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Value versus Growth: The International Evidence
by Kenneth R. French, Eugene F. Fama
Value versus Growth: The International Evidence
Kenneth R. French, Eugene F. Fama
The Journal of Finance
Updated: February 5th, 2013
THE JOURNAL OF FINANCE .VOL LIII, NO 6 .DECEMBER 1998
Value versus Growth:
The International Evidence
EUGENE li: FAMA and mNNETH R. FRENCH*
Value stocks have higher returns than growth stocks in markets around the world. For the period 1975 through 1995, the difference between the average returns on global portfolios of high and low book-to-market stocks is 7.68 percent per year, and value stocks outperform growth stocks in twelve of thirteen major markets. An international capital asset pricing model cannot explain the value premium, but a two-factor model that includes a risk factor for relative distress captures the value premium in international returns.
INVESTMENTMANAGERS CLASSIFY FIRMS that have high ratios of book-to-market equity (B/M), earnings to price (E/P), or cash flow to price (C/P) as value stocks. Fama and French (1992, 1996) and Lakonishok, Shleifer, and Vishny (1994) show that for U.S. stocks there is a strong value premium in average returns. High B/M, E/P, or C/P stocks have higher average returns than low B/M, E/P, or C/P stocks. Fama and French (1995) and Lakonishok et al. (1994) also show that the value premium is associated with relative distress. High B/M, E/P, and C/P firms tend to have persistently low earnings; low B/M, E/P, and C/P stocks tend to be strong (growth) firms with persistently high earnings.
Lakonishok et al. (1994) and Haugen (1995) argue that the value premium in average returns arises because the market undervalues distressed stocks and overvalues growth stocks. When these pricing errors are corrected, dis- tressed (value) stocks have high returns and growth stocks have low re- turns. In contrast, Fama and French (1993, 1995, 1996) argue that the value premium is compensation for risk missed by the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965). This conclusion is based on evidence that there is common variation in the earnings of distressed firms that is not explained by market earnings, and there is common variation in the returns on distressed stocks that is not explained by the market return. Most directly, including a risk factor for relative distress in a multifactor version of Merton's (1973) intertemporal capital asset pricing model (ICAPM)
+Graduate School of Business, University of Chicago (Fama), and Sloan School of Manage- ment, Massachusetts Institute of Technology (French). The paper reflects the helpful comments of David Booth, Ed George, Rex Sinquefield, Ren6 Stulz, Janice Willett, and three referees. The international data for this study were purchased for us by Dimensional Fund Advisors.
The Journal of Finance
or Ross's (1976) arbitrage pricing theory (APT) captures the value premiums in U.S. returns generated by sorting stocks on B/M, E/P, C/P, or D/P (div- idend yield).
Still another position, argued by Black (1993) and MacKinlay (1995), is that the value premium is sample-specific. Its appearance in past U.S. re- turns is a chance result unlikely to recur in future returns. A standard check on this argument is to test for a value premium in other samples. Davis (1994) shows that there is a value premium in U.S. returns before 1963, the start date for the studies of Fama and French and others.
We present additional out-of-sample evidence on the value premium. We examine two questions.
- Is there a value premium in markets outside the United States?
- If so, does it conform to a risk model like the one that seems to de- scribe U.S. returns?
There is existing evidence on (i). Chan, Hamao, and Lakonishok (1991) document a strong value premium in Japan. Capaul, Rowley, and Sharpe (1993) argue that the value premium is pervasive in international stock re- turns. Their sample period is, however, short (ten years).
Our results are easily summarized. The value premium is indeed perva- sive. Section I1 shows that sorts of stocks in thirteen major markets on B/M, E/P, C/P, and D/P produce large value premiums for the 1975 to 1995 pe- riod. Sections I11 and IV then show that an international two-factor version of Merton's (1973) ICAPM or Ross's (1976) APT seems to capture the value premium in the returns for major markets. Section V suggests that there is also a value premium in emerging markets.
1. The Data
We study returns on market, value, and growth portfolios for the United States and twelve major EAFE (Europe, Australia, and the Far East) coun- tries. The U.S. portfolios use all NYSE, AMEX, and Nasdaq stocks with the relevant CRSP and COMPUSTAT data. Most of the data for magor markets outside the United States are from the electronic version of Morgan Stan- ley's Capital International Perspectives (MSCI). The twelve countries we use are all those with MSCI accounting ratios (B/M, E/P, C/P, and DIP) for at least ten firms in each December from 1974 to 1994. We do not require that the same firms have data on all ratios. (See Table 11, below, for details on how we construct the portfolios.)
The MSCI data have an important advantage. Other international data- bases often include only currently traded firms and so are subject to survi- vor bias. The MSCI database is just a compilation of the hard-copy issues of Morgan Stanley's Capital International Perspectives. It includes historical data for firms that disappear, but it does not include historical data for newly added firms, so there is no backfilling problem. Thus, the data are Value versus Growth: The International Evidence 1977
relatively free of survivor bias. Because the accounting data on MSCI are also from Capital International Perspectives, their availability on the hard- copy publication date is clear-cut.
MSCI includes only a subset of the firms in any market, primarily those in Morgan Stanley's EAFE index or in the MSCI index for a country's mar- ket. This means that most of the MSCI firms are large-in fact they account for the majority (MSCI's target is 80 percent) of a market's invested wealth, so they provide a good description of the market's performance. Preliminary tests we have done (but do not show) confirm, however, that a database of large stocks does not allow meaningful tests for a size effect, such as that found by Banz (1981) in U.S. returns, and that suggested by Heston, Rou- wenhorst, and Wessels (1995) for international returns.
Table I summarizes our samples. The more complete U.S. sample (from CRSP and COMPUSTAT) always has at least ten times more firms than any of the twelve EAFE countries. But because MSCI covers mostly large stocks, the median and average market capitalizations of the MSCI stocks are typ- ically several times those of the U.S. sample. (Other features of the samples reported in Table I are discussed later.)
Calculating returns from the MSCI data presents a problem. Stock prices are available for the end of each month, but information about dividends is limited to the dividend yield, defined as the ratio of the trailing year of dividends to the end-of-month stock price. The dividend yield allows accu- rate calculation of an annual return (without intrayear reinvestment of div- idends). Annual returns suffice for estimating expected returns, but tests of asset pricing models (which also require second moments) are hopelessly imprecise unless returns for shorter intervals are used. To estimate monthly returns, we spread the annual dividend for a calendar year across all months of the year so that compounding the monthly returns reproduces the annual return. This approach maintains the integrity of average returns. But it assumes that the capital gain component of monthly returns, which is mea- sured accurately, reproduces the volatility and covariance structure of total monthly returns.
11. The Value Premium
Tables I1 and I11 summarize global and country returns for 1975 through 1995 for value and growth portfolios formed on B/M, E/P, C/P, and D/P. For the twelve MSCI EAFE countries, the portfolios are formed at the end of each calendar year from 1974 to 1994, and returns are calculated for the following year. (Table 11 gives details.) We also form the U.S. portfolios at the end of December of each year, using year-end CRSP stock prices and COMPUSTAT accounting data for the most recent fiscal year. Because the availability date for accounting data is less clear-cut for COMPUSTAT than for MSCI, we calculate returns on the U.S. portfolios beginning in July, six months after portfolio formation (as in Fama and French (1996)).
The Journal of Finance
Some Characteristics of the Country Samples
Panel A shows the number of firms for each country in the Morgan Stanley Capital Inter- national (MSCI) database at the beginning of 1975, 1985, and 1995, and the average number of firms for all years (Ave). Panel B shows the MSCI country weights used to form the global portfolios in later tables. Panel C shows the average size (market capitalization, price times shares outstanding) of firms in the market, high book-to-market (HB/M) and low book-to- market (LB/M) portfolios of each country. (See Table I1 for details on how the portfolios are constructed.) The averages are calculated first across firms for a given year and then across years. Panel D shows the median firm size for the three portfolios, averaged across years. Panel E shows the value weight average of B/M for the three portfolios, averaged across years. The thirteen countries are the United States (US), Japan (JP), Great Britain (UK), France (FR), Germany (GM), Italy (IT), the Netherlands (NL), Belgium (BE), Switzerland (SZ), Sweden (SD), Australia (AS), Hong Kong (HK), and Singapore (SG).
Panel A: Number of Firms in Country
|Panel B: MSCI Country Weights (%)|
|Panel C: Average Size (market capitalization, $millions)|
|--Panel D: Median Size (market capitalization, $millions)|
|Panel E: Value-Weight Average Book-to-Market Equity (N/||M)|
The value portfolio for a ratio (indicated with a leading H, for high) in- cludes firms whose B/M, E/P, C/P, or D/P is among the highest 30 percent for a country. The growth portfolio (indicated with a leading L, for low) includes firms in the bottom 30 percent. For example, HB/M is the high book-to-market (value) portfolio and LB/M is the low book-to-market (growth) portfolio. Firms are value-weighted in the country portfolios, and we use
Table II Annual Dollar Returns for Global Market, Value, and Growth Portfolios: 1975-1995 2
We form portfblios at the end of each year Gom 1974 to 1994, based on sorted values of B/M, E/P, C/P, and D/P. P and M are based on price per share at the time of portfolio formation, F:, C, and D are the most recent available trailing year of earnings, cashflow (earnings plus depreciation), c
and dividends per share. B is the most recent available book common equity per share. Value portfolios (indicated with a leading H, for high)
include firms whose ratio (B/M, E/P, C/P, or DIP) is among the highest 30 percent for a given country. Growth portfolios (indicated with a
leading L, tor low) include firms in the bott.on1 30 percent. H -L is the difference between the high and low returns. Market is the global market portfolio return. The global portfolios include the thirteen countries in Table I. Firms are weighted by their market capitalization in the country 9 portfolios; countries are weighted by Morgan Stanley's country (basically value) weights in the global portfolios. The international returns for 2 1975 through 1994 and all international accounting data are from MSCI. The international returns for 1995 are from Datastream. The account-
ing data for the United States are from CO1\IPIJSfL4'I' (as described in Fama and French 11996)), and stock prices and returns are from CRSP. Firms are included in a portfolio for a given ratio (B/M, E/P, C/P, or D/P) even if they do not have data on all four ratios. Mean is a portfolio's average annual return. Std. is the standard deviation of the annual returns; t1Mni is the ratio of the average return to its standard error. fr
..-------. ... .--.-.-.---... ...-,
Market HB/M LB/M H-LE/M HE/P I,E/P H-t,E/P IIC/P LC/P H-LC/P HD/P LD/P H-LD/P N
-. --~ ..-. ----. . ------
Panel A. Annual Value-Weight Dollar Returns in Excess of T-bill Rate R
~-~... ~ N
Mean 9.60 14.76 7.09 7.68 13.66 6.84 6.82 13.49 5.89 7.61 12.67 7.11 5.56 5 Std. 15.67 16.33 16.13 9.94 17.11 15.59 8.85 17.77 16.05 11.11 16.72 16.09 10.44 t(lL3n) 2.74 4.04 1.96 5.45 3.57 1.96 3.45 3.40 1.64 3.06 3.39 1.98 2.38
. ~ --.-----.. -. .~-..
Panel B: Annual Valtle-Wight Dollar Returns in Excess of Dollar Return on Local Market
-.---.--.. ----- ---.-----.. --.----.-------. .--.-.----
Mean 5.16 -2.62 4.06 -2.76 3.89 -3.72 3.07 -2.49
Std. 6.95 3.31 5.95 3.49 6.86 5.47 6.07 4.67
t(&) 3.32 --3.40 3.05 -3.54 2.54 --3.04 2.28 -2.39.
Table III F hnual Dollar Returns in Excess of U.S. 'F-Bill Rate for Market, Value, and Growth Portfolios: 1975-1995
Value and growth portfol~os are formed on book-to-market equity (RiM), earnmgs/price iE/P), cashflo-v\/pri~e IC/P), and dlvidend/price (D/P), as described 111 Table 11 We denote value (h~gh)and growth (low) portfolios by a leading H or L, the differen~e between them is N L The first row for each ~ountrg, ii the average annual return The second 1s the standard deviation of the annual returns (in parentheses) or the 1-statistic testing whether R -L is different from Aero [In brackets]
Netheriands Gelgiurn Swi tzerlnnd
Atisira1:a Eong Mong
Value versus Growth: The International Evidence 1981
Morgan Stanley's country (basically total value of market) weights to con- struct global portfolios. The country weights at the beginning of 1975, 1985, and 1995 are in Table I.
Tables I1 and I11 are strong evidence of a consistent value premium in international returns. The average returns on the global value portfolios in Table I1 are 3.07 percent to 5.16 percent per year higher than the average returns on the global market portfolio, and the average returns on the global value portfolios are 5.56 percent to 7.68 percent higher than the average returns on the corresponding global growth portfolios. Since the United States and Japan on average account for close to 75 percent of the global portfolios, the average returns for the global portfolios largely just confirm the results of Chan et al. (1991), Fama and French (1992, 1996), and Lako-nishok et al. (1994). Table I11 shows, however, that higher returns on value portfolios are also the norm for other countries. When portfolios are formed on B/M, E/P, or C/P, twelve of the thirteen value-growth premiums are positive, and most are more than four percent per year. Value premiums for individual coun- tries are a bit less consistent when portfolios are formed on dividend yield, but even here ten of thirteen are positive.
Table I11 says the value premium is pervasive. Thus, rather than being unusual, the higher average returns on value stocks in the United States are a local manifestation of a global phenomenon. Table I11 also shows that the
U.S. value premium is not unusually large. For example, the U.S. book-to- market value premium is smaller than six of the other twelve B/M premi- ums. The results for other countries are out-.of-sample relative to the earlier tests for the United States and Japan, so clearly the value premium is not the result of data mining.
Leaning on Foster, Smith, and Whaley (1997), a skeptic might argue that the correlation of returns across markets can cause similar chance patterns in average returns to show up in many markets. We shall see, however, that the correlations of the value premiums across countries are typically low. (The average for the B/M premiums is 0.09.) The simulations of Foster et al. (1997) then actually suggest that our results are rather good out-of-sample evidence for a value premium.
The value premiums for individual countries in Table I11 are large in eco- nomic terms, but they are not typically large relative to their standard er- rors. This is testimony to the high volatility of the country returns. The market returns of many countries have standard deviations of approxi- mately 30 percent per year, about twice that of the global mark.et portfolio in Table 11. The most precise evidence that there is a value premium in inter- national returns comes from the diversified global portfolios (Table 11). The smallest average spread between global value and growth returns, 5.56 per- cent per year for the D/P portfolios, is 2.38 standard errors from zero. The value premiums for portfolios formed on B/M, E/P, and C/P (7.68 percent,
6.82 percent, and 7.61 percent per year) are more than three standard errors from zero. We next examine whether the international value premium can be viewed as compensation for risk.
The Jozci.~zalof Fitzatzce
111. A Risk Story for the Global Value Preaniums
Researchers have identified several patterns in the cross section of inter- national stock returns. Heston et al. 11995) find that equal-weight portfolios of stocks tend to have higher average returns than value-weight portfolios in twelve European markets. They conclude that there is an international size effect. Dumas and Solnik (1995) find that exchange rate risks are priced in stock returns around the world. Cho, Eun, and Senbet (1986) and Korajczyk and Viallet (1989) find that APT factors (identified by factor analysis) are important in international stock returns. Finally, Ferson and Harvey (1993) present evidence that the loadings of country portfolios on international risk factors vary through time.
In light of these results, a full description of expected stock returns around the world would likely require a pricing model with several dimensions of risk and time-varying risk loadings. We take a more stripped-down ap- proach. We assume a world in which capital markets are integrated and investors are unconcerned with deviations from purchasing power parity. We test whether average returns are consistent with either an international CAPM or a two-factor ICAPM (or APT) in which relative distress carries an expected premium not captured by a stock's sensitivity to the global market return. Thus, m7e ignore other risk factors that might affect expected re- turns, and we do not allow for time-varying risk loadings. Fortunately, the tests suggest that, at least for the portfolios we examine, our simple ap- proach provides a reasonably adequate story for average returns.
We begin with asset pricing tests that attempt to explain the returns on the global value and growth portfolios. We then use the same models to explain the returns on the market, value, and growth portfolios of individual countries.
A. The CAPM
Suppose the relevant model is an international CAPM. Thus, the global market portfolio is mean-variance-efficient, and the dollar expected return on any security or portfolio is f~~lly
explained by its loading iunivariate re- gression slope) on the dollar global market return, M. In the regression of any portfolio's excess return (its dollar return, R, minus the return on a U.S. Treasury bill, F) on the excess market return,
the intercept should be statistically indistinguishable from zero.
The estimates of equation (1)in Table IV say that an iaternational CAPM cannot explain the average returns on global value and growth portfolios. The intercepts for the four value portfolios (HB/M, HE/P, HC/P, and HD/P) are at least 29 basis points per month above zero, and the intercepts for the four growth portfolios are at least 21 basis points per month below zero. All
CAPM and Two-Factor Regressions to Explain Monthly Excess Returns on Global Value
and Growth Portfolios: 1975-1995
All returns are monthly, in dollars. M is the global market return, Fis the one-month U.S. Treasury bill rate, and R is the global portfolio return to be explained. The global value and growth portfolios are formed on book-to-market equity (B/M), earnings/price (E/P), cashflow/price (C/P), or dividend/price (D/P), as described in Table 11. We denote value (high) and growth (low) portfolios by a leading H or L; the difference between them is H -L. Panel A describes regressions that use the excess market return (M -F) and the book-to-market value-growth return (H --LB/M) to explain excess returns on value and growth portfolios. t( ) is a regression coefficient (or, for the market slope b, the coefficient minus one) $ divided by its standard error. The regression R2 and residual standard errors s(e) are adjusted for degrees of freedom. Panel B summarizes sets $ of' regressions that use the excess market return and a value-growth return (H -LB/M, H --LE/P, H -LC/P, or H ---LD/P) as explanatory c variables. The dependent variables in a given set of regressions are the excess returns on the global value and growth portfolios that are not used 2 as explanatory variabies in that set. F(a) is the F-statistic of Gibbons, Ross, and Shanken (1989) testing the hypothesis that the true intercepts CO in a set of regressions are all zero; p(F) is the probability of a value of F(a) larger than the observed value if the true intercepts are all zero. Ave a, Aveal, and Ave a" are the mean, mean absolute, and mean squared values of the intercepts from a set of regressions. Ave R" and Ave s(e) are
the average values of the regression R" and residual standard errors. The method of estimation is ordinary least squares.
--.. .-.-.-------.--. -
R -F -a + bjM -F] + e(t) R -F = a + b(M --F] -t c[H -LB/M] + e(t1 Y
ft --F a h t(a) t(b-1) R2 s(e) a b c t(a) t(b -1) t(c) R2 s(e) +
HB/M 0.41 0.94 4.29 2.50 9.88 1.48 HE/P 0.32 0.95 3.96 -2.58 0.91 1.25 0.04 0.99 0.45 0.72 -0.62 20.09 0.97 9.77 2 HCIP 0.31 0.93 3.59 -3.43 0.89 1.37 -0.00 0.98 0.51 --~0.02 -1.97 21.95 0.96 0.80 FID/P 0.29 0.87 3.77 -6.80 0.90 1.22 0.10 0.90 0.32 1.46 --6.23 10.80 0.93 1.01 -' LH/M -0.21 1.03 -4.02 2.85 0.97 0.81 s
LE/P --0.23 1.04 --4.27 3.57 0.96 0.83 --0.07 1.02 -0.26 -1.63 2.26 -14.67 0.98 0.61 %
LC/P -0.28 1.01 -3.84 0.44 0.93 1.1.3 -0.16 0.99 -0.19 -2.27 --~0.62 --6.28 0.94 1.05
LD/P -0.22 1.07 -3.49 4.41 0.95 1.00 -0.03 1.04 -0.31 -0.64 3.37 --14.45 0.97 0.74 s.
Panel H f3
Aue a m 0
Explanatory -----------Variables F(a) p(F) All Value Growth Ave a/ Ave a' Ave RL Avr s(e)
M-F 3.718 0.000 0.050 0.333 -0.233 0.283 0.0839 0.924 1.135 M-P FI-LB/M 1.457 0.194 -0.020 0.045 -0.085 0.065 0.0069 0.959 0.830 M-F H-LEIP 1.578 0.154 --0.002 0.068 -0.071 0.070 0.0068 0.955 0.867 + ill-F FI-LCIP 0.987 0.435 0.028 0.102 -0.046 0.074 0.0066 0.959 0.818 Cr, M-F H-LD/P 2.292 0.036 0.026 0.156 -0.104 0.130 0.0192 0.949 0.929 8
-. ~ --. ~
The Journal of Finance
the CAPM intercepts for the global value and growth portfolios are more than 3.4 standard errors from zero. The GRS F-test (Gibbons, Ross, and Shanken (1989)) of the hypothesis that the true intercepts are all zero re- jects with a high level of confidence (p-value = 0.000). In both statistical and practical terms, the international CAPM is a poor model for global value and growth returns.
Why does the CAPM fail? If the CAPM is to explain the high returns on global value portfolios, they must have large slopes on the global market portfolio. Similarly, if the CAPM is to explain the lower returns on global growth portfolios, their market slopes must be less than one. In fact, the reverse is true. Table IV shows that the value portfolios' market slopes are slightly less than one, and the growth portfolios' slopes are slightly greater than one.
B. Two-Factor Regressions
Are the premiums on global value portfolios and the discounts on global growth portfolios compensation for risk? In an international two-factor (one- state-variable) ICAPM, expected returns are explained by the loadings of securities and portfolios on the global market return and the return on any other global two-factor MMV (multifactor-minimum-variance) portfolio (Fama (1996)). (Two-factor MMV portfolios have the smallest possible return vari- ances, given their expected returns and loadings on the state variable whose pricing is not captured by the CAPM.) Alternatively, the market return and the difference between the returns on two MMV portfolios can be used to explain expected returns.
We assume that the global high and low book-to-market portfolios, HB/M and LB/M, are two-factor MMV, so the difference between their returns, H -LB/M, can be the second explanatory return in a one-state-variable ICAPM. The model then predicts that the intercept in the time-series regression,
is zero for all the portfolios whose returns, R, we seek to explain. We use H -LB/M, rather than HB/M -F or LB/M -F, because the correlation of H -LB/M with M -F is only -0.17. The low correlation makes the slopes in equation (2) easy to interpret. Moreover, H -LB/M is an international version of HML, the distress factor in the three-factor model for U.S. stock returns in Fama and French (1993).
Table IV says that the two-factor model (2) provides better descriptions of the returns on global value and growth portfolios formed on E/P, C/P, and D/P than does the CAPM. The average intercept for the global value portfolios drops from 33.3 basis points per month in the CAPM regression (equation (1))to 4.5 basis points per month in the two-factor regression (equation (2)). Similarly, the average intercept for the global growth port-
Value versus Growth: The International Evidence 1985
folios rises from -23.3 basis points per month in equation (1)to -8.5 basis points in equation (2). The GRS test of the hypothesis that the intercepts are zero also favors equation (2). The F-statistic testing whether all (value and growth) intercepts are zero drops from 3.72 (p-value = 0.000) in the CAPM regressions to 1.46 (p-value = 0.194) in the two-factor regressions.
Why do the two-factor regressions produce better descriptions of global value and growth returns? The two-factor regressions and the CAPM re- gressions produce similar market slopes. Thus the improvements must come from the H -LB/M slopes. Table IV confirms that these dopes are at least ten standard errors above zero for the global value portfolios formed on E/P, C/P, and D/P, and they are at least six standard errors below zero for the growth portfolios. Since the average H -LB/M return is positive, the positive H -LB/M slopes for the global value portfolios are consistent with their high average returns, and the negative slopes for the growth portfolios are in line with their low average returns. Moreover, the success of the two-factor regressions in describing the returns on the global value and growth portfolios says that different approaches to measuring value and growth-specifically, portfolios formed on B/M, E/P, C/P, and D/P- produce premiums and discounts that can all be described as conlpensation for a single common risk. In other words, global value-growth premiums, however measured, are consistent with a one-state variable XCAPM (or a two-factor APT).
Table IV also shows that alternative measures of the value-growth pre- mium are largely interchangeable as the second explanatory return in equa- tion (2). Substituting H -LE/P or H -LC/P for H --LB/M produces similar average absolute intercepts, average squared intercepts, and GRS F-tests for the global value and growth portfolios that are not used as explanatory returns. In results not shown, we also obtain excellent explanations of av- erage returns when we use the excess return on a single global value or growth portfolio (e.g., HB/M -F or LB/M -F) as the second explanatory return. All this is consistent with one-state-variable ICAPM pricing of global value and growth portfolios, and with the hypothesis that, like the global market portfolio, different global value and growth portfolios are close to two-factor MMV.
One can argue that the global regressions do not provide a convincing test of a risk story for the international value premium. The four sorting vari- ables (B/M, E/P, C/P, and D/P) are all versions of the inverted stock price, 1/P, so different global value (or growth) portfolios have many stocks in common. But the portfolios are far from identical. The squared correlations between the four global value-growth returns (proportions of variance ex- plained) range from only 0.37 to 0.67. Thus, although a reasonable suspicion remains, there is no guarantee that the average returns on different value and growth portfolios will be described by their sensitivities to a single com- mon risk. Moreover, the properties of the global value pren~iunl examined next and the extension of the asset pricing tests to country portfolios in Section IV lend additional support to a risk story.
The Journal of Finance
C. Is the Global Tialue Premium Too Large?
MacKinlay (1995) argues that the value premium in U.X. returns is too large to be explained by rational asset pricing. Lakonishok et al. (1994) and Haugen (1995) go a step further and argue that the 1J.S. value premium is close to an arbitrage opportunity. Fama and French (1996, especially Table XI) disagree.
Is the international value prernium too large? The global market premium is a good benchmark for judging the global value premiums. The mean and standard deviation of the market premium (M -F) in Table I1 are 9.60 percent and 15.67 percent per year. The average value-growth premiums are smaller, ranging froin 5.56 percent per year when we sort on D/P to 7.68 percent per year for B/M, but their standard deviations are also smaller, between 8.85 per- cent and 11.11percent per year. The four t-statistics for the value-growth pre- miums, 2.38 to 3.45, bracket the t-statistic for the market premium, 2.74. We conclude that the value-growth premiums are no more suspicious than the mar- ket premium. At a minimum, the large standard deviations of the value- growth premiums say that they are not arbitrage opportunities.
PV. Regression Tests for Country Returns
Since the global portfolios are highly diversified, they provide sharp per- spective on the CAPM's inability to explain the international value pre- mium, and on the improvenients provided by a two-factor model. In contrast, portfolios restricted to individual countries are less diversified and their returns have large idiosyncratic components (e.g., Harvey (1991)). As a re- sult, asset pricing tests on country portfolios are noisier than tests on global portfolios. But the country portfolios have an advantage. Because most of the country portfolios are small fractions of the global portfolios ( Table I), and because all have large idiosyncratic components, there is no reason to think we induce a linear relation between average return and risk loadings by the way we construct the explanatory portfolios. Thus, the country port- folios leave plenty of room for asset pricing models to fail.
A. The CAPM versus a Two-Factor Model
In an international CAPM, all expected returns are explained by slopes on the global market return. Table V shows estimates of the CAPM time-series regression (equation (1))that attempt to explain the returns on three sepa- rate sets of country portfolios that include, respectively, the market, high book-to-market (HB/M), and low book-to-market (12B/M) portfolios of our thirteen countries. We group country portfolios by type (rather than doing joint tests on all portfolios and countries) to have some hope of power in formal asset pricing tests.
Like Solnik (1974), I-Tarvey (1991). and others, we find little evidence against the international CAPM as a model for the returns on the market portfolios of countries. The GRS test of the hypothesis that all the intercepts in the
Value versus Growth: The International Evidence 1987
CAPM regressions for the countxy market portfolios are zero produces an F-statistic, 1.08 (p-value = 0.37), near the median of its distribution under the null. The low book-to-market portfolios of the countries are also consis- tent with an international CAPM. The GRS p-value for the LB/M portfolios (the probability of a more extreme set of intercepts when the CAPM holds) is 0.92. Results not shown confirm that an international CAPM is also con- sistent with the average returns on the country growth portfolios formed on EIP, CIP, and DIP.
Confirming the global portfolio results in Table IV, however, Table V says that the international CAPM cannot explain the high average returns on the country value portfolios. For the high book-to-market (HBIM) portfolios, the average of the intercepts from the CAPM regressions is 0.51 percent per month. The GRS test produces an F-statistic of 2.23, which cleanly rejects (p-value = 0.01) the hypothesis that all the intercepts are zero. The results (not shown) for value portfolios formed on EIP, CIP, and DIP are similar.
Table V shows that a two-factor model that describes country returns with the global market return and the spread between the global high and low book-to-market returns, H -LBIM, does a better job on the country value portfolios. The average intercepts drop from 0.51 in the CAPM regressions to explain the HBIM returns of countries to 0.14 in the two-factor regres- sions. The p-value for the test of whether all the intercepts are zero rises from 0.01 in the CAPM regressions to 0.55 in the two-factor regressions. Results not shown confirm that, unlike the CAPM, the two-fi3ctor regres- sions also capture the average returns on country value portfolios formed on EIP, CIP, and DIP.
There is an interesting pattern in the way the country portfblios load on the international distress factor in Table V. Not surprisingly, every country's HBIM value portfolio has a positive slope on the global value-growth return, H -LBIM. Every country's HBIM portfolio also has a larger slope on the global H -LBIM than its LBIM portfolio. What is surprising is that, except for the United States, Japan, and Sweden, every country's LBIM portfolio has a positive slope on the global H -LBIM return. In other words, the growth portfolios of ten of the eleven smaller markets load positively on the international distress factor. Similarly, in the two-factor regressions to ex- plain the market returns of the countries, only the United States and Japan have negative slopes on the global value-growth return. The H -LBIM slopes for the market portfolios of the eleven smaller markets are all at least 0.96 standard errors above zero, and seven are more than 2.0 standard errors above zero. In short, measured by sensitivity to the global H -LB/M return, the eleven smaller markets tilt toward return behavior typical of value stocks.
Finally, a caveat is in order. Country returns have lots of variation not explained by global returns. The average R' in the two-factor regressions for the countries is only about 0.35. As a result, the two-factor regression inter- cepts are estimated imprecisely, so our failure to reject international two- factor pricing for the country portfolios may not be impressive. But we do not, in any case, mean to push a two-factor model too hard. Additional risk
|CAPM and Two-Factor Regressions that Use Monthly Excess Returns on the Global Market Portfolio|
|(M -F) and the Global Book-to-Market Value-Growth Return (H -LBIM) to Explain Monthly Excess|
|Returns on Countrv Portfolios: 1975-1995
|All returns are monthly, in dollars. The explanatory variables are the return on the global market portfolio in excess of the one-month U.S. Treasury bill return (M F), and the difference between the global high and low book-to-market returns (H LBIM). The dependent variables (R F) are the excess returns on market (M-F), high book-to-market (HBIM F), and low book-to-market (LBIM F) portfolios for individual||1-3 23|
|countries, described in Table 11. t( ) is a regression coefficient (or, for the market slope b, the coefficient minus one) divided by its standard error. The regressions R%re adjusted for degrees of freedom. The method of estimation is ordinary least squares.||Q 5|
U.K. France Germany Italy Netherlands Belgium Switzerland Sweden Australia Hong Kong Singapore
U.K. France Germany Italy Netherlands Belgium Switzerland Sweden Australia Hong Kong Singapore
1990 The cJour~zal of Fina~zce
factors are likely to be necessary to describe average returns when, for ex-. ample, the tests are extended to small stocks. Like the more precise tests on the global portfolios in Table IV, however, the tests on the country portfolios in Table V do allow us to conclude that the addition of an international distress factor provides a substantially better explanation of value portfolio returns than an international CAPM.
B. Global Risks in Country Returns
The hypothesis that an international CAPM or ICAPM explains expected returns around the world does not require security returns to be correlated across countries. International asset pricing just says that the expected re- turns on assets are determined by their covariances with the global market return (CAPM and ICAPM) and the returns on global MMV portfolios needed to capture the effects of priced state variables (ICAPM). But covariances with these global returns (and the variances of the global returns them- selves) may just result from the variances and covariances of asset returns within markets; that is, covariances between the asset returns of different countries may be zero.' Still, it is interesting to ask whether the global mar- ket and distress risks that seem to explain country returns arise in part from covariances of returns across countries.
For direct evidence on the local and international components of global portfolio returns, we decompose the variances of the global M -P and H LB/M returns into country return variances and the covariances of returns across countries,
where w, is the weight of country i in the global portfolio and R, is the return for the portfolio of country i. If there were no common component in returns across countries, the covariances in equation (3) would contribute nothing to the global variance. At the other extreme, with perfect correlation of returns across countries, the contribution of the covariances depends on country weights and variances. Using the average country weights for I975 through 1995, country covariances would then account for about 75 percent of the variances of the global M -F and H -LB/M returns. In fact, international components (the covariances in equation (3)),are 52 percent of the variance of the global M -F return, and 19 percent of the variance of the global EH LBIM return. Thus, although country-specific variances account for 81 per-
A similar argument implies that excluding left-hand-side country returns from right-hand- side global returns in regressions (1)and (2) (an approach often advocated to avoid inducing a spurious relation between average return and risk) would corrupt the estimates of risk loadings in tests for international asset pricing.
Value uersus Growth: The International Evidence 1991
cent of the variance of the global H -LB/M return, both the global market return and the global value-growth return contain important international components.
The correlations between country returns in Table VI provide perspective on these calculations. Not surprisingly, the correlations of the excess market returns of the thirteen countries are all positive (the average is 0.46), and much like those of earlier studies. Given the estimates of equation (3), it is also not surprising that the correlations of the value-growth (H -LB/M) returns of the countries are smaller. The average is only 0.09, but more than three-quarters of the correlations (61 of 78) are positive. The correlations of the country H -LB/M returns with the global H -LB/M return tend to be larger. This is due in part to the diversification of the global H -LB/M return, but it also reflects the fact that the global return is constructed from the country returns.
From an asset pricing perspective, the important point is that the lower correlation of the II -LB/M returns of the countries does not result in low volatility for the global H --LB/M return; the global value-growth pre- mium is not an arbitrage opportunity. The standard deviation of the global H -LB/M return, 9.94 percent per year, is about two-thirds that of the global market return, 15.67 percent. The lower volatility of H -LB/M is also associated with a smaller average premium, '7.68 percent, versus 9.60 percent for &I -I?. And the Sharpe ratio for H -LB/M (mean/standard deviation) is 0.77, well within striking distance of the Sharpe ratio for M --F, 0.61.
C. Coun,try 'Weights, Average Returns, and Biased Coefficient
The intercepts in the CAPM regressions of the market portfolios of coun- tries on the global market return in Table V are surprising. If the country tveights in the global market portfolio were constant, the weighted average of the intercepts would be zero and the weighted average of the market slopes would be one. Using the average weights of countries for 1975 through 1995, the average slope (0.964) is close to one. But the average intercept is
0.128 percent per month, and the CAPM intercept for every market but Italy is positive. Positive intercepts also seem to be the norm in other studies that use country market portfolios and a value-weight global market to test an international CAPM (e.g., Harvey (1991), Ferson and Harvey (1993)).
Our preliminary work on this problem suggests that the positive inter- cepts in the CAPM regressions are in large part due to the evolution of the country weights in the global market portfolio. The issues are complicated, however, and a full explanation awaits future research.
V. Value and Growth in Emerging Markets
Emerging markets allow another out-of-sample test of the value premium. The International Finance Corporation (IFCj provides return, book-to- market equity, and earnings/price data for firnis in more than thirty emerg-
L?e,c? in 9y":7L?
Value versus Growth: The International Evidence 1993
ing markets. Although stock returns for some countries are available earlier, B/M and E/P data are not available until 1986. Thus, our sample period for emerging markets is for 1987 through 1995.
Like the MSCI data, the IFC data are attractive because we can construct a sample uncontaminated by backfilled returns. The IFC included up to seven years of historical returns when it released its first set of emerging market indices in 1982. They continue to backfill when developing data for new countries. But IFC does not backfill when they expand their coverage of countries already in the indices. Thus, we avoid backfilled returns simply by starting the tests for countries on the date they are added to the IFC emerg- ing market indices.
Table VII summarizes market, value, and growth portfolio returns for the sixteen countries where IFC has data on at least ten firms in at least seven years. Firms are weighted by their market capitalization in the country port- folios. The value-weight indices covering all emerging markets weight coun- tries by IFC's estimate of their market capitalization at the beginning of each year; the equal-weight indices weight countries equally.
As Harvey (1995) and others observe, emerging market returns have un- usual features. At least during our sample period, average returns in emerg- ing markets are higher than in developed markets. The average excess dollar return for the equal-weight index of emerging markets is 24.47 percent per year for 1987 through 1995, and the value-weight excess return is 25.93 per- cent. Measured in dollars, Argentina's average excess return is 64.71 percent per year. Only two of sixteen emerging markets (India and Jordan) have average returns below 9.47 percent, the value-weight average of developed market returns in Table 11. Of course, as Goetzmann and Jorion (1996) em- phasize, recent returns may not give a representative picture of the expected performance of emerging markets.
It is also well known that emerging market returns are volatile. The mar- ket portfolios of ten of the sixteen countries have annual return standard deviations above 50 percent; the standard deviations for Argentina and Ven- ezuela are 137 percent and 221 percent per year. In contrast, the standard deviation of the annual U.S. market return is 14.64 percent. Only four of the other twelve developed markets in Table 111 have standard deviations above 30 percent, and the largest (Italy) is 43.8 percent.
The links among emerging market returns are weak. The average corre- lation between the excess market returns of individual countries is only 0.07, and 37 of 120 (not shown) are negative. In contrast, the average of the cor- relations of the excess market returns of the developed countries in Table VI is 0.44, and none are negative. Because emerging market returns are not very correlated, much of their higher volatility disappears when they are combined in portfolios. The annual standard deviation is 41.05 percent for the value-weight portfolio of emerging markets and 26.23 percent for the equal-weight portfolio. Even the more-diversified equal-weight emerging mar- ket return, however, has almost twice the standard deviation of the return on the value-weight portfolio of developed market returns, 15.67 percent.
Table ViI Annual Dollar Returns in Excess of U.S. T-Bill Rates ifor Emerging Markets
The emerging market data are from the TFC Value and growth portfol~os uslng book-to-market equlty 1B/M) and earn~ngsiprice (E/P) as In Table I1 The Small and Big portfolios are formed on market cap~tal~~at~on,
in an analogous manner We denote value (high) and growth (low) portfolios by a leadlnq H or L, thc difference between them is H 1, S B 15 the difference between the Small and Big portfolioi Countries are included in the table (and indices) if the 1FC database includes at least ten firms with positive book equity in at least seven years. Countries are
not included in a year's B/M (or E/P) portfolios if the 1VC has fewer than ten firms with positive book equity (or earnings) at the end of the rn previous year. Thus, the B/M and E/P portfolio returns for Chile do not include 1988, and the E/P portfolio returns for Jordan do not include C 1987 and 1988. The V%' indices weight countries by the IFC's estimate of' their total market capitalization. The EW indices weight countries 0
equally. The first row for each country or index is the average annual return. The second is the standard deviation of the annual returns (in
parentheses) or the t-statistic testing whether H L or S --I3 is different from zero [in brackets]. %
Market 13B/&I LB/M 3 -LB/XZ HE/P LE/P ti LE/P Srnall Big S I: r:
WV indices 25 93 39 77 22 86 16 91 29 52 25 49 4 04 39 78 24 89 14 89 $
1987 1995 (41 05) (49 88) (35 40) 13 061 (47 36) (38 03) [O 581 (52 42) (39 87) 11691 ;; EW indices 24 47 33 21 19 07 14 13 29 60 19 18 10 43 32 01 23 32 8 70 " 1987-1995 (26 23) (31 43) (21 48) /3 011 i14 09) (34 32) 11861 (26 41) (26 32) 981
Chile 35.58 48.07 32.86 15.21 39.17 29.57 9.60 45.02 36.33 8.69 1987---I995 (30.03) (49.93) (41.68) [1.12] (36.56) (48.21) 11.231 (39.67) (30.50) 10.981 Colombia 33.16 4.90 22.37 --17.47 21.68 31.97 -10.29 11.08 31.61 -20.54 1988-1995 (65.85) (51.10) (50.07) [-2.181 (85.79) (53.69) /--0.561 (45.97) (62.71) j-i.981 Greece 19.92 22.36 19.73 2.63 17.44 15.08 2.36 9.49 21.06 --11.57 1989-1995 (47.49) if53.33) (,45.08) 10.391 151.51) (53.01) j0.191 139.61) (48.27) 1.-1.041
The Journal of Finance
The novel results in Table VII are the returns for portfolios formed on book-to-market equity, earnings/price, and size (market capitaliza- tion). Like the results for major markets in Tables TI and 111, there is a value premium in emerging market returns. The average difference be- tween annual dollar returns on the high and low book-to-market port- folios (H -LB/M) is 16.91 percent when countries are value-weighted, and
14.13 percent when they are weighted equally. Positive value-growth re- turns are also typical of individual emerging markets. Twelve of sixteen B/M value-growth returns for countries are positive, and ten of sixteen E/P spreads are positive.
Emerging market returns are quite leptokurtic and right skewed so sta- tistical inference is a bit hazardous. With this caveat in mind, we note that the 16.91 percent and 14.13 percent value-weight and equal-weight H LB/M average returns are more than three standard errors from zero. The value premium is less reliable when we sort on E/P. Because emerging mar- ket returns are so volatile and our sample period is so short, average E/P value premiums of 4.04 percent (obtained when countries are value-weighted) and 10.43 percent (equal weights) are only 0.58 and 1.86 standard errors from zero.
The out-of-sample test provided by emerging markets confirms our results from developed markets. The value premium is pervasive. We guess, how- ever, that the expected 19 -LB/M value-growth return in emerging markets is smaller than the realized equal- and value-weight average premiums, 14.13 percent or 16.91 percent. Moreover, without this good draw, the short nine- year sample period and the high volatility of emerging market returns would have prevented us from concluding that the value premiuni in these markets is reliably positive.
Unlike the MSG1 data, the IFC data cover small stocks, so we can do some rough tests for a size effect in emerging market returns. Table VII compares the returns on portfolios of small and big stocks. Each country's small and big portfolios for a year contain the stocks that rank in the country's bottom 30 percent and top 30 percent by market capitalization at the end of the previous year. Like the value and growth portfolios, the stocks in a country's big and small portfolios are value-weighted.
Again, the emerging market results confirm the evidence from developed markets. Small stocks tend to have higher average returns than big stocks. The average difference between the returns on the value-weight small and big stock portfolios is 1.4.89 percent per year (t = 1.69). The average differ- ence for the equal-weight portfolios is 8.70 percent (t = 1.98). Small stocks have higher average returns than big stocks in eleven of sixteen emerging markets. Thus, like stock returns in the United States (Banz (1981)) and other developed countries (Heston et al. (1995)), there seems to be a size effect in emerging market returns.
The results in Table VII seem inconsistent with Claessens, Dasgupta, and Glen (1996). Their cross-section regressions use seven variables, market beta, firm size, price-to-book-value (PBV, the inverse of book-to-market equity), Value versus Growth: The International Evidence 1997
earnings/price, dividend yield, turnover, and sensitivity to exchange rate changes, to explain average returns on individual stocks in nineteen emerg- ing markets. Although they find that size, PBV, and E/P have explanatory power in many countries, the signs of the coefficients are often the reverse of ours. For example, they find a positive coefficient on PBV in ten of nine- teen emerging markets. Slightly different sample periods may explain some of the differences between our results and theirs. We suspect, however, that different estimation techniques are the main factor. Cross-section regres- sions like theirs are sensitive to outliers, and extreme outliers are common in the returns on individual stocks in emerging markets. Our portfolio re- turns are probably less subject to such influential observations. In any case, our value-weight returns give an accurate picture of investor experience in these markets.
Finally, given the short sample period and the high volatility of emerging market returns, asset pricing tests for emerging markets are quite impre- cise, so we do not report any.
Value stocks tend to have higher returns than growth stocks in markets around the world. Sorting on book-to-market equity, value stocks outperform growth stocks in twelve of thirteen major markets during the 1975-1995 period. The difference between average returns on global portfolios of high and low B/M stocks is 7.68 percent per year (t = 3.45). There are similar value premiums when we sort on earningslprice, cash flow/price, and dividend/ price. There is also a value premium in emerging markets. Since these re- sults are out-of-sample relative to earlier tests on U.S. data, they suggest that the return premium for value stocks is real.
An international CAPM cannot explain the value premium in inter- national returns. But a one-state-variable international ICAPM (or a two- factor APT) that explains returns with the global market return and a risk factor for relative distress captures the value premium in country and global returns.
We do not, however, mean to push a strong asset pricing story for our results, here or in Fama and French (1993, 1996). For example, a reasonable conclusion, agnostic with respect to equilibrium asset pricing, is that a glo- bal market portfolio and a global portfolio formed to mimic relative distress are close to two-factor MMV in the limited set of portfolic! opportunities covered by (i) global value and growth portfolios formed in various ways; and (ii) market, value, and growth portfolios of individual countries. In this view, the international two-factor model simply provides a parsimonious way to summarize the general patterns in international returns. Similarly, the apparent success of the three-factor model in Fama and French (1993, 1996) simply says that the three U.S. portfolios they use to describe returns are close to three-factor MMV in the set of investment opportunities covered by
The Journal of Finance
the U.S. portfolio returns they attempt to explain. Thus, the three U.S. explanatory returns provide a parsimonious way to summarize most of the general patterns in U.S. stock returns.
Banz, Rolf W., 1981, The relationship between return and market value of common stocks, Journal of Financial Economics 9, 3-18.
Black, Fischer, 1993, Beta and return, Jour~zal of Portfolio Management 20, 8-18.
Capaul, Carlo, Ian Rowley, and William F. Sharpe, 1993, International value and growth stock returns, Financial Analysts Joz~rnaZ, January-February, 27-36. Chan, Louis K. C., Yasushi Hamao, and Josef Lakonishok. 1991, Fundamentals and stock re- turns in Japan, Jour~zal of Finance 46, 1739-1789. Cho, D. C., C. S. Eun, and Lemma W. Senbet, 1986, lnternational arbitrage pricing theory: An empirical investigation, Jor~rnal of Finance 41, 313-329. Claessens, Stijn, Susmita Dasgupta, and Jack Glen, 1996, The cross-section of stock returns: Evidence from the emerging markets, Working paper, International Finance Corporation. Davis, James, 1994, The cross-section of realized stock returns: The pre-COMPUSTAT evidence, Journal of Finance 49, 1579-1593. Dumas, Bernard, and Bruno Solnik, 1995, The world price of foreign exchange risk, Journal of Finance 50, 445-479. Fama, Eugene F., 1996, Multifactor portfolio efficiency and multifactor asset pricing, Jor~rnal of Financial and Quantitative Analysis 31, 441-465. Fama, Eugene F., and Kenneth R. French, 1992, The cross-section of expected stock returns, Journal of Finance 47, 427-465. Fama, Eugene F,, and Kenneth R. French, 1993, Comn~on risk factors in the returns on stocks and bonds, Jor~r~zal
of Financial Economics 33, 3-56. Fama, Eugene F., and Kenneth R. French, 1995, Size and book-to-market factors in earnings and returns, Journal of Finance 50, 131-155. Fama, Eugene F., and Kenneth R. French, 1996, Multifactor explanations of asset pricing anom- alies, Joz~rnal of Filzance 51, 55-84. Ferson, Wayne E, and Campbell R. Harvey, 1993, The risk and predictability of international equity returns, Review of Financial Studies 6, 527-566.
Foster, F. Douglas, Tom Smith, and Robert E. Whaley, 1997, Assessing goodness-of-fit of asset pricing models: The distribution of the maximal RZ, Jour~zal of Finance 52, 591-607. Gibbons, Michael R., Stephen A. Ross, and Jay Shanken, 1989, A test of the efficiency of a given portfolio, Econometrics 57, 1121-1152.
Goetzmann, William N., and Phili~pe Jorion, 1996, A century of global stock markets, Working paper, Yale School of Management. Harvey, Campbell R., 1991, The world price of covariance risk, Journal of Finance 46, 111-155. Harvey, Campbell R., 1995, Predictable risk and returns in emerging markets, Review of Fi-
nancial Studies 8, 773-816. Haugen, Robert, 1995, The New Finance: The Case against Efficient 144arlzets (Prentice Hall, Englewood Cliffs, N. J.).
Heston, Steven L., K. Geert Rouwenhorst, and Roberto E. Wessels, 1995, The structure of international stock returns and the integration of capital markets, Jot~r~zalof Empirical Finance 2, 173-197.
Korajczyk, Robert A,, and Claude J. Viallet, 1989, An empirical investigation of international asset pricing, Review of Financial Studies 2, 553-585. Lakonishok, Josef, Andrei Shleifer, and Robert W. Vishny, 1994, Contrarian investment, extrap- olation, and risk, Journal of Finance 49, 1541-1578. Lintner, John, 1965, The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics 47, 13-37.
Value versus Growth: The International Evidence
MacKinlay, A. Craig, 1995, Multifactor models do not explain deviations from the CAPM, Journal of Financial Economics 38, 3-28. Merton, Robert C., 1973, An intertemporal capital asset pricing model, Econometrica 41, 867-
887. Ross, Stephen A,, 1976, The arbitrage theory of capital asset pricing, Journccl of Economic Theory 13, 341-360. Sharpe, William F., 1964, Capital asset prices: A theory of market equilibrium under conditions of risk, Joz~rnal of Finance 19, 425--42.
Solnik, Bruno, 1974, The international pricing of risk: An empirical investigation of world cap- ital structure, Journal of Finance 29, 48-54.