``The ®rst shall be last''. Size and value strategy
premia at the London Stock Exchange
Michele Bagella
*, Leonardo Becchetti, Andrea Carpentieri
Dipartimento di Economia e Istituzioni, Facoltadi Economia, UniversitaTor Vergata, Roma,Via di Tor Vergata snc, 00133 Roma, Italy
Abstract
The paper analyses the determinants of cross-sectional stock returns at the London Stock Exchange in the last 26 years. It ®nds that portfolio strategies based on low values of earning per share (EPS), market to book value (MTBV), market value (MV) and return on equity (ROE) signi®cantly outperform the index. Do size and value (S&V) strategy premia disappear when risk-adjusted or do they reveal gains from trading against noise, near rational, liquidity or ``weak-hearted'' traders? We ®nd that the sig-ni®cance of cross-sectional determinants of these strategies is not absorbed by ex post betas. They are not riskier in terms of monthly return standard deviations, covariation with GDP growth and their premia do not disappear when survivorship bias is taken into account. Portfolio mean monthly returns (MMRs), regressed on several risk factors in 3-CAPM models, con®rm that S&V strategy premia persist when risk adjusted. Empirical results also mark the dierence between ROE and MTBV portfolios, on the one side, and MV and EPS portfolios, on the other. Descriptive statistics on prefor-mation and postforprefor-mation returns, average balance sheet values and preforprefor-mation standard deviations clearly show that ROE and MTBV portfolios have a common ®-nancial distress factor and are then more exposed to systematic risk.Ó2000 Elsevier
Science B.V. All rights reserved.
JEL classi®cation:G11
Keywords:Size and value strategies; CAPM models; Cross-sectional stock returns www.elsevier.com/locate/econbase
*Corresponding author. Tel.: +39-6-2025-361; fax: +39-6-2020-500.
E-mail address:Bagella@uniroma2.it (M. Bagella).
0378-4266/00/$ - see front matterÓ2000 Elsevier Science B.V. All rights reserved.
One of the basic principles of statistical prediction, which is also one of the least intuitive, is that the extremeness of predictions must be moderated by considerations of predictability. ¼the prediction should
be regressive; that is, it should fall between class average and the val-ue that best represents oneÕs impression of the case at hand. The lower the predictability the closer the prediction should be to class average. Intuitive predictions are often nonregressive: people often make ex-treme predictions on the basis of information whose reliability and predictive validity are known to be low (Kahneman and Tversky, 1982).
1. Introduction
1.1. The literature on S&V strategies
UK). Haugen and Baker (1996) evaluate 12 return factors in ®ve indus-trialised countries.1
This branch of empirical research has recently become the battle®eld of advocates and opponents of the Ecient Market Hypothesis (EMH). Fama and French (1995, 1996) defend the EMH by testing an alternative three-factor model where excess returns from size and value (S&V) strategies are explained by the traditional excess returns on broad market portfolio, the return dier-ential between two portfolios respectively containing high and low book-to-market stocks and the return dierential between a small ®rm and a large ®rm portfolio. This econometric speci®cation captures the idea that average stock returns are in¯uenced by three risk factors which are proxied by the above described explanatory variables. This hypothesis is not rejected by data as excess returns, corrected by the three risk factors (intercepts of the three-variable regression), are shown to be not signi®cantly dierent from zero. A strong criticism of Fama±French (FF) results comes from Daniel and Titman (1997) who claim the rejection of the three-factor model, showing that return premia on small size and high book to market ratios disappear once ®rm characteristics are taken into account.2
Interpretations of empirical ®ndings on S&V strategies then focus on three main explanations. The ®rst is consistent with the Ecient Market Hypothesis and argues that size and book to market variables proxy for multidimensional risk factors not captured by marketbs (Fama and French, 1992, 1993, 1995, 1996). The second explanation maintains that return premia on small size and low market to book stocks are too high and that they may be partly explained by the irrational behaviour of noise- (De Long et al., 1990), near rational-(Wang, 1993), liquidity- or ``weakhearted''- traders overreacting to shocks and
1Emerging stock markets, which until recently have been characterised by high segmentation
and relatively low correlation with global risk factors, are another interesting ®eld to test whether S&V premia are related to a common behaviour of investors across all ®nancial markets. Results which support the existence of these premia come from Fama and French (1998); Claessens et al. (1995) and Rouwenhorst (1998) showing that lower liquidity is not sucient to explain the outperformance of small versus large, and low market to book versus high market to book stocks in these markets.
2
extrapolating past stock price behaviour (Lakonishok et al., 1994, from now on LSV).3 The third explanation (Fama and French, 1992, 1993, 1995, 1996) considers that premia from S&V strategies may be a spurious eect for at least two reasons: (i) they may be the result of data-snooping and the relevance of book to market and size factors may be sample-speci®c; (ii) they may be af-fected by a survivorship-bias given that the Compustat database gives excessive weight to distressed ®rms that survived than to distressed ®rms that ®eld.
1.2. The aim of the paper
Which of the three above mentioned interpretations best ®ts results on re-turns from S&V strategies at the London Stock Exchange? Are empirical regularities on determinants of cross-sectional variations in average stock re-turns country-speci®c or do they extend also to European stock markets such as the LSE ? This paper explores the issue showing that UK stocks have similar patterns but also some distinctive features when compared to US stocks.
The empirical analysis on 541 stocks between July 1971 and June 1997 shows (Section 2) that S&V portfolio strategies based on earning per share (EPS), return on equity (ROE), MVs and market to book values (MTBVs) signi®cantly outperform the index in terms of 26-year average monthly returns. We try to discriminate between two alternative explanations for these premia,
the latent risk factor hypothesis, which would reconcile these anomalies with the EMH (Fama and French, 1992, 1995) and the LSV hypothesis, which implies that S&V strategies are not any riskier and that their premia are earned in transactions with irrational agents erroneously extrapolating market trends. We investigate (Section 3) the issue looking at dierent risk measures and ®nd that S&V strategies do not covariate more than other strategies with GDP, they are still signi®cantly more pro®table when corrected for their standard deviations, they are not explained by ex post systematic nondiversi®able risk or by latent risk factors. Empirical ®ndings also show a dierence between ROE and MTBV strategies, on the one side, and MV and EPS strategies, on the other side. There are at least four pieces of evidence suggesting that the former strategies bet on ®rms which are more ®nancially distressed and are then ®-nancially riskier. Firms included in lowest ROE and MTBV portfolios have on average far higher debt±equity ratios and ROE values than ®rms in lowest MV and EPS portfolios. MTBV and ROE preformation performance present at least one long period of negative cross-sectional mean returns leading to a cumulative four±®ve month loss of at least 10% prior to portfolio formation. This is an indication of the presence of a common distress factor and of an
3An alternative agency cost explanation suggests that fund managers choice of past winners may
overexposure to systematic risk which is also evidenced by a higher beta and by an overreaction to upturns and downturns after portfolio formation. On the contrary, EPS and MV portfolios have none of the above characteristics. Their preformation cross-sectional mean returns do not present any sign of ®nancial distress and their postformation performance evidences lower exposure to systematic risk.
The paper also investigates the impact of survivorship bias on these results. Empirical results are compared with the benchmark of the total sample buy-and hold portfolio which is 20% higher in terms of mean monthly returns (MMRs) than the Financial Times All Share Index Benchmark. In addition, a speci®c analysis on the universe of stocks delisted from the LSE shows that the share of delisted ®rms on which investors would have lost all their money and that belong to our successful portfolios is quite small. S&V strategies when corrected for risk of delisting and loss of shareholders capital still outperform stock market index and our total sample index.
Final conclusions and further directions for research are addressed in Section 4.
2. Premia from S&V strategies on the UK stock market
We select from Datastream a sample of 541 stocks listed on the London Stock Exchange for which we gather daily stock exchange prices, and other indicators such as the ratio of MV to book value, ROE, leverage (LEV), earnings per share, price earnings and pre-portfolio ranking betas.4
For all these stocks we collect data from 1970 to 1997. Every year we rank all stocks on ascending values of the selected indicator and we form 11 port-folios using all deciles and the ®rst ventile as breakpoints in the distribution of the selected indicator. For all indicators that include balance sheet values (price earning, EPS, MTBV, ROE and LEV) we use the end of December value in the yeart)1 to build portfolios and calculate average monthly stock
returns of the portfolios in the period running from July of the yeartto June of the yeart+ 1.5When we rank portfolios on size we use MV as a proxy and we consider the end-of-June value of the yeart. Pre-ranking betas are calcu-lated by using two-year monthly returns of stocks and of the Financial Times
4
MTBV is equal to the percentage value of (MV)/(equity capital and reserves minus total intangibles). LEV is equal to (subordinated debt plus total loan capital plus short-term (one-year) borrowings)/(total capital employed plus short-term (one-year) borrowings minus total intangibles minus future income tax bene®ts). ROE is equal to (net pro®t after tax, minority interests and preference dividends)/(equity capital and reserves minus intangibles plus total deferred tax).
5This lag is necessary to allow end-of-year balance sheet statistics to be fully known by investors.
All Share Index minus the risk-free interest rate, proxied by the monthly equivalent of the yield on the three month UK average bank deposit rates. The estimation period runs from June of the yeart)2 to June of thet. Tables 1
and 2 present descriptive features of the 11 equally weighted portfolios built on ranked values of the four selected indicators. Descriptive results from these tables show that the distribution of MMRs obtained from our 11 portfolios in the July 1971±June 1997 period has similar features to those found by FF (1992) in the US. The portfolio formed every year with the 5% lowest MTBV stocks (Table l) has a performance of 2.54% MMRs for the 26-year period, which is signi®cantly higher than 1.02% value which represents the return for the 26-year buy-and-hold strategy on the Financial Times All Share Index, and also higher than the 1.29 which is the MMR for the 26-year buy-and-hold strategy on our total sample portfolio.T-statistics indicate that fund managers following the two strongest S&V strategies (selection of the 5%, or of the 10%, stocks with lowest MTBVs) would have signi®cantly outperformed both these two passive strategies.6If we look at other portfolio characteristics we ®nd that, apart from the highest market to book portfolio, lower market to book portfolios earn higher returns and are composed of ®rms which also have lower returns on investments and are smaller in size. Stocks in the lower market to book portfolios behave quite similarly to LSV (1994)value stocks7
and the market seems to understand it. In fact, following LSV (1994) and Gordon and Shapiro (1956), a high price earning should indicate, holding constant discount rates and payout ratios, a high expected growth rate of earnings which is typical of value stocks. Portfolios containing stocks with extremely low MTBV and ROE values have, in fact, higher average price earnings. This implies that ®rms included in these portfolios are expected to grow more in the future. If the empirical ®ndings will demonstrate that S&V strategy premia persist even when risk adjusted, we should conclude from these price earnings that the market understood, but underestimated, the growth potential of these stocks.
MV portfolios (Table 1) provide a similar and even clearer ranking as the two smallest size strategies (0±5 and 0±10 portfolios) signi®cantly outperform
6
In absolute terms, MMRs are higher than those found by FF (1992) as 1963±1990 average for the US stock market on the top 10% book to market portfolio (1.92%) and presumably higher than the Lakonishok et al. (1994) and Brouwer et al. (1996) results (respectively, average yearly returns on the highest book to market portfolio of 17% in the US between 1968 and 1989 and of 14% in four European Stock Exchanges between 1983 and 1992).
7
Table 1
Mean monthly returns and economic fundamentals of portfolios formed on market-to-book values and market values (percent values, LSE: July 1971±June 1997)a
MTBV PE EPS LEV ROE MV MMR t 20±30 0.73 17.09 25.46 0.28 7.69 157.24 1.36 4.61 0.29 1.15 30±40 0.87 17.61 12.99 0.57 8.43 200.44 1.34 4.26 0.20 1.02 40±50 1.04 20.87 13.92 0.42 9.88 295.11 1.32 4.06 0.11 0.92 50±60 1.22 16.87 11.96 0.41 11.29 401.82 1.04 3.36
)1.05 0.06 60±70 1.45 14.61 19.18 0.43 12.30 364.46 1.17 3.60
)0.49 0.46 70±80 1.76 19.30 17.20 0.42 14.98 340.62 1.12 3.44
)0.72 0.31 80±90 2.30 18.74 50.67 0.41 17.00 444.26 0.97 2.94
)1.29 )0.15 90±100 7.01 44.15 20.36 0.87 23.11 698.15 0.97 2.85
)1.38 )0.15
MV portfolios
0±5 0.45 30.89 8.46 0.31 3.10 0.82 2.65 8.21 4.96 5.05 0±10 0.87 29.74 8.76 0.37 4.19 1.23 2.17 7.73 3.76 4.09 10±20 0.94 34.39 11.15 0.51 2.43 3.11 1.60 5.37 1.18 1.95 20±30 1.04 22.71 11.94 0.35 12.93 6.25 1.29 4.10
)0.01 0.86 30±40 1.11 18.22 25.22 0.39 9.92 11.53 1.30 4.13 0.02 0.89 40±50 1.55 19.14 18.48 0.40 10.97 20.87 1.18 3.70
)0.39 0.50 50±60 1.54 23.20 15.32 0.37 12.87 37.09 1.19 3.57
)0.35 0.51 60±70 1.54 15.78 26.54 0.40 13.06 71.37 1.20 3.34
)0.28 0.50 70±80 2.02 17.20 19.52 0.53 15.39 159.05 1.23 3.22
)0.18 0.55 80±90 2.23 17.56 40.47 0.51 13.18 411.32 1.13 2.79
)0.45 0.27 90±100 2.41 14.75 14.50 0.76 17.34 2239.26 0.99 2.73
)0.93 )0.08 aWe consider a dataset of 541 stocks listed in the UK stock exchange. For each of these stocks we gather balance
sheet and stock price data from July 1971 to June 1997. We select six variables which may help in stock selection: MTBV (market to book value); MV (market value), EPS (earnings per share), PE (price earnings), ROE (return on equity and LEV (leverage). Market to book value (MTBV) is equal to the percentage value of the ratio (market value)/(equity capital and reserves minus total intangibles). Leverage (LEV) is equal to (subordinated debt plus total loan capital plus short term year) borrowings)/(total capital employed plus short term (one-year) borrowings minus total intangibles minus future income tax bene®ts). ROE is equal to (net pro®t after tax, minority interests and preference dividends)/(equity capital and reserves minus intangibles plus total deferred tax). 11 Portfolios are formed according to ascending values of return on equity (ROE) and of earning per share (EPS) values using as breakpoints percentile values of this indicator (i.e. the ®rst portfolio includes stocks with the lowest ®ve percent return on equity values on all considered stocks). Portfolios are formed at the end of June of any yearton values that the ranking variable assumes at the end of December of yeart)1 (June of yeartfor MV portfolios) and are held for one year (until June of yeart+ 1). MMRs are mean monthly returns for each of the 11 portfolios calculated from July of periodtto June of periodt+ 1 and averaged across all portfolio for-mation years.
b
t(mean) is at-statistics testing whether mean monthly returns of the selected portfolio are signi®cantly dierent from zero.
ct(mean) is at-statistics testing whether mean monthly returns of the selected portfolio are signi®cantly dierent
from the July 1971±June 1997 total sample mean monthly returns (1.293).
dt(mean) at-statistics testing whether mean monthly returns of the selected portfolio are signi®cantly dierent
from the July 1971±June 1997 mean monthly returns of the Financial Times All Share Index (1.02). *MMRs are signi®cantly dierent from the considered mean at 99%.
**
Table 2
Mean monthly returns and economic fundamentals of portfolios formed on return on equity and on earning per share values (percent values, UK: July 1971±June 1997)a
MTBV PE EPS LEV ROE MV MMR t 10±20 0.95 52.57 10.58 0.46 3.53 110.40 1.47 4.66 0.62 1.43 20±30 0.91 21.48 9.39 0.39 6.29 174.07 1.33 4.21 0.13 0.98 30±40 1.20 16.94 12.25 0.44 8.33 301.85 1.46 4.43 0.60 1.33 40±50 1.39 20.94 11.49 0.41 10.17 284.19 1.20 3.85
)0.34 0.58 50±60 1.49 14.20 14.78 0.37 12.03 297.02 1.30 4.16 0.02 0.90 60±70 1.61 12.09 24.50 0.44 13.97 346.97 1.13 3.65
)0.56 0.36 70±80 2.09 15.37 18.65 0.37 16.34 402.05 1.16 3.56
)0.44 0.43 80±90 2.12 12.82 52.69 0.41 19.79 415.54 0.91 2.90
)1.29 )0.35 90±100 3.83 13.80 21.85 0.57 44.23 651.75 1.15 3.17
)0.45 0.36
EPS portfolios
0±5 1.69 137.26 0.46 0.49 7.52 26.80 2.21 6.44 3.02 3.47 0±10 1.44 89.36 0.80 0.50 9.05 36.00 2.03 6.05 2.48 3.01 10±20 1.43 20.01 2.04 0.35 10.77 63.54 1.76 5.63 1.64 2.37 20±30 1.54 17.68 3.21 0.41 12.36 104.93 1.54 4.84 0.85 1.63 30±40 1.86 17.42 4.43 0.36 12.96 130.87 1.33 4.25 0.13 0.99 40±50 1.60 14.01 5.85 0.42 13.35 258.05 1.33 4.41 0.14 1.03 50±60 1.88 16.98 7.52 0.42 13.06 350.92 1.28 4.08
)0.05 0.83 60±70 2.01 15.32 9.55 0.43 13.69 381.48 1.11 3.42
)0.63 0.28 70±80 1.45 12.46 12.30 0.60 15.77 549.34 0.89 2.74
)1.38 )0.40 80±90 1.51 11.80 16.64 0.38 12.23 661.70 0.73 2.28
)1.93 )0.91 90±100 1.99 12.08 136.29 0.31 16.31 725.10 0.65 2.10
)2.34 )1.19 aWe consider a dataset of 541 stocks listed in the UK stock exchange. For each of these stocks we gather balance
sheet and stock price data from July 1971 to June 1997. We select six variables which may help in stock selection: MTBV (market to book value); MV (market value), EPS (earnings per share), PE (price earnings), ROE (return on equity and LEV (leverage). Market to book value (MTBV) is equal to the percentage value of the ratio (market value)/(equity capital and reserves minus total intangibles). Leverage (LEV) is equal to (subordinated debt plus total loan capital plus short term year) borrowings)/(total capital employed plus short term (one-year) borrowings minus total intangibles minus future income tax bene®ts). ROE is equal to (net pro®t after tax, minority interests and preference dividends)/(equity capital and reserves minus intangibles plus total deferred tax). 11 Portfolios are formed according to ascending values of return on equity (ROE) and of earning per share (EPS) values using as breakpoints percentile values of this indicator (i.e. the ®rst portfolio includes stocks with the lowest 5% return on equity values on all considered stocks). Portfolios are formed at the end of June of any yearton values that the ranking variable assumes at the end of December of yeart)1 (June of yeartfor MV portfolios) and are held for one year (until June of yeart+ 1). MMRs are mean monthly returns for each of the 11 portfolios calculated from July of periodtto June of periodt+ 1 and averaged across all portfolio formation years.
b
t(mean) is at-statistics testing whether mean monthly returns of the selected portfolio are signi®cantly dierent from zero.
ct(mean) is at-statistics testing whether mean monthly returns of the selected portfolio are signi®cantly dierent
from the July 1971±June 1997 total sample buy-and-hold mean monthly returns (1.293).
dt(mean) is at-statistics testing whether mean monthly returns of the selected portfolio are signi®cantly dierent
from the July 1971±June 1997 mean monthly returns of the Financial Times All Share Index (1.02). *MMRs are signi®cantly dierent from the considered mean at 99%.
**
average total sample returns. Looking at other ®rm characteristics we ®nd that portfolios formed by stocks of poorly capitalised ®rms have relatively higher MMRs and price earnings, relatively lower ROE and LEV. Here again, small stocks seem to be value stocks in the LSV (1994) sense. Their earnings are expected to grow more than those of other stocks, yet consistent return premia from holding them in portfolios are earned for many years. An interesting dierence between MTBV and MV portfolios is that, in the second case, also LEV seems to be positively and monotonically related to portfolio size values. This may highlight the diculty of ®nancial markets to provide equity ®-nancing to small ®rms although expectations on the growth of their earnings are high.
ROE portfolios (Table 2) con®rm that value strategies earn large premia on index performance. Portfolio rankings seem to show that both LEV and MMRs are lower for groups of ®rms with higher returns on equity. Apart from the obvious relationship with LEV where, holding constant the ®rmÕs perfor-mance, a higher debt/equity ratio reduces returns on investment and increases returns on equity, no other variables exhibits a distribution which is correlated with descending values of the ranking variable. Price earnings and LEV are the two portfolio rankings which yield the lowest premia.8 The ®rst result is consistent with the surveyed literature on cross-sectional determinants of stock returns in the US where the impact of price earnings on future stock perfor-mance is overshadowed by that of size and book to MVs.
Descriptive evidence on EPS portfolio rankings (Table 2) seems to con®rm at ®rst glance that S&V strategies earn large return premia on buy-and-hold index strategies. Lower EPS portfolios have on average higher price earnings and then a higher ratio between expected future and current earnings.9
When we look at yearly values of the dierences between MMRs of 0±10 and 90±10 portfolios and the Financial Times All Share Index we can see that value strategies signi®cantly outperform glamour strategies even when we look at their relative success year by year. 0±10 size and MTBV portfolios have a lower performance than relative 90±100 portfolios only in four years and the 0±10 EPS portfolio only in two years out of 26.10
8
Estimates are omitted for lack of space and are available from the authors upon request.
9
We estimated also S&V premia for value weighted portfolios. Results yield, as expected, slightly lower MMRs than equally weighted portfolios given that large ®rms are generally less pro®table than small ®rms in our sample. S&V strategies are obviously more successful if we follow a dividend reinvestment strategy. Estimates with value weighted portfolios and with dividend reinvestment are omitted for lack of space and are available from the authors upon request.
10
Tables 1 and 2 show the success of S&V strategies, but are of no help in identifying the relative strength of the variables used building our portfolios. The correlation between most of them (positive of MTBV with ROE and MV; negative of EPS with price earnings, positive of EPS with ROE and MV; negative of ROE with LEV) indicates that a multivariate and econometric analysis is needed in order to identify the relative contributions of these factors to return premia.11
3. Do premia from S&V strategies disappear when risk adjusted?
The simple inspection of MMR rankings across dierent portfolios in Tables 1 and 2 seems to con®rm that S&V strategies are successful in the 1971± 1997 period. A general question arising from the inspection of these tables is why these return opportunities, which are partially incorporated in expecta-tions expressed by price earnings, are not rapidly exploited by market agents and why S&V strategy premia persist for so long (up to ®ve-year postformation portfolio returns). Do these strategies reveal a failure of the EMH hypothesis or do they re¯ect a latent relative risk factor? To answer this question we try to measure the exposure to dierent risk sources of S&V strategy premia: (i) MMRs standard deviation of individual stocks being part of S&V strategy portfolios; (ii) MMRs standard deviation of successful portfolios; (iii) covari-ation of S&V strategy returns with GDP growth; (iv) sensitivity of portfolio returns to downturns in total sample returns; (v) exposure to systematic non-diversi®able risk; (vi) exposure to additional risk factors (small ®rm risk factor and ®nancially distressed ®rm risk factor) which are usually not considered in single factor CAPM models; (vii) bankruptcy risk of ®rms selected in S&V portfolios.
11For a preliminary assessment of the marginal contribution of each factor we performed a
Only in the case of the lowest (0±5) ROE and of the lowest (0±5) MTBV strategies preliminary descriptive statistics present clear evidence that these portfolios include stocks of ®rms which are ®nancially distressed given that they have signi®cantly lower returns on equity and relatively higher bor-rowing ratios. If instead we look at the ®rst MV and at the ®rst EPS port-folios we do not ®nd evidence of higher ®nancial distress in spite of large MMR premia.12
To con®rm intuitions originating from descriptive statistics we propose an econometric estimate to identify the net impact of selected variables respec-tively on one year and two-year MMRs from buy-and-hold strategies. We adopt a mean group estimator approach by performing 25 cross-sectional es-timates for any observational year and then compute 25-year average coe-cient for each regressor and its time series standard error.13
As estimation period we consider one-year (or two-year) MMRs running from July of the year t to June of the year t+ 1 on the set of explanatory variables measured at the end of December of the yeart)1 (end of June of the
year t) when they do (do not) contain balance sheet data. To evaluate the impact of our variables, net of exposure to systematic risk, we propose two speci®cations (Tables 3a and b) in which we alternatively add preformation and postformation betas to the set of explanatory variables. Preformation betas are calculated on the basis of two-year monthly returns running from July t)2 to June t, while postformation betas run from July tto Junet+ 2. Results from the two dierent speci®cations show that the negative impact of EPS on MMRs is quite stable both with preformation and postformation betas. The negative impact of MTBV is weak in the speci®cation with pre-formation betas and is eliminated with postpre-formation betas. The relevance of the MTBV variable then seems to be much smaller than in the FF (1995) paper. This may be explained by the use of some variables (EPS and ROE) which are not considered in the FF experiment and by the fact that FF use postformation portfolio betas and not postformation betas of individual stocks. But our multicollinearity tests reject the hypothesis of a strong correlation between these two variables and book to MVs. It then seems that eective ex post
12
Returns on equity of the 0±5 MTBV and ROE portfolios are in fact negative and borrowing ratios are respectively 0.66% and 1.23%. Returns of equity of the 0±5 MV and EPS portfolios are small but positive and borrowing ratios are respectively 0.31% and 0.49%.
13
Table 3
Mean group estimators of determinants of cross-sectional variations in stock returnsa
Dep. variable MMR from 1-year buy-and-hold strategy
Dep. variable MMR from 2-year buy-and-hold strategy
Regressors Coecient t-statistics Regressors Coecient t-statistics
(a)Preformation betas used as regressors
C 1.57 23.31 C 1.38 21.93
LEV 0.12 2.74 LEV 0.13 1.97
ABETA )0.13 )1.86 ABETA )0.20 )2.92
(b)Postformation betas used as regressors
C 1.573 26.200 C 1.28 20.75
PE )0.024 0.198 PE )0.02 )2.75
PBETA 0.578 6.567 PBETA 0.48 6.21
a
We consider a dataset of 541 stocks listed in the UK stock exchange. For each of these stocks we gather balance sheet and stock price data from July 1971 to June 1997. We perform 26 cross-sectional estimates of mean monthly returns according to the two alternative speci®cations:
MMRta0a1ROEtÿ1a2EPStÿ1a3LEVtÿ1a4MVtÿ1a5MTBVtÿ1a6PEtÿ1
a7ABETAtÿ1e
or
MMRta0a1ROEtÿ1a2EPStÿ1a3LEVtÿ1a4MVtÿ1a5MTBVtÿ1a6PEtÿ1
a7PBETAtÿ1e;
exposure to systematic nondiversi®able risk of individual stocks kills the ex-planatory power of book to MVs.14
Another variable whose impact changes between the ®rst and the second speci®cation is MV. Size is negative and weakly signi®cant in the speci®cation with preformation betas and it becomes positive and highly signi®cant when we include postformation betas. Here again the MTBV argument applies. Small size seems here to be a proxy for ex post eective systematic nondiversi®able risk and not for an additional relative distress component when individual stock betas are considered. In our extended set of regressors, the two additional variables of EPS and ROE are those which most absorb the relative distress factor or, according to the alternative hypothesis, more clearly discriminate betweenvalueandglamourstocks. They are in fact a direct indication of ®rmsÕ
underperformance.
Premia from S&V strategies then seem not to be entirely explained by tra-ditional risk factors. The explanatory power of our regressors persists after controlling ex post systematic nondiversi®able risk. In addition, S&V strategies do not generally underperform the market in the most negative years when looking at their annual performances. If we consider risk as covariance with GDP or consumption growth, according to a consumption-CAPM approach (Breeden et al., 1989), we may see that betting on value stocks is often less risky than betting on glamour stocks. This because quarterly returns of value stock portfolios covariate less with GDP rates of growth than those of glamour stock portfolios (see Table 4). The only evidence that S&V strategies may be slightly riskier is that standard deviations of their portfolio MMRs are somewhat higher than those of glamour stock portfolios (the dierence between the top and the bottom portfolios ranges from 15% to 37% and is negative only in the case of MV portfolios). Portfolio diversi®cation though helps much more value than glamour strategies given that the top-bottom dierence among standard deviations is reduced when we pass from average individual stock standard deviations to portfolio average standard deviation. This is particularly evident for size portfolios (Table 4) where average standard deviation of individual stocks in the top value portfolio is far higher than that in the top glamour portfolio (+62.95%), while standard deviations of the top value (0±5) portfolio
14
A comparison of simple risk indicators for size and value strategiesa
0±10 11.33 5.99 1.75 12.49 4.96 0.17
40±50 9.22 5.74 1.82 10.06 5.64 1.65
90±100 9.03 6.00 2.69 8.25 6.42 1.38
Percent increase in S.D. between ®rst and last portfolio
39.51 10.72 62.95 )11.17
ROE portfolios EPS portfolios
0±5 14.69 6.88 1.67 12.38 6.06 1.32
0±10 13.25 6.22 1.58 12.02 5.93 1.37
40±50 9.52 5.50 2.02 9.39 5.32 0.86
90±100 10.05 6.40 3.29 9.15 5.47 2.19
Percent increase in S.D.
We consider a dataset of 541 stocks listed in the UK stock exchange. For each of these stocks we gather balance sheet and stock price data from July 1971 to June 1997. Market to book value (MTBV) is equal to the percentage value of the ratio (market value)/(equity capital and reserves minus total intangibles). Leverage (LEV) is equal to (subordinated debt plus total loan capital plus short term (one-year) borrowings)/(total capital employed plus short term (one-year) borrowings minus total intangibles minus future income tax bene®ts). ROE is equal to (net pro®t after tax, minority interests and preference dividends)/(equity capital and reserves minus intangibles plus total deferred tax). Portfolios are formed according to ascending values of the book value to market value ratio using percentile values of the same indicator as breakpoints (i.e. the ®rst portfolio includes stock with the highest ®ve percent book to market values on all sample stocks). Portfolios are formed at the end of June of any yearton values that the ranking variable assumes at the end of December of yeartÿ1 (June of yeartfor MV portfolios). For each portfolio we measure the average standard deviation of monthly returns for individual stocks included in the portfolio, the average S.D. of portfolio monthly returns and the covariance between portfolio monthly returns and GDP rate of growth.
are lower than that of the top glamour (90±100) portfolio ()11%). Our 0±10
value portfolios cannot be considered riskier even when we compare their standard deviations (6.22 for ROE, 5.93 for EPS, 5.99 for MTBV and 4.96 for MV portfolios) with that of a 25-year buy-and-hold strategy replicating the Financial Times All Share Index (6.33).
The inspection of the dynamics of cross-sectional averages of monthly re-turns for the same type of portfolios15 ®ve years after and before portfolio formation gives us further information on exposure to risk for value and glamour portfolios and marks the dierences between ROE and MTBV strategies, on one side, and MV and EPS strategies, on the other (Fig. 1a±d). Strategies based on the ®rst two factors seem relatively riskier than those based on the last two factors for two reasons. Firstly, there is clear evidence of preformation underperformance of the 0±10 portfolios with 2±3 series of consecutive negative cross-sectional averages of monthly returns before the formation year. Secondly, postformation returns of 0±10 portfolios seem to perform better. Their returns grow more in upturns of both value and glamour portfolios (when the entire stock market is presumably growing), while their performance is not worse than that of glamour stocks in downturns of both types of portfolios. These ®ndings are consistent with average balance sheet values of 0±10 MTBV and ROE portfolios (Tables 1 and 2) which reveal signs of ®nancial distress for these ®rms.
On the contrary, 0±10% MV and EPS portfolios do not present any evidence of preformation underperformance and have the nice feature of outperforming 90±100 portfolios after portfolio formation both in downturns and in upturns of cross-sectional mean returns calculated before and after the formation pe-riod (Fig. 1a±d). Downturn smoothing in these portfolios cuts almost all negative tails in cross-sectional averages of monthly returns which are instead very frequent in the 90±100 portfolios.
Fig. 1a±d also show the presence of a strong seasonality eect generated by high average January returns. The signi®cance of the January eect disappears when correction for exposure to systematic nondiversi®able risk is considered in FF 3-factor CAPM estimates.16
When inspecting preformation and postformation standard deviations of monthly returns in our factor portfolios we replicate the Daniel and Titman (1997) test on the alternative between common distress factors and common characteristics as determinants of S&V strategy premia. According to the
15
These are not time series averages of monthly returns for the same strategy across sample years as in Tables 1 and 2 but cross-sectional averages of monthly returns for the same type of portfolios (i.e. 0±10 size portfolio) formed in dierent years. All these are centered around the portfolio formation date.
163 and 4 factor CAPM estimates with the January dummy are not presented here and are
Fig. 1. (a) Preformation and postformation cross-sectional mean returns of MTBV 0±10 and 90±100 portfolios. (b) Preformation and postformation cross-sectional mean returns of 0±10 and 90±100 MV portfolios. (c) Preformation and postformation cross-sectional mean returns of 0±10 and 90±100 ROE portfolios. (d) Preformation and postformation cross-sectional mean returns of 0±10 and 90±100 EPS portfolios.
standard deviations is instead much ¯atter and seems more consistent with the common characteristics hypothesis.17
A test on the signi®cance of intercepts in speci®cations in which monthly returns are regressed on various risk factors is another fundamental step to check whether S&V strategies persist even when risk-adjusted. FF (1995) propose on this point the extension of the original one-factor CAPM to a three-factor CAPM where two additional risk factors, related to size and book to MVs, are added to the traditional speci®cation. The rationale for adopting a multifactor capital asset pricing model is that some risk factors are not cap-tured by sensitivity to stock market index. Sensitivity to stock market index measures exposure to macro economic or to political news and is likely to be higher for ``blue chips'' than for small ®rms. There are other risk factors though to which small ®rms or ®nancially distressed ®rms are particularly exposed. Shocks in asset values may, for instance, reduce the value of collateral aecting both solvency of ®nancially distressed ®rms and the capacity to obtain credit of small ®rms in a framework of asymmetric information (Bernanke and Gertler, 1987). Debt de¯ation negatively aects ®nancially distressed (low MTBV) ®rms more than others. Expectations of liquidity squeezes, in econo-mies in which the Kashyap et al. (1993) conditions for the existence of a credit view may apply, could generate negative eects on the price and quantity of credit available to ®nancially distressed ®rms, to ®rms with low earnings per share (therefore with low self-®nancing capacity) and to small ®rms which are more likely to be victims of ®nancial constraints (Fazzari et al., 1988, Devereux and Schiantarelli 1989, Becchetti 1995, Schiantarelli and Georgoutsos, 1990, Gilchrist and Himmelberg, 1995).
Fama and French (1995) demonstrate that intercept coecients of 3-CAPM regressions are not signi®cantly dierent from zero and argue that this result proves that returns premia on their factor portfolios are explained by latent risk factors captured by the two additional regressors and not by a failure of market eciency. We estimate the 3-CAPM model18for the UK stock market for our 44 factor portfolios formed on ROE, EPS, MTBV and MV. Our
17
Results of the Daniel and Titman (1997) test are presented here for lack of space and are available from the authors upon request.
18
3-CAPM estimates show that on the UK stock market S&V strategy premia persist even when risk adjusted (Tables 5 and 6). In particular excess returns from the two lowest MV and MTBV strategies and from the three lowest EPS strategies are still signi®cantly positive when corrected for exposure to the three FF (1995) risk factors. The signi®cance of other balance sheet indicators suggests an estimate of 4-factor19 (MTBV, MV and EPS) CAPM models in which the signi®cance of the intercept for the above mentioned portfolios is not reduced.20
A further inspection of these results seems to con®rm that successful MV and EPS portfolios are relatively less risky than successful MTBV and ROE portfolios. Small ®rm portfolios are less exposed to systematic nondiversi®able risk than large ®rm portfolios. They have, as expected, large and signi®cant exposure to the size speci®c risk factor but their exposure to the poor capi-talisation speci®c risk factor is not signi®cant. MTBV portfolios are largely exposed to three distinct sources of risk: systematic nondiversi®able risk, size speci®c and MTBV speci®c risk factor. The same occurs for ROE portfolios, while EPS portfolios present an exposure to dierent risk factors which is very similar to that of MV portfolios.
The comparison between econometric results from mean group estimators (Tables 3a and b) and those from 3-CAPM estimates seems to con®rm that premia from holding low MV portfolios,but not those from holding individual small ®rm stocks, remain positive after risk adjustment. The impact of indi-vidual ®rm size is in fact absorbed by ex post betas when we use mean group estimators, while intercepts of low MV portfolios remain signi®cantly positive when corrected for the three risk factors in Tables 5 and 6. This ®nding,
19Orthogonal factors in 3-CAPM are estimated as in FF. To estimate them in 4-CAPM we
compute market to book (HML), size (SMB) and EPS risk factors, we divide the sample each year into two subgroups: the 50% largest ®rms (group B) and the 50% smallest ®rms (group S). These two subgroups are divided in turn into three subgroups containing respectively the largest 30% (group BH and SH), the mid 40% (group BM and SM) and the smallest 30% group BL and SL) MTBVs. Any of these subgroups is divided in two halves which contains 50% (l) lowest and 50% highest (h) EPS values. SMB is calculated, by using subgroup mean returns, as SHl
SMlSLlSHhSMhSLh=6 ÿ BHlBMlBLlBHhBMhBLh=6. HML is calculated as SLlBLlSLhBLh=4 ÿ SHlBHlSHhBHh=4. REPS is calculated as
BHlBMlBLlSHlSMlSLl=6 ÿ BHhBMhBLhSHhSMhSLh=6. Results on the 4-CAPM estimates are not presented here for lack of space and are available from the authors upon request.
20
Table 5
Risk adjustment of returns from size and value strategies with 3-CAPM FF (1995) model (GMM estimates)a
aWe consider a dataset of 541 stocks listed in the UK stock exchange. For each of these stocks we
gather balance sheet and stock price data from July 1971 to June 1997. 11 Portfolios are formed according to ascending values of market value (MV), market to book values (MTBV) using as breakpoints percentile values of these indicators (i.e. the ®rst portfolio includes stocks with the highest 5% earning per share values on all considered stocks). Market to book value (MTBV) is equal to the percentage value of the ratio (market value)/(equity capital and reserves minus total intangibles). Portfolios are formed in July ofany year ton values that the ranking variable assumes for the end of December of yeartÿ1 (June of yeartfor MV portfolios) and held for one year (until June of yeart+ 1). MMR are mean monthly returns for each of the 11 portfolios formed every year. The table reports coecients andt-tests of the following 3-CAPM regression:
RpkÿRf ab RmÿRf cSMBdHMLe;
whereRpkis the monthly return of portfoliop p1;. . .;11formed on factork,Rfis the monthly
return of the 3-month UK average deposit interest rate for the same period,Rmis the monthly
combined with the sharp reduction in MMR standard deviation that we obtain when switching from individual small ®rm stock to small ®rm portfolios (Table 4), suggests that gains from portfolio diversi®cation are crucial in determining the pro®tability of low MV strategies and that high liquidity requirements may represent serious entry costs preventing individuals from exploiting returns from these strategies.
A last fundamental objection to the existence of risk-adjusted excess returns from S&V strategies comes from thesurvivorship biasargument. All empirical studies on the US stock market admit the problem but do not provide a so-lution to it. FF (1992, 1995) recognise that back®lling of successful stock balance sheet data may have determined a virtuous selection of stock included in the Compustat database. An indirect con®rmation of the existence of this problem, also in our data, is given by the ®nding that the 26-year MMR of our total sample buy-and-hold portfolio (1.29%) is about 20% higher than that of the Financial Times All Share Index (1.02%).
By testing whether our strategies give an MMR which is signi®cantly higher than the ®rst benchmark, and not of the second one, we implicitly correct results for this type of survivorship bias.
This is not enough, though. We think that most of the past literature (with the exception of Clare et al., 1997) neglected a second serious aspect of the survivorship bias problem. Every year some ®rms go bankrupt, their stocks are then delisted and shareholders lose all their money. There is a possibility that a relatively larger share of these ®rms may belong to our successful S&V strategy portfolios given that we bet on small, poorly capitalised ®rms with low pre-formation earnings.21
We propose two approaches to tackle this issue: a sensitivity analysis and a research regarding the universe of delisted stocks. The sensitivity analysis measures the impact of the presence of some delisted bankrupt stocks in our successful portfolios. A simple calculation shows that if we assume that 1/25 of stocks selected in our 0±5 and 0±10 portfolios yield a 100% return, instead of the average portfolio return, the portfolio average yearly return is about 7% lower.
Table 5 (continued)
Equations are estimated with a GMM (Generalised Method of Moments) approach with Heter-oskedasticity and Autocorrelation Consistent Covariance Matrix. The BartlettÕs functional form of the kernel is used to weight the covariances in calculating the weighting matrix. Newey and WestÕs (1994) automatic bandwidth procedure is adopted to determine weights inside kernels for auto-covariances. The same regressors are used as instruments.
*
The coecient is signi®cantly dierent from zero at 99%.
**
The coecient is signi®cantly dierent from zero at 95%.
21In our empirical analysis we obviously do not select any of these ®rms, but in this way we
Table 6
Risk adjustment of returns from value strategies with 3-CAPM FF (1995) model (GMM esti-mates)a
We consider a dataset of 541 stocks listed in the UK stock exchange. For each of these stocks we gather balance sheet and stock price data from July 1971 to June 1997. 11 Portfolios are formed according to ascending values of earnings per share (EPS) and return on equity (ROE) using as breakpoints percentile values of these indicators (i.e. the ®rst portfolio includes stocks with the highest ®ve percent earning per share values on all considered stocks). ROE is equal to (net pro®t after tax, minority interests and preference dividends)/(equity capital and reserves minus intangibles plus total deferred tax). Portfolios are formed in July ofany year t on values that the ranking variable assumes for the end of December of yeartÿ1 and held for one year (until June of year t+ 1). MMR are mean monthly returns for each of the 11 portfolios formed every year. The table reports coecients and t-tests of the following 3-CAPM regression:
RpkÿRf ab RmÿRf cSMBdHMLe;
whereRpkis the monthly return of portfoliop p1;. . .;11formed on factork,Rfis the monthly
return of the 3-month UK average deposit interest rate for the same periodRmis the monthly
According to this hypothesis our 0±5 and 0±10 strategies on MTBV, MV and EPS portfolios still outperform the total sample average and also the stock market index. Is this hypothesis too severe or too indulgent? Are all other (non 0±5 or 0±10) portfolios completely unaected by consequences of stock de-listing? If we look at the overall phenomenon we ®nd more than 2500 stocks delisted from the London Stock Exchange in the last 30 years. Delisting may be good or bad news according to four possible stories. In the ®rst case (probably good news) the ®rm is part of a takeover or of a merger. In the second, the stock is suspended for some reasons but shareholders get back the value of their share (i.e. the majority shareholder may decide to go private and buy-back small shareholder equities to reduce dilution). In the last two cases de-listing is bad news since either the stock is suspended and its value is not reimbursed, or the ®rm goes bankrupt and its value goes down to zero. Based on information obtained from the London Stock Exchange we evaluated preformation balance sheet and size characteristics of delisted stocks of ®rms that did not merge, or were not part of successful acquisition from 1985 to 1997 (we gathered detailed information only for this subsample) to check how many of them fall in our (0±5 and 0±10) value portfolios. We then computed the likelihood of selecting one of these ®rms in our successful portfolios in any one of these 13 years. This probability is lower, or in line with our sensitivity analysis for MV and MTBV successful portfolios (1/25 and 1/33, respectively for the 0±5 and for the 0±10 MV portfolios and 1/25 for the 0±5 MTBV portfolio). Moreover, a case study from historical records indicates that about 80% of the stocks belonging to the subset of nonmergered ®rms which were delisted actually went bankrupt, while the remaining 20% were delisted for other reasons. This leads to a downward correction of no more than 5% per year for our successful portfolios, which is too severe if we consider that dead stocks which were takeover targets usually exhibit a signi®cant positive ab-normal return (Bradley et al., 1988).
4. Conclusions
There is a large branch of empirical literature which shows that medium-term investment strategies, which select stocks on the basis of fundamentals,
Table 6 (continued)
Equations are estimated with a GMM (Generalised Method of Moments) approach with Heter-oskedasticity and Autocorrelation Consistent Covariance Matrix. The BartlettÕs functional form of the kernel is used to weight the covariances in calculating the weighting matrix. Newey and WestÕs (1994) automatic bandwidth procedure is adopted to determine weights inside kernels for auto-covariances. The same regressors are used as instruments.
*
The coecient is signi®cantly dierent from zero at 99%.
**
yield substantial premia on total market returns. Who is ``responsible'' for these returns? Theoretical and empirical models which ineciently adjust stock return for risk? The EMH which is wrong as it does not take into account the presence on the market of liquidity, near rational, noise or weak-hearted traders? The databases used for empirical research purposes (Compustat, Datastream) which implicitly select successful ®rms and delete unsuccessful ones from their data records?
The paper addresses these issues and investigates the London Stock Ex-change. Its results are broken into two parts. In the ®rst part it shows the existence of a wide range of S&V strategies which would yield consistent premia in the London Stock Exchange over the last 26 years. Single or multi-year portfolio investment strategies which bet on stocks with low MV, MTBV, earnings per share and ROE systematically outperform the index.
In the second part, the paper investigates whether these abnormal returns disappear when risk adjusted. Dierent risk measures are taken into account: (i) standard deviation of MMRs for individual stocks being part of S&V strategy portfolios; (ii) standard deviation of MMRs for successful portfolios; (iii) covariation of S&V strategy returns with GDP growth; (iv) sensitivity of portfolio returns to downturns in total sample returns; (v) exposure to sys-tematic nondiversi®able risk; (vi) exposure to additional risk factors (small ®rm risk factor and ®nancially distressed ®rm risk factor) by using multi-factor CAPM models; (vii) bankruptcy risk of ®rms selected in successful portfolios.
Our empirical ®ndings seem to exclude that abnormal returns from S&V strategies can be entirely explained by a higher risk. Interestingly, MTBV and ROE portfolios appear much more exposed to risk than MV and EPS port-folios. For these last two strategies in particular, MMR standard deviation of low MV, low EPS stocks is lower than that of Financial Times All Share Index MMRs. Covariation with GDP growth is also lower than that of portfolios composed of higher MV and EPS stocks. Successful MV and EPS portfolios are relatively less exposed to systematic nondiversi®ble risk. Their returns do not disappear when corrected for additional and independent risk factors typically related to small and ®nancially distressed ®rms.
savers ®nd it dicult to justify the tracking of errors in the S&V strategy perfomance.
This leaves room for further theoretical and empirical research in several interesting directions. We live in a paradoxical world where more information is always available at lower costs, but (at the same time) costs related to processing, selecting and learning in continuous time are steadily increasing (Allen and Santomero, 1997). As a consequence of this asset management is increasingly being delegated by households to ®nancial intermediaries and the so-called market-oriented ®nancial systems are being increasingly intermedi-ated. Could delegation of investing decisions (from a pool of less informed households to rational investment fund managers) be accountable for some anomalies such as premia from S&V strategies? What are the consequences of these anomalies in the real economy? Does inadequate evaluation of value stock growth perspectives, due to short-term attitudes of fund managers, have price or quantity eects on the availability of external ®nance for these ®rms? Is the success of S&V strategies country speci®c and does it depend on institu-tional features of domestic ®nancial systems? A determinant of return reversal for small or ®nancially distressed ®rms may in fact be their probability of becoming takeover targets which, in turn, depends on the development of a market for corporate control.
Further research in these directions would better link empirical literature regarding S&V strategies to these relevant theoretical issues.
Acknowledgements
The paper is part of a joint research activity withFondazione Sichelgaita. We thank C.A.E. Goodhart, G. Marseguerra, A. Salvatore, A. Santomero, P.L. Scandizzo, G. Szego, the participants of the VI Tor Vergata Financial Con-ferenceof November 1997 and an anonymous referee for useful comments and suggestions. Though the paper is the result of joint eorts Section 1 may be attributed to M. Bagella, Section 3 to L. Becchetti, Sections 2 and 4 to A. Carpentieri. The usual disclaimer applies.
References
Allen, F.J., Santomero, A.M., 1997. The theory of ®nancial intermediation. Journal of Banking and Finance 21, 1461±1485.
Barber, B.M., Lyon, J.D., 1997. Firm size, book-to-market ratio and security returns: A holdout sample of ®nancial ®rms. Journal of Finance 52, 875±883.
Bernanke, B.S., Gertler, M., 1987. Financial Fragility and Economic Performance, Working Paper no. 2318. NBER, Cambridge, MA.
Black, F., 1972. Capital market equilibrium with restricted borrowing. Journal of Business 45, 444± 454.
Bradley, M., Desai, A., Kim, E.H., 1988. Synergistic gains from corporate acquisition and their division between the stockholders of target and acquiring ®rms. Journal of Financial Economics 21, 3±40.
Breeden, D.T., Gibbons, M.R., Litzenberger, R.H., 1989. Empirical tests of the consumption-oriented CAPM. Journal of Finance 44 (2), 231±262.
Brouwer, I., Van der Put, J., Veld, C., 1996. Contrarian investment strategies in a European context. Mimeo.
Campbell, J.Y., Lo, A.W., Mackinlay, A.C., 1997. The Econometrics of Financial Markets. Princeton University Press, Princeton, NJ.
Chan, K.C., Hamao, Y., Lakonishok, J., 1991. Fundamentals and stock returns in Japan. Journal of Finance 46, 1739±1789.
Claessens, S., Dasgupta, S., Glen, J., 1995. The cross section of stock returns: Evidence from emerging markets. World Bank Policy Research Paper no. 1505.
Clare, A.D., Smith, P.N., Thomas, S.H., 1997. UK stock returns and robust tests of mean variance eciency. Journal of Banking and Finance 21 (5), 641±660.
Daniel, K., Titman, S., 1997. Evidence on characteristics of cross-sectional variation in stock returns. Journal of Finance 52, 2±33.
De Bondt, W.F.M., Thaler, R.H., 1985. Does the stock market overreact? Journal of Finance 40, 793±808.
De Long, J.B., Shleifer, A., Summers, L., Waldmann, R.J., 1990. Noise trader risk in ®nancial markets. Journal of Political Economy 98, 701±738.
Devereaux, M., Schiantarelli, F., 1989. Investment, Financial Factors, and Cash Flow: Evidence from UK Panel Data. NBER Working, p. 3116.
Fama, E.F., French, K.R., 1992. The cross-section of expected stock returns. Journal of Finance 47, 427±465.
Fama, E.F., French, K.R., 1993. Common risk factors in the returns on stock and bonds. Journal of Financial Economics 33, 3±56.
Fama, E.F., French, K.R., 1995. Size and book-to-market factors in earnings and returns. Journal of Finance 50, 131±156.
Fama, E.F., French, K.R., 1996. Multifactor explanations of asset pricing anomalies. Journal of Finance 51, 55±84.
Fama, E.F., French, K.R., 1998. Value versus growth: The international evidence. Journal of Finance 53, 1975±1999.
Fazzari, S.M., Hubbard, G.R., Petersen, B.C., 1988. Financing Constraints and Corporate Investment. Brooking Papers on Economic Activity, pp. 141±195.
Gordon, M., Shapiro, E., 1956. Capital equipment analysis: The required rate of pro®t. Management Science 3, 102±110.
Hansen, L., 1982. Large sample properties of generalised methods of moments estimators. Econometrica 50, 1029±1054.
Hansen, L., Singleton, K., 1982. Generalised instrumental variables estimation in non-linear rational expectations models. Econometrica 50, 1269±1286.
Haugen, R.A., Baker, N.L., 1996. Commonality in the determinants of expected stock returns. Journal of Financial Economics 41, 401±439.
Heston, S.L., Rouwenhorst, K.G., Wessels, R.E., 1995. The structure of international stock returns and the integration of capital markets. Journal of Empirical Finance 2, 173±197.
Kahneman, D., Tversky, A., 1982. Intuitive prediction: Biases and corrective procedures. In: Kahneman, D., Slovic, P., Tversky, A. (Eds.), Judgement Under Uncertainty: Heuristics and Biases. Cambridge University Press, Cambridge, England.
Kashyap, A.K., Lamont, O.A., Stein, J.C., 1993. Credit conditions and the cyclical behaviour of inventories, Federal Reserve Bank of Chicago, Working Paper no. 7.
Lakonishok, J., Shleifer, A., Vishny, R.W., 1994. Contrarian investment, extrapolation and risk. Journal of Finance 49, 1541±1578.
Linter, J., 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.
Loughran, T., 1997. Book-to-market across ®rm size, exchange and seasonality: Is there an eect. Journal of Financial and Quantitative Analysis 32 (3), 249±268.
MacKinlay, C., Richardson, M., 1991. Using generalised method of moments to test mean± variance eciency. Journal of Finance 46 (2), 511±527.
Newey, W., West, K., 1994. Automatic lag selection in covariance matrix estimation. Review of Economic Studies 61 (4), 631±635.
Reinganum, M., 1990. Market microstructure and asset pricing: An empirical investigation of NYSE and NASDAQ securities. Journal of Financial Economics 28, 127±147.
Rosenberg, B., Reid, K., Lanstein, R., 1985. Persuasive evidence of market ineciency. Journal of Portfolio Management 11, 9±17.
Rouwenhorst, K.G., 1998. International momentum strategies. Journal of Finance 53, 267±284. Schiantarelli, F., Georgoutsos, D., 1990. Monopolistic competition and the Q theory of investment.
European Economic Review 34, 1061±1078.
Sharpe, W.F., 1964. Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance 19, 425±442.
Stattman, D., 1980. Book values and stock returns. The Chicago MBA: A Journal of Selected Papers 45, 25±45.
