08% -0.06% 1.53% 0.34% 0.04% 0.68%2.04% 1.90% 1.10% 2.36% 4.20% 2.13% 2.34% 4.17%0.10% 1.46% 0.01% 1.47% -1.09% 2.24% 0.19% 2.42%2.65% 1.84% 2.42% 2.25% 2.99% 2.64% 2.27% 6.12%-0.83% 0.04% 0.77% -0.03% 0.26% -0.93% 0.94% 0.41%3.02% 1.47% 2.59% 2.32% 8.72% 4.68% 4.98% 5.58%1.13% 0.99% -0.02% 2.25% 0.03% -1.36% 1.85% 1.92%3.11% 1.64% 1.48% 2.64% 3.25% 2.92% 3.02% 3.98%0.87% 1.26% 0.71% -0.10% 0.56% -0.03% -0.15% 0.81%3.84% 2.48% 3.41% 2.69% 2.23% 2.56% 2.68% 2.57%-0.70% -0.04% -0.35% 1.54% -2.07% -0.70% -0.79% 2.65%4.87% 2.17% 2.55% 2.42% 4.27% 1.47% 2.04% 1.67%-0.45% -1.18% 1.05% -1.80% 0.07% 1.75% -1.38% 3.28%5.28% 2.12% 2.71% 5.31% 2.42% 2.09% 2.19% 5.01%0.49% 1.13% 0.09% 1.60% -0.61% 1.97% -0.33% 2.37%3.94% 2.44% 2.05% 3.28% 2.06% 3.57% 4.09% 2.43%2.07% 1.71% 0.22% 1.34% 1.97% 2.41% 0.64% 2.26%3.41% 2.55% 1.97% 2.03% 3.09% 3.23% 2.35% 4.94%-0.50% -0.38% 2.21% 0.73% -0.37% -0.74% 1.70% 0.13%4.74% 1.97% 1.84% 4.15% 3.69% 2.12% 3.39% 3.13%-2.93% -0.20% 1.48% 2.19% 0.68% 0.97% -0.21% 1.95%6.36% 4.25% 4.60% 3.34% 2.77% 1.69% 2.33% 3.19%1.09% 1.55% -0.17% -1.93% 1.99% 0.08% 0.77% 1.21%6.27% 3.68% 3.69% 5.67% 3.43% 3.87% 3.57% 2.99%0.72% 0.48% -0.07% 2.25% 1.42% -0.60% 1.69% 5.75%3.69% 1.90% 3.94% 2.49% 4.35% 3.73% 2.98% 5.97%0.38% 1.87% 0.45% 1.99% -0.09% -0.81% -0.80% 3.99%3.58% 1.55% 2.82% 2.06% 7.35% 3.09% 3.58% 6.26%1.41% 0.87% 1.21% -0.68% 2.28% 1.93% -3.85% 4.00%4.58% 2.72% 3.05% 4.23% 4.56% 4.28% 8.23% 7.42%0.71% 1.85% 0.17% 3.50% 0.55% -1.49% -0.01% -0.39%4.58% 2.63% 2.80% 4.22% 5.58% 9.03% 8.64% 6.87%0.77% 2.38% 0.84% 1.51% -2.14% 1.51% 6.69% 2.97%6.79% 3.77% 2.89% 8.34% 6.91% 2.05% 7.90% 11.43%

% positive 83.33% 79.76% 85.71% 86.90%

2000

2001

1996

1997

1998

1999

1992

1993

1994

1995

1988

1989

1990

1991

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1974

1975

1976

1977

1970

1971

1972

1973

1966

1967

1968

1969

1962

1963

1964

1965

Table 4: Summary statistics on the annual four factor returns (Rm-Rf, SMB, HML and WML) on the July

1960 - April 2001 period (N=42)Rm stands for the value-weighted market return obtained from the firms considered in the sample. Rf represents the return on aportfolio of Canadian 91-day Treasury Bills (source: Scotia Capital). SMB is the return from a hedged portfolio for which thesecurities whose stock exchange capitalization is small are bought and the securities for which the stock exchange capitalization islarge are shorted. HML is the return from a hedged portfolio for which the securities for which the ratio book-to-market is highare bought and the securities for which the ratio book-to-market is low are shorted. Lastly, WML represents the return of ahedged portfolio for which securities with the best prior performance over the previous period (t-12 with t-2) are bought and thesecurities with the worst performance during the same period are shorted. The average monthly return and standard deviationrespectively appear for each year in the first and second lines.

1960

1961

31

Month Statistics Rm-Rf SMB HML WMLJanuary mean 1.95% 2.56% -0.05% -0.49%

standard deviation 4.99% 4.07% 4.10% 5.62%t (mean) 2.51 4.03 -0.08 -0.55

February mean 0.12% 1.28% 0.94% 1.49%standard deviation 3.62% 3.59% 5.53% 4.50%

t (mean) 0.21 2.27 1.09 2.12March mean 0.31% 0.57% 1.37% 1.01%

standard deviation 4.16% 3.37% 3.18% 4.49%t (mean) 0.48 1.09 2.76 1.44

April mean 0.33% -0.09% 1.45% 1.10%standard deviation 4.30% 3.53% 2.66% 4.14%

t (mean) 0.50 -0.15 3.50 1.70May mean -0.10% 0.51% -0.06% 1.13%

standard deviation 3.54% 2.60% 3.30% 3.21%t (mean) -0.19 1.25 -0.11 2.25

June mean -0.36% -0.27% 0.59% 2.18%standard deviation 4.10% 2.80% 3.38% 4.67%

t (mean) -0.56 -0.62 1.11 2.99July mean 0.52% 0.25% 0.09% 1.80%

standard deviation 3.71% 2.53% 2.14% 3.99%t (mean) 0.90 0.62 0.26 2.89

August mean 0.47% 0.12% -0.32% 0.77%standard deviation 5.39% 2.53% 2.74% 4.40%

t (mean) 0.56 0.29 -0.74 1.13September mean -1.25% 0.31% 0.55% 0.78%

standard deviation 4.04% 2.29% 3.25% 4.11%t (mean) -1.98 0.87 1.09 1.22

October mean -0.94% -0.56% 0.79% 1.54%standard deviation 5.78% 3.11% 4.02% 4.57%

t (mean) -1.04 -1.15 1.27 2.15November mean 1.08% 0.32% -0.50% 2.50%

standard deviation 4.31% 3.31% 5.04% 4.73%t (mean) 1.60 0.62 -0.64 3.38

December mean 2.35% 0.07% 0.23% 2.28%standard deviation 3.21% 2.97% 3.15% 4.32%

t (mean) 4.69 0.15 0.46 3.38mean 0.23% 0.23% 0.47% 1.51%

standard deviation 4.32% 3.00% 3.63% 4.30%t (mean) 1.14 1.61 2.72 7.43

8.41 11.24 -0.11 -0.32

Table 5: Summary statistics per month on the four factor returns : Rm-Rf, SMB,

HML and WML returns (July 1960-April 2001).

Months other than January

Ratio January to other months

Rm-Rf, SMB, HML and WML monthly excess returns are partitioned relatively to months to examineseasonality in returns. t (mean) is the mean return divided by its standard error (standarddeviation/489^0.5).

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Panel A: periods of down-marketsN= 220 observations Rm-Rf SMB HML WML

mean -3.26% 0.34% 1.40% 1.05%standard deviation 3.28% 3.02% 3.30% 4.21%

t (mean) -14.73 1.64 6.27 3.69minimum -23.27% -14.12% -7.87% -17.08%maximum -0.02% 14.02% 17.40% 13.64%

compounded mean return -3.33% 0.30% 1.32% 0.97%Panel B: periods of up-marketsN= 270 observations Rm-Rf SMB HML WML

mean 3.34% 0.50% -0.37% 1.57%standard deviation 2.60% 3.28% 3.77% 4.63%

t (mean) 21.11 2.48 -1.61 5.59minimum 0.01% -10.88% -21.92% -19.09%maximum 17.10% 15.52% 15.44% 17.50%

compounded mean return 3.31% 0.44% -0.44% 1.47%

Table 6: Summary statistics on the four factors monthly returns (Rm-Rf,SMB, HML and WML) when the period analyzed is stratified in up anddown markets.Rm stands for the value-weighted market return obtained from the firms considered in thesample. Rf represents the return on a portfolio of Canadian 91-day Treasury Bills (source:Scotia Capital). SMB is the return from a hedged portfolio for which the securities whosestock exchange capitalization is small are bought and the securities for which the stockexchange capitalization is large are shorted. HML is the return from a hedged portfolio forwhich the securities for which the ratio book-to-market is high are bought and the securitiesfor which the ratio book-to-market is low are shorted. Lastly, WML represents the returnof a hedged portfolio for which the securities with the best prior performance over theprevious period (t-12 with t-2) are bought and the securities with the worst performanceduring the same period are shorted. Periods of up- and down-markets are defined on thebasis of the sign of Rm-Rf. t (mean) is defined as the mean return divided by its standarderror.

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Panel A: restrictive monetary policy periodsN= 258 observations Rm-Rf SMB HML WML

mean -0.11% 0.16% 0.28% 1.61%standard deviation 4.57% 3.41% 3.90% 4.40%

t (mean) -0.41 0.75 1.18 5.92minimum -19.93% -14.12% -21.92% -17.08%maximum 11.95% 15.52% 10.85% 17.50%

compounded mean return -0.10% 0.04% 0.09% 0.66%Panel B: expansive monetary policy periodsN= 232 observations Rm-Rf SMB HML WML

mean 0.92% 0.72% 0.58% 1.04%standard deviation 4.14% 2.85% 3.40% 4.49%

t (mean) 3.61 4.08 2.75 3.75minimum -23.27% -8.64% -9.39% -19.09%maximum 17.10% 11.25% 17.40% 14.93%

compounded mean return 0.33% 0.27% 0.21% 0.37%

Table 7: Summary statistics on the four factors monthly returns (Rm-Rf,SMB, HML and WML) when the period analyzed is stratified inrestrictive and expansive monetary periods.Rm stands for the value-weighted market return obtained from the firms considered in thesample. Rf represents the return on a portfolio of Canadian 91-day Treasury Bills (source:Scotia Capital). SMB is the return from a hedged portfolio for which the securities whosestock exchange capitalization is small are bought and the securities for which the stockexchange capitalization is large are shorted. HML is the return from a hedged portfoliofor which the securities for which the ratio book-to-market is high are bought and thesecurities for which the ratio book-to-market is low are shorted. Lastly, WML representsthe return of a hedged portfolio for which the securities with the best prior performanceover the previous period (t-12 with t-2) are bought and the securities with the worstperformance during the same period are shorted. Periods of restrictive or expansivemonetary policy are respectively defined as the months when the Bank of Canada discountrate is greater (lesser) than the previous 12 month trailing average. t (mean) is defined asthe mean return divided by its standard error.

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NOTES

1 However, using two arbitrage pricing theory benchmarks, Brennan, Chordia and Subrahmanyam (1998) also find a persistent negative relation between returns and trading volume which is consistent with a liquidity premium in asset prices. See also Lee and Swaminathan (2000) for less conclusive examples. 2 These reported results hold for quarterly rebalancing frequencies, which yield higher returns than portfolios rebalanced on semi-annual or annual frequencies. 3 Jegadeesh and Titman (2001) used 10 momentum portfolios and the numbers reported hold for the hedge portfolio: the top 10% minus the bottom 10%. 4 To avoid a look-ahead bias, the book equity corresponding to the end of the fiscal 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+1 to June of year y+2. 5 The correlation between our sample market return and the TSE 300 index is more than 96%. 6 The portfolio ranking is in t-2 and not t-1, for the bid-ask bounce (Jegadeesh, 1995) can attenuate the continuation effect (see Moskowitz and Grinblatt, 1997; Rouwenhorst, 1998 or Jegadeesh and Titman, 2001). 7 Liew and Vassalou (2000) used three sequential sorts, Carhart (1997) did not construct size-neutral momentum portfolios and Brav, Gezcy and Gompers (2000) used 50 percent breakpoints for momentum. 8 Ickenberry, Lakonishok and Vermaelen (2000) also reports significant SMB and HML premiums over the July 1990-March 1998 period, but this study focussed on examining the excess performance of stock repurchase programs measured relative to the Fama-French (1993) three-factor model using BARRA’s methodology. 9 They rank stocks based on their capitalization, splitting them into two universes of large and small stocks. The first one, comprising large capitalization stocks, encompasses 70% of the total country market capitalization, while the second universe, which comprises small capitalization stocks, covers the bottom 30%. SMB is consequently the spread between the return of the two universes. HML is the high minus low return spread formed by selecting the highest book-to-price stocks one-by-one from the top of the list until one half of the capitalization of each market has been accumulated; these stocks become the constituents of the value portfolio and the remaining stocks form the growth portfolio once a year, based on data available in June. 10 Using panel data, Calvet and Lefoll (1989) test a non-conditional version of the CAPM over the February 1963-December 1982 period and reject the null hypothesis. 11 Fama and French (1998) use data from MSCI in 13 developed markets (United States and EAFE) and 16 emerging markets. Because MSCI firms are large, Fama and French could not test for the size effect and comparison is impossible.

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12 On the TSE 100, over the period 1978-1992, Foerster, Prihar and Schmitz (1994) obtained for the top 10% and bottom 10% an annualized return of 41.2% and 10.9% respectively. They rank stocks based on the weighted average of their past four quarters of price changes and repeat the procedure each quarter. 13 This low average return is mainly due to the negative performance of the momentum strategy during the 1926-1945 period (-0.91% per month, t-statistic=-1.36). 14 The HML premium of 10.73% reported by Arshanapalli, Coggin and Doukas (1998) for Canada over the 1975-1995 period significantly differs from the those reported by Arshanapalli, Coggin, Doukas and Shea (1998), Liew and Vassalou (2000) and us. 15 Using five portfolios, they find that the return spread between large and small firms in January is -8.45% on average in January, and that the return spread between high book-to-market and low book-to-market firms is 6.46%. 16 This size premium is measured by the difference between small and large firm returns (the two extreme quintiles). 17 The return spread between high book-to-market and low book-to-market stocks is very close to zero in the up-market months but climbs to 1.37% per month across the down-market months’ (p.169). The return spread between large and small firms is -0.90% in up-market months and 0.35% in down-market months. 18 We thank an anonymous referee of the Journal for this comment. 19 There exist three other explanations. The first explanation is that these phenomena are due to chance: data snooping (Black, 1993 and Lo and MacKinlay, 1990), data problems (survivorship and look-ahead biases; Kothari, Shanken and Sloan, 1995) or extreme data (Knez and Ready, 1997). The second explanation put forth by Lakonishok, Shleifer and Vishny (1994) and Haugen (1995) is that these results are due to irrational pricing. Investors overreact to firm performance and tend to place higher value on investment opportunities of growth stocks that seem to present stronger fundamentals: earnings and sales. The third explanation suggests that investors may be drawn to firm characteristics that are not related to an asset's covariance with any economic factor (Daniel and Titman, 1997, 1998; Daniel, Titman and Wei, 2001). It encompasses everything that produces a premium and is not the result of risk. 20 Jensen, Johnson and Mercer (1997) identify “rate change series” when the Federal Reserve changes the discount rate in the opposite direction of the previous change. The target for the overnight rate which is the middle of the Bank’s operating band for overnight financing is the main tool used by the Bank of Canada to conduct monetary policy. Formerly (before February 1996) the official rate was the Bank Rate, which is the top of the operating band. We consequently use the Bank Rate to ensure continuity in the series. We do not exclude, as did Jensen, Johnson and Mercer (1997), the month in which the Bank of Canada changed from an expansive to a restrictive monetary policy or from a restrictive to an expansive policy, because we wanted to preserve the integrity of the series of risk factors. We selected the difference between the Bank Rate and the previous 12-month trailing average to gauge the monetary policy and to avoid the months when the Bank of Canada reversed direction in the short run.