*We are grateful to John Doukas, and an anonymous referee for helpful feedback. We would also like to thank seminar participants at the University of Regensburg for their help and suggestions.

Original Article

# The Alternative Three-Factor Model: An Alternative beyond US Markets?

Article first published online: 13 OCT 2011

DOI: 10.1111/j.1468-036X.2011.00628.x

© 2013 John Wiley & Sons Ltd

Additional Information

#### How to Cite

Walkshäusl, C. and Lobe, S. (2014), The Alternative Three-Factor Model: An Alternative beyond US Markets?. European Financial Management, 20: 33–70. doi: 10.1111/j.1468-036X.2011.00628.x

#### Publication History

- Issue published online: 10 DEC 2013
- Article first published online: 13 OCT 2011

- Abstract
- Article
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- Cited By

### Keywords:

- alternative three-factor model;
- classic three-factor model;
- international markets

### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Related Literature
- 3. Economic Framework
- 4. Data, Explanatory Variables, and Summary Statistics
- 5. Return Predictability
- 6. Explanatory Factors
- 7. Time-Series Factor Regression Tests
- 8. Robustness
- 9. Conclusions
- Appendix A
- Appendix B
- Appendix C
- References

We investigate the performance of the alternative three-factor model across markets. The important US evidence of Chen et al. (2010) in favour of the alternative model does not translate to a test setting using data from 40 non-US stock markets. The three-factor model of Fama and French provides persistently a better description of average returns. Our analysis is robust across developed and emerging markets, robust to alternative measures of investment and profitability, to seasonality effects, to size-segmented subsamples and subperiods, to various test assets, and to the two-stage cross-section regression approach to test for priced factors.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Related Literature
- 3. Economic Framework
- 4. Data, Explanatory Variables, and Summary Statistics
- 5. Return Predictability
- 6. Explanatory Factors
- 7. Time-Series Factor Regression Tests
- 8. Robustness
- 9. Conclusions
- Appendix A
- Appendix B
- Appendix C
- References

Fama and French (1992) find that size (ME) and book-to-market equity (B/M) contribute significantly to the explanation of the cross-section of average US returns provided by the market beta of the Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner (1965). Building on this insight, they turn the two anomalies into common factors that provide a parsimonious description of US stock returns. The three-factor model of Fama and French (1993) consisting of the market portfolio and mimicking factor portfolios related to size (SMB) and book-to-market equity (HML) has become by now the standard model in asset pricing (Subrahmanyam (2010)).

In their important work, Chen *et al*. (2010) propose a novel three-factor model capable of explaining several of the latest documented average-return anomalies (including momentum as the premier anomaly) which cause problems for the classic three-factor model. Their alternative factor model thus challenges the Fama-French model in asset pricing. Specifically, their model says that the expected return on a portfolio in excess of the risk-free rate is explained by the sensitivity of its return to three factors: the market excess return (MKT), the difference between the return on a portfolio of low investment-to-assets stocks and the return on a portfolio of high investment-to-assets stocks (DMI, disinvest minus invest), and the difference between the return on a portfolio of high earnings-to-assets stocks and the return on a portfolio of low earnings-to-assets stocks (PMU, profitable minus unprofitable). In analogous manner to Fama and French's (1996a) approach then, Chen *et al*. (2010) confront their model with testing portfolios formed on a wide range of recent anomaly variables (beside the traditional size-B/M, e.g., momentum, accruals, net stock issues, and asset growth) and compare its performance with the Fama-French model. Since their model captures most of the recent average-return anomalies left unexplained by the Fama-French model, they reject the classic model in favour of their alternative factor model.

Their insights have greatly enhanced our understanding of the impact of investment and profitability on asset pricing in the USA.1 However, since the performance of the alternative three-factor model in comparison to the classic three-factor model could be a chance result on the US market within the meaning of Lo and MacKinlay (1990), we independently examine a large international sample consisting of 40 individual non-US countries over a 27-year period between 1982 and 2009. Specifically, we test whether international returns, developed and emerging market returns, and country returns are better explained by the alternative factor model or the Fama-French model. As international markets provide fresh samples, our non-US investigation delivers a very useful out-of-sample test.

Previous research in this vein testing the return-predictability of variables in international markets, initially identified on the US market, includes Heston *et al*. (1999), and Amel-Zadeh (2011) for the size effect, Bauer *et al*. (2010) for the size and value effect, and Doukas, and McKnight (2005) for the momentum effect altogether in European countries, Capaul *et al*. (1993), Fama and French (1998), and Fama and French (2011) for the value premium in developed markets, and Rouwenhorst (1999) for an investigation of size, value, and momentum in emerging markets.

Furthermore, factor models are useful for many purposes like estimating the cost of equity capital for the valuation of cash flows, measuring mutual fund performance, and calculating abnormal returns within event studies. Therefore, our paper provides important insights for researchers and practitioners helping to make an informed decision whether to choose the classic or the alternative three-factor model in an international setting.

Our results are easily summarised. This paper uncovers that the alternative three-factor model notwithstanding its economic appeal has limitations in explaining international average returns and is therefore unlikely to become an international standard. The US evidence of Chen *et al*. (2010) in favour of the alternative model seems to be sample-specific. Our out-of-sample investigation does not support their story in an international context. In our powerful test setting using data from 40 non-US stock markets, accounting for two-thirds of the most recent world market capitalisation, the Fama-French model provides pervasively a better description of average returns.

However, we not only want to point out which issues are addressed in this paper, but also which issues are not addressed. First, while evaluating the performance of the popular Fama-French model versus its recent contestant, the alternative factor model, we purposely restrict our tests solely to these two models in their original version. We acknowledge that a vast literature (only a fraction of which cited below) exists on Fama-French style models in the USA and in international markets suggesting that there is still much room left to optimise the ability to explain the cross-section of average returns by adding factors, using new variable definitions or a new construction methodology (Pástor and Stambaugh (2003), Hoberg and Welch (2009), Cremers *et al*. (2010), Hirshleifer and Jiang (2010), Hirshleifer *et al*. (2011), Novy-Marx (2010), Fama and French (2011)). However, in favour of the infant and internationally (as well in emerging markets as in developed markets) succumbing alternative factor model we test out several variable definitions. Nevertheless, our success to equip the alternative factor model with a better competitive position has been very mild. Second, we do not seek to enter the debate on whether stocks are priced locally or globally in an integrated market (Griffin, 2002). Third, given our research question, we also do not intend to challenge the importance of the market factor, the efficacy of macroeconomic factor risks, the specific role of exchange rate risk (we mainly use US-dollar denominated returns, but also check whether our country-based inferences hold when using domestic returns), and do not seek to examine the changing nature of global markets.

Our approach is straightforward. In Section 2, we discuss the related literature. In Section 3, we assess the economic framework of the alternative factor model and the Fama-French model. Section 4 describes the international data used in our analysis and introduces the explanatory variables of the two competing models. Section 5 evaluates the joint roles of investment and profitability against size and book-to-market equity in the cross-section of international returns. In Section 6, we construct and study the related mimicking factor portfolios and employ them in Section 7 to evaluate the explanatory power of the two competing models in time-series factor regression tests. In Section 8, we perform a battery of robustness tests highlighting amongst other things that the results hold equally in emerging and developed markets. Finally, Section 9 concludes.

### 2. Related Literature

- Top of page
- Abstract
- 1. Introduction
- 2. Related Literature
- 3. Economic Framework
- 4. Data, Explanatory Variables, and Summary Statistics
- 5. Return Predictability
- 6. Explanatory Factors
- 7. Time-Series Factor Regression Tests
- 8. Robustness
- 9. Conclusions
- Appendix A
- Appendix B
- Appendix C
- References

Our study contributes to the international asset pricing literature. To the best of our knowledge, we are the first to compare the performance of the alternative factor model against the Fama-French model in an international setting.

Our paper is related to several areas of domestic US and international research. The literature prior to the asset pricing model of Chen *et al*. (2010) investigates the impact of an investment factor in traditional asset pricing models with the focus on explaining US anomalies. Xing (2008) shows that an investment factor, defined as the difference in returns between low investment stocks and high investment stocks, contains information similar to Fama and French's (1993) value factor (HML), and explains the value premium approximately as well as HML. Lyandres *et al*. (2008) document that adding such an investment factor into the Capital Asset Pricing Model (CAPM) and the Fama-French model helps to explain the underperformance following initial public offerings, seasoned equity offerings, and convertible bond offerings. In the same direction, Wu *et al*. (2010) find that an investment factor-augmented CAPM and Fama-French model substantially reduces abnormal returns from the accruals anomaly left unexplained by traditional variants of asset pricing models. Using a structural estimation model derived from the q-theory of investment, Liu *et al*. (2009) study the cross-section of expected stock returns in the USA. They find that the q-theory model outperforms traditional asset pricing models in explaining portfolios sorted by earnings surprises, book-to-market equity, and capital investment. While the evidence in Li and Zhang (2010) provides only weak support for the q-theory with investment frictions as an explanation for investment-related anomalies, Lam and Wei (2011) seem to overturn their disapproving conclusion employing a broader set of limits-to-arbitrage measures. Novy-Marx (2010) highlights the importance of a gross profitability factor.

Moreover, our study complements prior literature conducting international horse races of Fama-French style pricing models. Fama and French (1998) propose an international two-factor model that uses the global market portfolio and a global value factor based on book-to-market equity to explain returns. Testing its explanatory power against an international CAPM, they find that their two-factor model provides a better description of international and country returns. Building on this insight, Griffin (2002) examines whether international or country-specific versions of Fama and French's (1993) three-factor model provide a better description of country returns. His findings document that domestic versions of the three-factor model do a better job in explaining country returns than an international Fama-French model. We use country-specific versions to explain country returns, but do not intend to re-evaluate this issue.

Finally, other studies examining the relation between average returns and investment in international markets have emerged contemporaneously. Titman *et al*. (2010) and Watanabe *et al*. (2011) independently study investment effects in the cross-section of international returns from the anomalies perspective using the asset growth definition of Cooper *et al*. (2008) (an alternative measure of investment to Chen *et al*. (2010)). They document the existence of an international investment anomaly similar to the USA. However, they do not study the joint roles of investment and profitability in the cross-section of international returns or employ their findings in horse race tests between the alternative factor model and the Fama-French model in an international setting.

### 3. Economic Framework

- Top of page
- Abstract
- 1. Introduction
- 2. Related Literature
- 3. Economic Framework
- 4. Data, Explanatory Variables, and Summary Statistics
- 5. Return Predictability
- 6. Explanatory Factors
- 7. Time-Series Factor Regression Tests
- 8. Robustness
- 9. Conclusions
- Appendix A
- Appendix B
- Appendix C
- References

We typically assess a model based on the rigorousness of the theory behind and the ability of the model to explain the reality. When comparing the alternative three-factor model with the Fama-French model, we therefore have to start from their economic framework.

The classic three-factor model of Fama and French (1993) is at large a reaction to the empirical shortcomings of the Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner (1965) which has long shaped the way risk and return is evaluated by academics and practitioners. Though the one-factor model provides a theoretically elegant description of average returns, its empirical performance is fairly limited (see, e.g., the classic CAPM anomalies, Banz (1981), Basu (1983), DeBondt and Thaler (1985), Rosenberg *et al*. (1985), Bhandari (1988)).

The Fama and French (1993) model delivers in empirical tests a better description of average returns than the CAPM. However, SMB and HML are merely the incorporation of the observed size and B/M anomalies into asset pricing factors due to their return-predictive ability (see Fama and French (1992)). Therefore, SMB and HML lack an economic theory that governs the underlying asset pricing process (Barberis and Thaler, 2003). Though the model is ex-ante purely motivated from the data, two main economic interpretations of the Fama-French model can be distinguished in ex-post reflection: rational pricing and irrational pricing.2

Although the choice of their factors appears rather ad hoc, Fama and French (1993, 1996a, 2011) advocate a rational pricing story arguing that SMB and HML represent compensations for risk in the context of a multi-factor version of Merton's (1973) intertemporal capital asset pricing model (ICAPM) or Ross's (1976) arbitrage pricing theory (APT). The set of explanatory portfolios in the classic three-factor model may span the superior (but not optimal) ex-ante mean-variance-efficient tangency portfolio relative to the one-factor model.3 In support of the rational pricing argument, Fama and French (1995) find that size (SMB) and book-to-market equity (HML) reflect firm fundamentals in earnings.

In contrast to the risk-based interpretation, Lakonishok *et al*. (1994) suggest that the premium on HML does not arise from rational pricing as compensation for risk but is rather the result of mispricing in the sense that investors incorrectly extrapolate a firm's past earnings behaviour in the future. Moving down the same alley, Daniel and Titman (1997) document that it is the characteristics of small and value stocks rather than the factor loadings on SMB and HML which determine expected returns. However, this finding is not supported by Davis *et al*. (2000) in a longer sample period and therefore remains controversial.4 Thus, a sound economic fundament of the Fama-French model is pending even after almost twenty years of intensive research.

In contrast to the empirically-motivated Fama and French (1993) approach, Chen *et al*. (2010) derive their alternative pricing factors through the q-theory of investment ( Cochrane, 1991, 1996; Liu *et al*., 2009) which explains stock returns from the production perspective. The economic intuition behind their DMI and PMU factors is easily illustrated by the following characteristics-based expected-return equation:5

- (1)

Equation (1) shows that profitability and investment are the two fundamental drivers of expected returns in the investment-based asset pricing framework that links returns and firm characteristics. The expected return of a firm is the expected profitability divided by marginal cost of investment (which increases with investment). Thus, given expected profitability, the expected return decreases with increasing investment-to-assets, while, given investment-to-assets, firms with higher expected profitability should earn higher expected returns. Though Chen *et al*. (2010) motivate their additional pricing factors from the production side, they also include the traditional market factor from the consumption side. However, they remain silent on the underlying motivation. Fama and French (1996b) note that the inclusion of the market premium in their three-factor model is necessary to explain the substantial return difference between risk bearing assets (like stocks) and the risk-free rate. We assume a similar interpretation applies here as well.

While Chen *et al*. (2010) use the q-theory of investment as the economic intuition behind the alternative three-factor model, their model can also be motivated by fundamental valuation theory (following, e.g., Fama and French, 2006a).

In the dividend discount model, the firm's stock is worth the present value of expected dividends. Under clean surplus accounting, the dividend at time t can be formulated as equity earnings, E_{t}, minus retained earnings (reinvestments of earnings), RE_{t}. The present market value, M, of the firm's equity is then derived as

- (2)

where r is the required rate of return on expected dividends. Using fundamental accounting relationships equation (2) can be further formulated as

- (3)

where ROE_{t} is the return on stockholder's equity, and B is the book value of common equity. Similar to the investment-based asset pricing framework, Equation (3) grounded on valuation theory suggests that ceteris paribus a higher return on book equity, i.e., profitability, implies a higher expected return of the firm, while a rising change in book value of common equity, i.e., investment, implies lower expected returns.

Summing up, based on its sound economic framework, the alternative factor model has an advantage over the Fama-French model which struggles with the important critique of its ad hoc nature. In the following sections, we will assess whether the alternative three-factor model can transfer its strong economic standing also to empirical tests in international markets.

### 4. Data, Explanatory Variables, and Summary Statistics

- Top of page
- Abstract
- 1. Introduction
- 2. Related Literature
- 3. Economic Framework
- 4. Data, Explanatory Variables, and Summary Statistics
- 5. Return Predictability
- 6. Explanatory Factors
- 7. Time-Series Factor Regression Tests
- 8. Robustness
- 9. Conclusions
- Appendix A
- Appendix B
- Appendix C
- References

#### 4.1 Data

Using the premier source for multi-country data, DataStream International, we study in our non-US sample monthly total returns (that is, including dividends) from 40 individual countries.6 These data include surviving and non-surviving firms that appear on DataStream at any time in the sample period. Thus, no survivor bias is present in our analysis. All returns are denominated in US dollars and we calculate excess returns by subtracting the one-month US Treasury bill rate.7 Firm-level data are from WorldScope International. The sample period is July 1982 through December 2009 (henceforth 1982–2009), yielding 330 monthly observations. The start dates vary across countries due to the availability of data on DataStream. Although stock return data for some countries are available earlier than 1982, accounting information from WorldScope is not available for calendar years before 1980. Since the construction of the investment and profitability variables for the alternative factor model requires accounting data for two successive calendar years, we have to choose 1982 as the earliest possible start date for our study.

We restrict our data set to common stocks, which are listed on the major stock exchange(s) in each country.8 A cross-listed stock is included only in its home market.9 As common in empirical asset pricing studies, financial firms with Standard Industrial Classification (SIC) codes between 6000 and 6999 are excluded. In addition, we do not use firms with negative book equity throughout the paper. To reduce the impact of outliers, we winsorise all variables at the 0.5% and 99.5% percentile levels.10 This technique is in particular useful to filter out suspicious stock returns and thus ensures that our conclusions in this study are not driven by tiny or illiquid stocks.11 However, the screening procedures do not affect the paper's general findings.

In order to draw meaningful inferences, especially from the analysis of individual markets, we need a reasonable number of stocks. Therefore, we require each country to have at least thirty stocks in any month after the inclusion in the sample and a return history of at least five years. Taking into account these standards, our final sample contains more than 200,000 firm-year observations during the 1982–2009 time period.

Table 1 presents summary statistics for the resulting non-US sample. The table lists the countries included in our study along with the major exchange(s) from which the stocks are taken, the start year of returns, and further market characteristics. Japan represents the largest market in our sample, accounting on average for 1,433 firms and 24.2% of the total market capitalisation. The second largest market is the UK, which has an average of 924 firms and 10.4% of the total market capitalisation. The rest of the countries is typically smaller in terms of firms and total market capitalisation.

Country | Stock Exchange | Start Year | Firms | Weight (%) |
---|---|---|---|---|

Argentina | Buenos Aires | 1998 | 51 | 0.4 |

Australia | Australian | 1982 | 414 | 2.4 |

Austria | Vienna | 1994 | 55 | 0.5 |

Belgium | Brussels | 1992 | 72 | 0.9 |

Brazil | Sao Paulo | 1996 | 178 | 2.0 |

Canada | Toronto | 1982 | 381 | 3.8 |

Chile | Santiago | 1993 | 96 | 0.8 |

China | Hong Kong, Shanghai, Shenzen | 1997 | 95 | 0.3 |

Denmark | Copenhagen | 1989 | 104 | 0.7 |

Finland | Helsinki | 1995 | 100 | 1.4 |

France | Paris | 1982 | 369 | 6.8 |

Germany | Frankfurt | 1982 | 323 | 5.3 |

Greece | Athens | 1994 | 188 | 0.7 |

Hong Kong | Hong Kong | 1988 | 330 | 2.9 |

India | Bombay | 1994 | 377 | 3.1 |

Indonesia | Jakarta | 1993 | 152 | 0.6 |

Ireland | Dublin | 1990 | 37 | 0.4 |

Israel | Tel Aviv | 1998 | 52 | 0.6 |

Italy | Milan | 1982 | 122 | 2.2 |

Japan | Tokyo | 1982 | 1,433 | 24.2 |

Korea | Korea | 1990 | 370 | 2.6 |

Malaysia | Kuala Lumpur | 1986 | 309 | 1.1 |

Mexico | Mexico City | 1993 | 72 | 1.5 |

Netherlands | Amsterdam | 1989 | 119 | 2.8 |

New Zealand | New Zealand | 1995 | 64 | 0.3 |

Norway | Oslo | 1989 | 114 | 1.0 |

Pakistan | Karachi | 1994 | 62 | 0.2 |

Peru | Lima | 2001 | 49 | 0.2 |

Philippines | Manila | 1995 | 86 | 0.3 |

Portugal | Lisbon | 1990 | 48 | 0.4 |

Russia | Moscow | 2004 | 74 | 4.7 |

Singapore | Singapore | 1989 | 210 | 1.3 |

South Africa | Johannesburg | 1990 | 185 | 1.5 |

Spain | Madrid | 1989 | 92 | 2.8 |

Sweden | Stockholm | 1989 | 183 | 1.8 |

Switzerland | Zurich | 1989 | 141 | 2.5 |

Taiwan | Taiwan | 1994 | 413 | 3.5 |

Thailand | Thailand | 1993 | 242 | 0.7 |

Turkey | Istanbul | 1995 | 120 | 0.5 |

United Kingdom | London | 1982 | 924 | 10.4 |

International | 1982 | 7,332 | 100.0 |

#### 4.2 Explanatory variables

We follow Chen *et al*. (2010) and Fama and French (1993) in defining the explanatory variables for the two competing asset pricing models.12

Specifically, investment-to-assets (I/A, investment) is the annual change in gross property, plant, and equipment plus the annual change in inventories from t – 2 to t – 1 divided by total assets for t – 2. Earnings-to-assets (E/A, profitability) is income before extraordinary items in t – 1 divided by total assets for t – 2. Size (ME) is market equity (price times shares outstanding) at the end of June of year t. Book-to-market equity (B/M) is book value of common equity for the fiscal year ending in calendar year t – 1 divided by market equity at the end of December of t – 1.13

Table 2 presents summary statistics for the explanatory variables during the sample period 1982–2009. A typical firm in our international sample invests about 10% per annum of its last year's total assets and exhibits on average an earnings-to-assets ratio of 2.63% per annum. The average firm size is $851 million and the book-to-market ratio has a mean of 0.87. Further summary statistics for the considered variables at the country level are provided in Appendix B.

Variable | Mean | SD | 25th | Median | 75th |
---|---|---|---|---|---|

I/A | 9.93 | 24.25 | −0.85 | 6.32 | 15.23 |

E/A | 2.63 | 14.81 | 0.44 | 3.38 | 7.38 |

ME | 851 | 2,669 | 54 | 169 | 537 |

B/M | 0.87 | 0.83 | 0.38 | 0.64 | 1.06 |

#### 4.3 Deciles formed on explanatory variables

To obtain a first insight how international returns are related to the proposed explanatory variables investment and profitability (alternative factor model) in comparison to size and B/M (classic factor model), we examine whether portfolios formed on these variables produce wide spreads in average returns. This simple approach gives us a first impression which variables drive the common variation in international returns. We will also look at individual countries from developed and emerging markets a little bit later to gauge potential differences.

Table 3 summarises average monthly excess returns for deciles formed from sorts on investment, profitability, size, and book-to-market equity. Specifically, at the end of June of each year t (1982 to 2009), all stocks in the sample are allocated to ten portfolios based on the decile breakpoints for I/A, E/A, ME, and B/M. We then calculate monthly equal-weighted returns on the portfolios from July of year t to June of t + 1, and the portfolios are rebalanced in June of t + 1.14

Panel A: Portfolios formed on I/A | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Low | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | High | L − H | |

Average | 1.40 | 1.06 | 0.98 | 0.95 | 0.93 | 1.08 | 1.04 | 0.97 | 0.88 | 0.61 | 0.79 |

t-statistic | 4.18 | 3.25 | 3.25 | 3.26 | 3.26 | 3.72 | 3.59 | 3.35 | 2.96 | 1.86 | 4.07 |

Panel B: Portfolios formed on E/A | |||||||||||

Low | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | High | H − L | |

Average | 1.13 | 0.97 | 0.99 | 0.97 | 0.90 | 0.94 | 1.02 | 1.01 | 0.97 | 0.91 | −0.23 |

t-statistic | 3.12 | 2.69 | 3.00 | 3.25 | 3.26 | 3.46 | 3.83 | 3.77 | 3.56 | 3.20 | −1.22 |

Panel C: Portfolios formed on ME | |||||||||||

Low | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | High | L − H | |

Average | 1.99 | 1.27 | 1.13 | 0.92 | 0.85 | 0.73 | 0.77 | 0.71 | 0.76 | 0.70 | 1.29 |

t-statistic | 6.56 | 4.52 | 4.00 | 3.21 | 2.92 | 2.45 | 2.47 | 2.26 | 2.43 | 2.34 | 5.92 |

Panel D: Portfolios formed on B/M | |||||||||||

Low | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | High | H − L | |

Average | 0.34 | 0.57 | 0.73 | 0.79 | 0.93 | 0.95 | 0.97 | 1.22 | 1.30 | 2.01 | 1.67 |

t-statistic | 0.94 | 1.76 | 2.37 | 2.66 | 3.24 | 3.42 | 3.65 | 4.56 | 4.82 | 6.38 | 6.90 |

Our sorts in Table 3 produce strong spreads in international returns for I/A, size, and B/M. We find that low investment firms outperform high investment firms with a difference of 0.79% per month (t = 4.07). Small stocks achieve substantially higher returns than large stocks, indicating a difference of 1.29% per month (t = 5.92) between the two extreme deciles. Firms with high B/M ratios earn a premium of 1.67% per month (t = 6.90) over firms with low B/M ratios. These results are consistent with US findings (e.g., Fama and French (1992, 1993, 1996a), Titman *et al*. (2004), Cooper *et al*. (2008)) and international evidence (e.g., Heston *et al*. (1999), Fama and French (1998), Rouwenhorst (1999), Titman *et al*. (2010), Watanabe *et al*. (2011)). In contrast to the wide spread of average returns for the portfolios formed on I/A, size, and B/M, it seems that profitability does not account for much cross-sectional variation in international returns. The simple sorts on E/A show that profitable firms have not outperformed unprofitable firms during the 1982–2009 time period. The difference in returns between the top and bottom deciles is even negative, −0.23% per month, though not statistically significant (t = −1.22). The international data do not echo the US findings of Fama and French (2006a), and Wang and Yu (2010), but correspond to the US result in Fama and French (2008) who document that negative profitability is not associated with unusually lower average returns. Since the alternative factor model employs a similar zero-investment mimicking portfolio from long-short positions in high E/A stocks and low E/A stocks as one of its independent factors, this may be interpreted as a first weakness for the model's capability in explaining international stock returns.

### 5. Return Predictability

- Top of page
- Abstract
- 1. Introduction
- 2. Related Literature
- 3. Economic Framework
- 4. Data, Explanatory Variables, and Summary Statistics
- 5. Return Predictability
- 6. Explanatory Factors
- 7. Time-Series Factor Regression Tests
- 8. Robustness
- 9. Conclusions
- Appendix A
- Appendix B
- Appendix C
- References

It is straightforward to assume that variables producing large spreads in average returns are candidates for common return factors. However, an explanatory factor that may account for substantial return co-movement is not necessarily associated with a large spread in average returns, as Chan *et al*. (1998) note. Therefore, we consider cross-section regressions to examine systematically the ability of the variables to predict international returns. We use the approach of Fama and MacBeth (1973) to compare the joint explanatory power of the variables used in the alternative factor model of Chen *et al*. (2010) and the classic three-factor model of Fama and French (1993).

Table 4 shows average slopes and their t-statistics for two regressions: (a) the cross-section of stock returns on investment and profitability, and (b) returns on size and book-to-market equity. Starting in July 1982, we estimate the cross-section regressions monthly using explanatory variables updated on an annual basis (at the end of June) to predict monthly returns from July of year t to June of t + 1.15 As in Fama and French (1992), market equity for the size variable is measured at the end of June of t, whereas the other explanatory variables are for the fiscal year ending in calendar year t–1. The six-month (minimum) gap ensures that the accounting-based variables are known before the returns.

Country | Int | I/A | E/A | t(Int) | t(I/A) | t(E/A) |
---|---|---|---|---|---|---|

Panel A: Cross-Section Regressions on I/A and E/A | ||||||

International | 1.45 | −0.61 | −0.94 | 4.91 | −2.92 | −1.22 |

Argentina | 1.13 | −2.20 | −3.37 | 1.09 | −1.47 | −0.40 |

Australia | 1.48 | −0.81 | 1.49 | 3.62 | −2.86 | 1.31 |

Austria | 0.81 | 0.45 | 2.12 | 2.18 | 0.76 | 1.01 |

Belgium | 0.75 | −1.15 | 2.55 | 2.04 | −2.44 | 1.26 |

Brazil | 2.50 | −1.20 | 2.55 | 3.07 | −2.62 | 1.37 |

Canada | 1.50 | −0.12 | 0.35 | 4.62 | −0.48 | −0.44 |

Chile | 1.24 | 0.36 | −1.12 | 2.67 | 0.62 | −0.65 |

China | 2.18 | −0.01 | −5.29 | 2.04 | −0.01 | −1.53 |

Denmark | 1.05 | −0.39 | −1.56 | 3.09 | −0.82 | −0.91 |

Finland | 1.33 | −0.68 | 1.46 | 2.90 | −1.08 | 0.68 |

France | 1.63 | −1.27 | −0.28 | 4.81 | −2.78 | −0.20 |

Germany | 0.86 | −0.89 | 0.55 | 2.56 | −0.45 | 0.61 |

Greece | 1.40 | −0.22 | −2.46 | 1.63 | −0.45 | −1.20 |

Hong Kong | 1.62 | −0.38 | −1.49 | 2.88 | −1.19 | −1.29 |

India | 1.86 | −0.12 | −1.65 | 2.18 | −0.30 | −0.99 |

Indonesia | 1.59 | −1.37 | −0.49 | 1.51 | −2.24 | −0.20 |

Ireland | 0.97 | 1.07 | 0.08 | 2.04 | 1.01 | 0.04 |

Israel | 1.13 | 1.76 | −1.18 | 1.60 | 1.08 | −0.43 |

Italy | 1.01 | −0.12 | 2.09 | 2.53 | −0.28 | 1.09 |

Japan | 1.14 | −0.36 | −1.68 | 2.69 | −1.03 | −0.71 |

Korea | 1.27 | −0.10 | 1.03 | 1.53 | −0.19 | 0.22 |

Malaysia | 1.60 | −0.42 | −2.56 | 2.18 | −0.77 | −1.22 |

Mexico | 0.98 | 1.07 | 1.02 | 1.64 | 1.18 | 0.46 |

Netherlands | 0.70 | −0.47 | 4.27 | 1.89 | −1.55 | 3.89 |

New Zealand | 1.48 | −0.66 | −0.82 | 3.00 | −1.29 | −0.49 |

Norway | 1.39 | −0.53 | 2.01 | 3.03 | −0.96 | 1.26 |

Pakistan | 0.90 | −2.43 | 2.40 | 1.28 | −2.62 | 0.95 |

Peru | 3.03 | 1.09 | 2.79 | 4.83 | 0.53 | 1.00 |

Philippines | 0.99 | 0.65 | 0.34 | 1.31 | 0.78 | 0.17 |

Portugal | 0.83 | 0.43 | −1.03 | 1.87 | 0.75 | −0.33 |

Russia | 2.10 | 1.66 | −0.65 | 1.47 | 1.67 | −0.29 |

Singapore | 1.33 | −0.76 | 0.69 | 2.07 | −2.21 | 0.42 |

South Africa | 1.79 | −1.08 | −1.87 | 3.78 | −1.81 | −1.23 |

Spain | 0.96 | 0.16 | −0.71 | 2.33 | 0.45 | −0.45 |

Sweden | 1.03 | −1.07 | 2.95 | 2.24 | −2.48 | 1.61 |

Switzerland | 0.91 | −1.83 | 2.89 | 2.62 | −3.28 | 1.87 |

Taiwan | 0.88 | 0.45 | 1.14 | 1.16 | 0.82 | 0.50 |

Thailand | 1.09 | −0.13 | −1.25 | 1.52 | −0.24 | −0.72 |

Turkey | 2.42 | −0.54 | −0.68 | 1.95 | −0.92 | −0.49 |

United Kingdom | 1.29 | −0.91 | −1.09 | 3.89 | −5.44 | −1.17 |

Country | Int | ME | B/M | t(Int) | t(ME) | t(B/M) |

Panel B: Cross−Section Regressions on ME and B/M | ||||||

International | 2.20 | −0.12 | 0.40 | 6.81 | −3.64 | 5.19 |

Argentina | 0.76 | −0.02 | 0.45 | 0.74 | −0.15 | 1.52 |

Australia | 2.00 | −0.10 | 0.36 | 3.78 | −1.51 | 2.95 |

Austria | 0.54 | 0.09 | 0.59 | 1.14 | 1.19 | 2.91 |

Belgium | 0.47 | 0.09 | 0.16 | 1.05 | 1.28 | 0.91 |

Brazil | 2.12 | 0.02 | 0.79 | 2.79 | 0.17 | 5.37 |

Canada | 2.71 | −0.23 | 0.17 | 5.96 | −4.63 | 1.50 |

Chile | 0.92 | 0.07 | 0.31 | 2.36 | 0.90 | 2.34 |

China | 3.54 | −0.37 | 0.58 | 2.08 | −1.37 | 1.28 |

Denmark | 0.73 | 0.08 | 0.56 | 1.79 | 1.28 | 3.43 |

Finland | 1.34 | 0.00 | 0.19 | 2.70 | 0.05 | 0.85 |

France | 1.98 | −0.05 | 0.45 | 4.27 | −0.96 | 4.31 |

Germany | 0.93 | 0.05 | 0.43 | 2.54 | 1.25 | 4.55 |

Greece | 2.57 | −0.28 | 0.02 | 1.68 | −1.39 | 0.15 |

Hong Kong | 2.66 | −0.23 | 0.41 | 3.00 | −2.11 | 4.05 |

India | 2.78 | −0.27 | −0.07 | 2.63 | −2.49 | −0.42 |

Indonesia | 2.24 | −0.16 | 0.37 | 2.10 | −1.16 | 1.99 |

Ireland | 1.22 | −0.01 | 0.22 | 1.64 | −0.11 | 0.88 |

Israel | 0.61 | 0.12 | 0.16 | 0.54 | 0.76 | 0.50 |

Italy | 0.71 | 0.08 | 0.43 | 1.53 | 1.13 | 3.62 |

Japan | 2.07 | −0.12 | 0.36 | 3.03 | −1.67 | 3.65 |

Korea | 1.21 | −0.05 | 0.67 | 1.06 | −0.34 | 3.76 |

Malaysia | 2.43 | −0.15 | 0.53 | 2.07 | −1.15 | 4.02 |

Mexico | 0.32 | 0.27 | 0.59 | 0.52 | 2.74 | 2.47 |

Netherlands | 0.80 | 0.07 | 0.35 | 1.74 | 1.42 | 2.64 |

New Zealand | 1.45 | −0.01 | 0.47 | 2.15 | −0.14 | 2.59 |

Norway | 2.05 | −0.18 | 0.21 | 3.44 | −1.83 | 1.24 |

Pakistan | 1.00 | −0.06 | 0.14 | 1.64 | −0.34 | 0.42 |

Peru | 3.34 | −0.03 | 0.27 | 5.83 | −0.26 | 1.05 |

Philippines | 1.64 | −0.18 | 0.54 | 1.69 | −1.57 | 2.86 |

Portugal | 1.20 | −0.05 | 0.31 | 2.01 | −0.41 | 1.31 |

Russia | 3.30 | −0.14 | 0.14 | 1.64 | −0.73 | 0.36 |

Singapore | 1.96 | −0.12 | 0.38 | 1.97 | −1.11 | 2.55 |

South Africa | 2.91 | −0.27 | 0.37 | 5.68 | −3.70 | 2.17 |

Spain | 0.31 | 0.14 | 0.42 | 0.54 | 2.11 | 3.50 |

Sweden | 0.95 | 0.06 | 0.20 | 1.67 | 0.68 | 0.98 |

Switzerland | 0.75 | 0.06 | 0.36 | 1.95 | 1.29 | 3.28 |

Taiwan | 0.21 | 0.08 | 0.01 | 0.18 | 0.56 | 0.04 |

Thailand | 1.18 | −0.04 | 0.62 | 1.91 | −0.32 | 3.63 |

Turkey | 2.81 | −0.12 | 0.22 | 2.03 | −0.73 | 0.86 |

United Kingdom | 1.36 | 0.00 | 0.38 | 3.50 | −0.10 | 5.06 |

The cross-section regressions explaining average returns with the variables investment-to-assets and earnings-to-assets as used in the alternative factor model reveal certain shortcomings. Panel A of Table 4 shows that average international returns are reliably negatively associated with investment-to-assets (−0.61, t = −2.92), however, the coefficient for earnings-to-assets (−0.94, t = −1.22) is negative as well which is the opposite of what the alternative factor model states. Whatever the story, since it is not significant it seems to have no role in explaining the international cross-sectional variation in average returns during the 1982–2009 time period.16 These findings are confirmed in individual countries.

The average regression slope on investment is negative in the majority of individual countries and more than two standard errors from zero in ten countries. Among those countries that have significant I/A slopes, we find seven countries from 25 developed markets and three countries from 15 emerging markets in our sample.17 This documents that the variable investment-to-assets is somewhat present in developed and emerging countries. However, like the results on the international portfolio, the estimates of the country regressions do not provide much basis that profitability adds to the explanation of average returns in international markets. Except for the Netherlands, the average regression slopes on E/A are within two standard errors from zero and random in sign. Half of the slopes are positive, the other half is negative.

We are aware that the definition of earnings differs across countries from an accounting perspective mainly due to varying international standards. How do we address this issue? First, the Worldscope database standardises accounting data to make economically meaningful comparisons between countries possible.18 Second, Leuz *et al*. (2003) using the Worldscope database develop earnings management scores and find that the degree of earnings management disagrees significantly across countries. Hence, we check whether there is a relationship between earnings management and E/A from an economic perspective. The correlation between a country's earnings management score and E/A is low and insignificant. Further (untabulated) multiple-comparison tests show no differences between E/A clusters grouped by earnings management according to Leuz *et al*. (2003).19

As in related previous US work (e.g., Fama and French 1992), Panel B of Table 4 shows that the combination of size and the book-to-market ratio helps to shed light on international returns. Average returns are negatively related to size (−0.12, t = −3.64). Thus, small firms have higher average returns than big firms. Likewise, there is a strong positive relation between average returns and B/M. The average slope on B/M is 0.40 and more than five standard errors from zero. Thus, high book-to-market (value) firms are associated with higher average returns than low book-to-market (growth) firms.

The majority of individual countries exhibits a negative regression slope on size and thus confirms the results of the regression that uses all stocks across countries (international portfolio).20 Moreover, the country regressions highlight the importance of book-to-market equity in explaining the cross-section of non-US returns. The average B/M slope is positive in 39 of the 40 considered countries and more than two standard errors from zero in 22 countries. To be more specific, 15 countries are from 25 developed markets and seven are from 15 emerging markets. This documents that the variable B/M is present in developed as well as in emerging countries. Thus, the largest part of the cross-sectional variation in international returns is absorbed by book-to-market equity with a support from size.

The cross-section regression technique is useful in identifying variables for the description of average returns. However, given the fact that in a Fama-MacBeth regression each stock is treated equally, the economic substance of the results is not always easy to assess. Although the average coefficient slopes measure the effect of a typical firm, putting the same weight on a very small firm as on a very large firm could produce noise and thus could give rise to misleading inferences. To mitigate this concern, we construct value-weighted factor portfolios in the next section. Following a value-weighted approach is in the spirit of reducing variance given the fact that return variances and size are negatively related to each other. Additionally and what is more important, the use of value-weighted returns leads to more meaningful factor portfolios because they capture the return behaviour in a way that corresponds to realistic investment opportunities (see Fama and French, 1993).

### 6. Explanatory Factors

- Top of page
- Abstract
- 1. Introduction
- 2. Related Literature
- 3. Economic Framework
- 4. Data, Explanatory Variables, and Summary Statistics
- 5. Return Predictability
- 6. Explanatory Factors
- 7. Time-Series Factor Regression Tests
- 8. Robustness
- 9. Conclusions
- Appendix A
- Appendix B
- Appendix C
- References

We specify international and domestic versions of the alternative factor model and the classic factor model. Therefore, we construct related international return factors across countries and domestic versions for each country, where the market, investment, profitability, size, and value factors are formed in the corresponding national market. The formation date for the factor portfolios is in general June (international and domestic versions), except for countries with non-December fiscal year ends. In that case, the portfolios are formed analogously in September (Japan and India) respectively December (Australia, New Zealand, Pakistan, and South Africa). The six-month gap is consistent with Fama and French (1993).

*Market*. The market factor (MKT), used in both models, is the return on the value-weighted portfolio of all stocks across countries or within a country in excess of the one-month US Treasury bill rate.

*DMI and PMU*. The construction of the investment factor (DMI, disinvest minus invest) and the profitability factor (PMU, profitable minus unprofitable) follows Chen *et al*. (2010).21

We devise the investment factor DMI by forming six portfolios on size and investment-to-assets.22 Specifically, at the relevant portfolio formation date of each year t, we sort all stocks across countries (international version) or within a country (domestic version) into two size groups and three I/A groups.23 The size breakpoint for the international version is the 80th percentile of the aggregate market equity at the end of June. This is in line with the international works of Fama and French (2006b, 2011) to mitigate the effect that sorts across countries may be dominated by the plentiful but economically less important tiny stocks.24 At the country level, stocks with market equity below the median size at the formation date are small (S) and those above are big (B). We also assign stocks to disinvest (D), neutral (N), and invest (I) groups if their I/A is in the bottom 30%, middle 40%, or top 30% of the ranked values of I/A for the fiscal year ending in calendar year t–1. We form six portfolios from the intersections of the two size groups and three I/A groups. Monthly value-weighted returns on the six portfolios are calculated for the following twelve months (e.g., from July of year t to June of t + 1). Designed to mimic the common variation in returns related to I/A, the investment factor, DMI, is the simple average of the returns on the two disinvest (low I/A) portfolios (S/D and B/D) minus the simple average of the returns on the two invest (high I/A) portfolios (S/I and B/I).

The profitability factor PMU is construed in a similar way.25 At the relevant portfolio formation date each year t, we sort all stocks across countries (international version) or within a country (domestic version) into two size groups and three profitability groups. For the international version, we use the 80th size percentile of June market equity as the relevant size breakpoint. At the country level, stocks with market equity below the median size at the formation date are small (S) and those above are big (B). We also assign stocks to unprofitable (U), neutral (N), and profitable (P) groups if their E/A is in the bottom 30%, middle 40%, or top 30% of the ranked values of E/A for the fiscal year ending in calendar year t–1.26 We form six portfolios from the intersections of the two size groups and three E/A groups. Monthly value-weighted returns on the six portfolios are calculated for the following twelve months (e.g., from July of year t to June of t+1). Designed to mimic the common variation in returns related to E/A, the profitability factor, PMU, is the simple average of the returns on the two profitable (high E/A) portfolios (S/P and B/P) minus the simple average of the returns on the two unprofitable (low E/A) portfolios (S/U and B/U).

*SMB and HML*. Ensuring the methodological correctness of our explanatory factors, we follow the original approach of Fama and French (1993) suggesting a construction procedure for the factor portfolios in such a way that the HML factor is formed neutral with regard to the size effect in returns, and that the SMB factor is formed neutral in relation to the value effect.27

Specifically, at the relevant portfolio formation date each year t, all stocks across countries (international version) or within a country (domestic version) are allocated to two size groups based on market equity (stock price times shares outstanding) using the 80th size percentile (international version) respectively median size (domestic versions) as the relevant size breakpoint. We also break all stocks across countries or within a country in an independent sort into three book-to-market equity (B/M) groups based on the breakpoints for the low 30%, middle 40%, and high 30% of the ranked values of book-to-market equity for the fiscal year ending in calendar year t–1. We form six portfolios from the intersections of the two size and three B/M groups. Monthly value-weighted returns on the six portfolios are calculated for the following twelve months (e.g., from July of year t to June of t + 1). Designed to mimic the common variation in returns related to size, the SMB (small minus big) factor is the monthly difference, between the simple average of the returns on the three small-stock portfolios and the simple average of the returns on the three big-stock portfolios. Meant to mimic the common variation in returns related to B/M, the HML (high minus low) factor is the difference, each month, between the simple average of the returns on the two high-B/M portfolios and the average of the returns on the two low-B/M portfolios.

Table 5 summarises international premiums for the market, investment, profitability, size, and value factors. The average value of the international market premium for the sample period 1982–2009 is 0.66% per month (t = 2.35). In contrast to the market premium, the investment premium (DMI) in international returns is effectively zero (−0.07% per month, t = −0.38). Is this zero premium in conflict with the results of the cross-section regressions on investment-to-assets? The answer is no. Cross-section regressions weight each firm equally, whereas the value-weighted factor returns give more weight to larger firms. As a consequence, low capitalisation stocks seem to be influential in the observed international investment effect.28 The profitability factor (PMU) produces an average premium of 0.17% per month, but is just 0.76 standard errors from zero.

MKT | DMI | PMU | SMB | HML | |
---|---|---|---|---|---|

Average | 0.66 | −0.07 | 0.17 | 0.02 | 0.72 |

t-statistic | 2.35 | −0.38 | 0.76 | 0.22 | 3.96 |

The average international SMB return is 0.02% per month (t = 0.22). In contrast to the more favourable results from above, the size premium derived from SMB is effectively zero due in part to the value-weighting of returns, but mainly caused by the fact that SMB is formed neutral in relation to B/M. Without this control, a simple size factor formed as the return difference between two value-weighted portfolios of stocks below and above the 80th percentile of aggregate market equity would have produced an average premium of 0.15% per month (t = 1.24) during the same time period. However, a simple size premium that is not neutral with regard to B/M has the shortcoming that it partly reflects the value premium in returns.29 Finally, as in Fama and French (1998), we find that the value premium in international returns is particularly strong and larger than the US value premium.30 The average HML return for 1982 to 2009 is 0.72% per month and strongly significant with a t-statistic of 3.96. Our international size and value premiums are very much in line with the contemporary results (ex US) of Fama and French (2011). As a robustness check, we regress the DMI and PMU factors respectively on the common return factors of the Fama-French model (MKT, SMB, and HML). However, this does not produce significant intercept estimates (untabulated results). Thus, DMI and PMU do not contain additional information about expected returns beyond the common return factors in the ex-US sample.31

Figure 1 shows further that country premiums are consistent with international premiums. The market premium is positive in all countries except the Philippines. Though the investment factor is positive in more than half of the individual countries, the average premium on DMI is more than two standard errors from zero in only four of the 40 countries (in particular, Germany, South Africa, Sweden, and the United Kingdom). Similar to the investment factor, the country premiums on PMU are positive in the majority of individual countries. However, only the PMU factors of Israel and Sweden exhibit a positive premium that is more than two standard errors from zero. Thus, the country premiums on DMI and PMU reaffirm the weak evidence for the importance of investment and profitability in explaining international returns.

Similar to the international SMB premium, the size premium in country returns measured by SMB is noticeably weaker not only in terms of statistical significance, but also in terms of magnitude. In fact, the average premium across countries is close to zero. Canada and Peru have significantly positive SMB returns, while Denmark and Sweden have significantly negative SMB returns. In contrast, based on the positive premiums for the HML factor, high B/M firms have outperformed low B/M firms in 39 of the 40 countries. Of these 39 countries, we find 21 displaying a value premium that is more than two standard errors from zero (16 from developed markets and five from emerging markets). The significant premiums range from 0.54% per month (t = 2.11) in the Netherlands to 1.49% per month (t = 2.32) in China.

### 7. Time-Series Factor Regression Tests

- Top of page
- Abstract
- 1. Introduction
- 2. Related Literature
- 3. Economic Framework
- 4. Data, Explanatory Variables, and Summary Statistics
- 5. Return Predictability
- 6. Explanatory Factors
- 7. Time-Series Factor Regression Tests
- 8. Robustness
- 9. Conclusions
- Appendix A
- Appendix B
- Appendix C
- References

Which of the two models can describe average returns in international markets better? The acid test of an asset pricing model is whether it can explain differences in average returns. We examine the explanatory power of the two competing asset pricing models using the 25 Fama and French (1993) value-weighted size-B/M portfolios formed from the universe of international stocks.32

At the end of June of each year t, we allocate all stocks in the sample to five size groups based on the quintile breakpoints for June market equity. We also break all stocks in an independent sort into five book-to-market groups based on the quintile breakpoints for B/M for the fiscal year ending in calendar year t−1. The 25 portfolios are constructed from the intersections of the five size and five B/M groups. Monthly value-weighted returns on the portfolios are calculated from July of year t to June of t + 1, and the portfolios are rebalanced in June of t + 1.

To evaluate the performance of the two models on the test portfolios, we run the following time-series regressions:

- (4)

- (5)

In these regressions, R_{i} is the return on portfolio i, R_{f} is the risk-free rate (the one-month US Treasury bill rate), MKT is the market excess return (the return on the value-weighted international market portfolio in excess of the risk-free rate), DMI, PMU, SMB, and HML, are, respectively, the returns on the factor portfolios related to investment, profitability, size, and value, a_{i}, the estimated intercept, is the average return left unexplained by the model and e_{i} is the regression residual. Regression (1) describes the alternative three-factor model of Chen *et al*. (2010) and regression (1) is the three-factor model of Fama and French (1993).

Table 6 shows average excess returns on the 25 value-weighted size-B/M portfolios for the time period 1982–2009, along with regression intercepts of the three-factor asset pricing models of (4) and (5). If a model describes average returns well, the regression intercepts should be statistically indistinguishable from zero. For comparison purposes, we additionally provide results of the one-factor regression.

Low | 2 | 3 | 4 | High | H − L | Low | 2 | 3 | 4 | High | H − L | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | t(Mean) | |||||||||||

Panel A: Average Monthly Excess Returns | ||||||||||||

Small | 0.70 | 1.04 | 1.08 | 1.32 | 1.77 | 1.08 | 2.01 | 3.33 | 3.78 | 4.64 | 5.79 | 5.24 |

2 | 0.45 | 0.77 | 0.93 | 1.20 | 1.43 | 0.99 | 1.32 | 2.62 | 3.38 | 4.44 | 4.98 | 4.57 |

3 | 0.38 | 0.65 | 0.82 | 0.89 | 1.20 | 0.83 | 1.08 | 2.23 | 2.98 | 3.36 | 4.11 | 3.52 |

4 | 0.27 | 0.64 | 0.82 | 0.88 | 1.19 | 0.92 | 0.79 | 2.04 | 2.81 | 3.21 | 3.89 | 3.97 |

Big | 0.39 | 0.59 | 0.84 | 0.88 | 1.31 | 0.92 | 1.26 | 1.95 | 2.90 | 3.37 | 4.18 | 3.75 |

a | t(a) | |||||||||||

Panel B: Alternative Three-Factor Model | ||||||||||||

Small | 0.01 | 0.39 | 0.47 | 0.73 | 1.16 | 1.14 | 0.05 | 1.68 | 2.08 | 3.12 | 4.44 | 4.20 |

2 | −0.27 | 0.12 | 0.33 | 0.61 | 0.84 | 1.11 | −1.30 | 0.74 | 1.98 | 3.18 | 3.87 | 4.08 |

3 | −0.37 | 0.03 | 0.21 | 0.34 | 0.60 | 0.97 | −2.14 | 0.21 | 1.70 | 2.02 | 2.83 | 3.52 |

4 | −0.48 | −0.02 | 0.21 | 0.30 | 0.57 | 1.05 | −3.68 | −0.20 | 1.70 | 1.99 | 2.97 | 4.52 |

Big | −0.31 | −0.07 | 0.25 | 0.29 | 0.60 | 0.91 | −2.99 | −1.14 | 2.79 | 2.64 | 3.40 | 3.53 |

Avg. |a| = 0.38, Avg. R^{2} = 0.74, GRS = 3.08, p(GRS) = 0.000 | ||||||||||||

Panel B: Classic Three-Factor Model | ||||||||||||

Small | −0.03 | 0.24 | 0.25 | 0.44 | 0.71 | 0.73 | −0.09 | 1.12 | 1.29 | 2.62 | 4.31 | 2.85 |

2 | −0.13 | 0.06 | 0.11 | 0.23 | 0.31 | 0.44 | −0.62 | 0.48 | 0.84 | 2.65 | 3.07 | 1.98 |

3 | −0.07 | 0.04 | 0.04 | −0.06 | 0.00 | 0.07 | −0.64 | 0.48 | 0.65 | −0.86 | −0.02 | 0.52 |

4 | −0.18 | 0.04 | 0.06 | −0.12 | −0.09 | 0.09 | −2.20 | 0.46 | 0.71 | −1.55 | −1.18 | 0.85 |

Big | 0.05 | 0.02 | 0.10 | −0.14 | −0.04 | −0.09 | 0.87 | 0.46 | 1.01 | −1.94 | −0.36 | −0.77 |

Avg. |a| = 0.14, Avg. R^{2} = 0.89, GRS = 2.35, p(GRS) = 0.000 | ||||||||||||

Panel D: CAPM | ||||||||||||

Small | 0.10 | 0.47 | 0.56 | 0.82 | 1.25 | 1.15 | 0.36 | 2.02 | 2.40 | 3.55 | 4.83 | 4.31 |

2 | −0.21 | 0.18 | 0.38 | 0.68 | 0.91 | 1.12 | −1.02 | 1.05 | 2.25 | 3.48 | 4.22 | 4.17 |

3 | −0.36 | 0.03 | 0.23 | 0.36 | 0.65 | 1.01 | −2.18 | 0.23 | 1.81 | 2.10 | 3.05 | 3.78 |

4 | −0.48 | −0.06 | 0.18 | 0.31 | 0.61 | 1.09 | −3.76 | −0.49 | 1.43 | 2.03 | 3.16 | 4.73 |

Big | −0.31 | −0.11 | 0.20 | 0.33 | 0.71 | 1.02 | −3.14 | −1.67 | 2.29 | 3.00 | 3.77 | 3.88 |

Avg. |a| = 0.42, Avg. R^{2} = 0.73, GRS = 3.22, p(GRS) = 0.000 |

Similar to previous US work, average returns increase monotonically from lower (growth) to higher (value) B/M quintiles and small stocks tend to have higher returns than big stocks. The average H-L return spreads are economically and statistically substantial. They range from 0.83% to 1.08% per month and are all more than 3.52 standard errors from zero.

The results in Panel B of Table 6 show that the alternative factor model cannot explain the average returns on the 25 size-B/M portfolios. Similar to the CAPM regressions in Panel D, a large number of portfolio returns is left unexplained. We observe that the time-series regression of (4) produces 14 intercepts that are more than two standard errors from zero. The average absolute intercept is 0.38% per month. The F-test of Gibbons *et al*. (GRS, 1989) clearly rejects the hypothesis that the true intercepts are all zero (GRS = 3.08, p-value = 0.000). Summing up, in both, statistical and economic terms, the alternative three-factor model provides a poor description of international returns during the time period 1982–2009. This conclusion is reinforced by the regression intercepts on the H-L spread portfolios. Because of their diversification, the spread portfolios have the lowest variance among the 25 size-B/M portfolios. The H-L portfolios thus provide a powerful overall test of the model's explanatory power. The five H-L intercepts strongly reject the alternative factor model; all intercepts are largely similar to the CAPM regressions and more than 3.52 standard errors from zero.

In contrast, the estimates of the three-factor model of (5) in Panel C of Table 6 show that the Fama-French model does capture most of the variation in the average returns on the international 25 size-B/M portfolios. We find that only five out of the 25 estimated intercepts exhibit a t-statistic of more than two. The intercepts are consistently low with an average absolute value of 0.14% per month. Hence, the average of the 25 regression R^{2} is significantly larger with a value of 0.89, compared to the average of 0.74 for the alternative factor model. In terms of the F-test (GRS = 2.35), the classic factor model improves greatly upon the alternative factor model. Nevertheless, the joint test that all intercepts are zero is rejected at the 0.000 level.33 Regarding the H-L spread portfolios, the model does a good job on the pricing of the set. Compared to the estimates of the CAPM and alternative model regressions, the magnitude of the intercepts is now significantly smaller. Only the smallest spread portfolio produces an estimate more than two standard errors from zero, the remaining portfolios have intercepts close to zero.

Lewellen *et al*. (2010) argue that asset pricing tests focusing on explaining size-B/M portfolios can be misleading because apparently strong explanatory power (in terms of R^{2}) provides only weak support for a model. We allay this concern by focusing on the intercept estimates from the time-series factor regressions as the benchmark criterion for model evaluation. Furthermore, we also confront the asset pricing models with portfolios sorted on other variables, as suggested by Lewellen *et al*. (2010) in robustness tests in the following section (8.4.).

### 8. Robustness

- Top of page
- Abstract
- 1. Introduction
- 2. Related Literature
- 3. Economic Framework
- 4. Data, Explanatory Variables, and Summary Statistics
- 5. Return Predictability
- 6. Explanatory Factors
- 7. Time-Series Factor Regression Tests
- 8. Robustness
- 9. Conclusions
- Appendix A
- Appendix B
- Appendix C
- References

In this section, subjecting our results to a battery of various tests we check the robustness of our inference that the classic model provides a better description of average returns in international markets than the alternative factor model. We first examine the sensitivity of the results presented above with respect to developed and emerging markets. Then, we explore alternative measures of investment and profitability. Cross-section split-sample regressions follow analysing the return-predictive ability of the explanatory variables for different subsamples and subperiods. We further test the explanatory power of the competing asset pricing models on six different test assets formed from the universe of international stocks. Finally, we evaluate whether DMI and PMU are important determinants of average returns in the presence of the Fama-French factors.

#### 8.1 Developed and emerging markets

The reader might conjecture that the analysis based on the international portfolio is potentially problematic. First, this paper uses data from 40 countries including both developed and emerging markets. The stock markets in these countries exhibit a differing degree of segmentation and efficiency. Thus, it may seem bold to draw inferences from an international portfolio. Second, the investment and profitability factors are formed from firm level characteristics, which may vary dramatically across countries. The sorting based on the pooled international sample could potentially be misleading. For example, profitability E/A in developed countries is, on average, lower (with a mean of 1.51 and a median of 3.08) than profitability in emerging countries (with a mean of 6.01 and a median of 5.10). As a result, the most profitable firms in the developed countries may rank low in the international portfolio. To address this concern of the heterogeneity of international data further we go one step in between the international level and the country level, and analyse developed and emerging markets independent from each other.34

To this end, we repeat the previous analysis on the explanatory power of the two competing asset pricing models using the 25 Fama and French (1993) value-weighted size-B/M portfolios formed from the universe of stocks now from (a) developed markets and (b) emerging markets. In developed countries, the average premiums for the market, DMI, PMU, SMB, and HML factors per month are 0.63% (t = 2.29), −0.16% (t = −0.83), 0.20% (t = 0.91), 0.03% (t = 0.28), and 0.56% (t = 2.88), respectively. The construction of the explanatory factors follows the methodology described in Section 6 using the 80th percentile of June market equity as the relevant size breakpoint.

The results in Table 7, Panel A echo, unsurprisingly, those of Table 6. We spare the reader the results from the CAPM as these are similar to those of the alternative factor model again. The alternative factor model does poorly on all dimensions compared to the classic factor model: it leaves more portfolios unexplained, the average absolute intercept is higher, the average R^{2} is lower, the F-test of Gibbons *et al*. (1989) is higher, and all five H-L intercepts are economically and statistically significant. Panel B substantiates that the same interpretation holds for emerging countries, while the average premiums for the market, DMI, PMU, SMB, and HML factors per month are 0.41% (t = 1.10), 0.40% (t = 1.57), 0.04% (t = 0.14), −0.05% (t = −0.28), and 1.10% (t = 4.40), respectively. This robustness exercise demonstrates nicely that our main approach of looking at international returns is justified.

Low | 2 | 3 | 4 | High | H − L | Low | 2 | 3 | 4 | High | H − L | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Panel A: Developed Markets | ||||||||||||

Mean | t(Mean) | |||||||||||

Small | 0.62 | 1.08 | 1.00 | 1.31 | 1.67 | 1.06 | 1.75 | 3.41 | 3.41 | 4.55 | 5.37 | 4.98 |

2 | 0.42 | 0.75 | 0.89 | 1.12 | 1.26 | 0.84 | 1.19 | 2.57 | 3.17 | 4.18 | 4.64 | 3.57 |

3 | 0.32 | 0.60 | 0.76 | 0.74 | 0.98 | 0.67 | 0.89 | 1.97 | 2.67 | 2.74 | 3.59 | 2.64 |

4 | 0.30 | 0.67 | 0.76 | 0.80 | 1.06 | 0.77 | 0.86 | 2.06 | 2.56 | 2.90 | 3.76 | 3.07 |

Big | 0.39 | 0.58 | 0.81 | 0.80 | 1.08 | 0.69 | 1.23 | 1.92 | 2.82 | 3.13 | 3.76 | 2.83 |

a | t(a) | |||||||||||

Alternative Three-Factor Model | ||||||||||||

Small | −0.05 | 0.46 | 0.41 | 0.72 | 1.07 | 1.13 | −0.18 | 1.72 | 1.63 | 2.90 | 3.71 | 4.05 |

2 | −0.28 | 0.13 | 0.32 | 0.58 | 0.74 | 1.02 | −1.13 | 0.75 | 1.74 | 2.93 | 3.45 | 3.57 |

3 | −0.38 | 0.01 | 0.17 | 0.24 | 0.48 | 0.85 | −1.94 | 0.06 | 1.29 | 1.37 | 2.24 | 2.95 |

4 | −0.41 | 0.03 | 0.20 | 0.27 | 0.56 | 0.96 | −2.90 | 0.26 | 1.51 | 1.68 | 2.73 | 3.81 |

Big | −0.30 | −0.07 | 0.25 | 0.22 | 0.44 | 0.74 | −2.72 | −1.17 | 2.85 | 2.14 | 2.78 | 3.02 |

Avg. |a| = 0.35, Avg. R^{2} = 0.72, GRS = 3.07, p(GRS) = 0.000 | ||||||||||||

Classic Three-Factor Model | ||||||||||||

Small | 0.03 | 0.40 | 0.27 | 0.57 | 0.83 | 0.81 | 0.09 | 1.69 | 1.24 | 2.84 | 3.70 | 3.07 |

2 | −0.07 | 0.11 | 0.14 | 0.26 | 0.34 | 0.41 | −0.30 | 0.81 | 1.04 | 2.59 | 3.02 | 1.69 |

3 | −0.15 | 0.01 | 0.00 | −0.17 | −0.04 | 0.11 | −1.35 | 0.14 | 0.02 | −2.14 | −0.51 | 0.85 |

4 | −0.17 | 0.07 | 0.00 | −0.16 | −0.02 | 0.15 | −2.21 | 1.00 | −0.01 | −2.11 | −0.22 | 1.45 |

Big | 0.02 | −0.01 | 0.11 | −0.09 | −0.03 | −0.05 | 0.34 | −0.13 | 1.29 | −1.38 | −0.24 | −0.44 |

Avg. |a| = 0.16, Avg. R^{2} = 0.87, GRS = 2.80, p(GRS) = 0.000 | ||||||||||||

Panel B: Emerging Markets | ||||||||||||

Mean | t(Mean) | |||||||||||

Small | 0.91 | 1.15 | 1.20 | 0.80 | 1.85 | 0.94 | 1.58 | 2.25 | 2.40 | 1.89 | 3.94 | 1.97 |

2 | 0.29 | 0.87 | 0.97 | 1.23 | 1.56 | 1.27 | 0.58 | 1.96 | 2.26 | 2.86 | 3.54 | 3.29 |

3 | 0.56 | 0.45 | 0.76 | 0.99 | 1.52 | 0.95 | 1.31 | 1.13 | 1.82 | 2.29 | 3.19 | 2.57 |

4 | 0.40 | 0.76 | 0.76 | 0.95 | 1.69 | 1.28 | 1.00 | 1.86 | 1.89 | 2.17 | 3.18 | 3.36 |

Big | 0.28 | 0.63 | 0.83 | 1.38 | 1.68 | 1.40 | 0.66 | 1.53 | 1.93 | 2.82 | 3.25 | 3.41 |

a | t(a) | |||||||||||

Alternative Three-Factor Model | ||||||||||||

Small | 0.08 | 0.39 | 0.53 | 0.20 | 1.09 | 1.01 | 0.18 | 1.06 | 1.47 | 0.64 | 3.18 | 2.17 |

2 | −0.46 | 0.24 | 0.28 | 0.58 | 0.86 | 1.32 | −1.56 | 0.86 | 1.19 | 2.00 | 3.24 | 3.95 |

3 | −0.12 | −0.15 | 0.18 | 0.30 | 0.77 | 0.89 | −0.47 | −0.78 | 0.79 | 1.16 | 2.67 | 2.76 |

4 | −0.24 | 0.17 | 0.16 | 0.26 | 0.88 | 1.12 | −1.30 | 1.00 | 0.75 | 1.17 | 3.45 | 3.56 |

Big | −0.39 | −0.05 | 0.26 | 0.66 | 0.88 | 1.28 | −2.95 | −0.42 | 1.25 | 2.83 | 2.12 | 2.63 |

Avg. |a| = 0.41, Avg. R^{2} = 0.68, GRS = 3.43, p(GRS) = 0.000 | ||||||||||||

Classic Three-Factor Model | ||||||||||||

Small | 0.12 | 0.51 | 0.39 | −0.10 | 0.81 | 0.69 | 0.26 | 1.45 | 1.34 | −0.38 | 2.74 | 1.33 |

2 | −0.43 | 0.23 | 0.17 | 0.11 | 0.23 | 0.66 | −1.52 | 1.01 | 0.89 | 0.52 | 1.21 | 2.15 |

3 | 0.05 | −0.14 | 0.00 | −0.20 | −0.03 | −0.08 | 0.23 | −0.99 | 0.02 | −1.21 | −0.16 | −0.30 |

4 | 0.00 | 0.28 | 0.05 | −0.23 | −0.01 | −0.01 | −0.02 | 2.02 | 0.25 | −1.63 | −0.07 | −0.04 |

Big | −0.12 | 0.10 | 0.08 | 0.14 | 0.06 | 0.18 | −1.02 | 0.82 | 0.41 | 0.64 | 0.19 | 0.53 |

Avg. |a| = 0.18, Avg. R^{2} = 0.76, GRS= 2.22, p(GRS) = 0.001 |

#### 8.2 Variants of investment and profitability measures

For robustness, all previously reported tables are also estimated using alternative definitions of investment-to-assets and earnings-to-assets. For investment-to-assets, we make use of the more comprehensive measure of investment, in particular, asset growth. The variable is computed as the percentage change in total assets from fiscal year ending in calendar year t–2 to fiscal year ending in calendar year t–1 according to Cooper *et al*. (2008). We further try two different definitions of profitability. One is equity income before extraordinary items in t–1 divided by book equity for t–1 as in Fama and French (2006a). Another one is revenues minus cost of goods sold in t–1 divided by assets for t–1 as in Novy-Marx (2010). Without showing all the results in detail, it suffices to report that the underperformance of the alternative factor model in comparison to the Fama-French model is pervasive and thus independent from the use of specific measures for investment and profitability in ex-US markets.

#### 8.3 Further cross-section regression tests

Keim (1983) highlights the seasonal impact of January on the size effect. Similar, Loughran (1997) argues that the value premium is driven by a January seasonal pattern and limited to small stocks.35 To address these concerns documented on the US market, we examine our results across subsamples and subperiods to check whether these findings also exist in international markets.

Table 8 presents average cross-section regression slopes from two regressions: (a) the cross-section of stock returns on investment and profitability for the three-factor model of Chen *et al*. (2010), and (b) returns on size and book-to-market equity for the three-factor model of Fama and French (1993).

Int | I/A | E/A | Int | ME | B/M | |
---|---|---|---|---|---|---|

Panel A: Baseline Regressions | ||||||

Average | 1.45 | −0.61 | −0.94 | 2.20 | −0.12 | 0.40 |

t-statistic | 4.91 | −2.92 | −1.22 | 6.81 | −3.64 | 5.19 |

Panel B: Regressions Excluding January Returns | ||||||

Average | 1.34 | −0.49 | −0.36 | 1.91 | −0.09 | 0.39 |

t-statistic | 4.30 | −2.29 | −0.45 | 5.69 | −2.46 | 4.70 |

Panel C: Size-Segmented Subsample Regressions | ||||||

Big | ||||||

Average | 1.09 | −0.16 | 0.24 | 1.48 | −0.01 | 0.32 |

t-statistic | 3.24 | −0.53 | 0.13 | 2.50 | −0.20 | 3.10 |

Not Big | ||||||

Average | 1.53 | −0.64 | −0.99 | 2.60 | −0.23 | 0.40 |

t-statistic | 5.20 | −3.06 | −1.41 | 7.98 | −5.18 | 5.36 |

Panel D: Subperiod Regressions | ||||||

1982-1996 | ||||||

Average | 1.86 | −0.55 | −2.41 | 2.43 | −0.10 | 0.32 |

t-statistic | 4.79 | −1.77 | −1.71 | 6.15 | −1.87 | 2.65 |

1996-2009 | ||||||

Average | 1.03 | −0.68 | 0.57 | 1.96 | −0.15 | 0.49 |

t-statistic | 2.30 | −2.42 | 1.01 | 3.80 | −3.45 | 5.07 |

The message from the average cross-section regression slopes for the international portfolio in the sample period 1982–2009 (see Table 4, reproduced in Panel A of Table 8 as baseline regressions) reiterates that average returns are related negatively to size, positively to book-to-market equity, and negatively to investment. Profitability shows no statistically significant relation with average returns.

##### January seasonal effect

Panel B shows average slopes when January returns are removed from the sample (leaving 303 monthly observations). We observe that removing January returns weakens both coefficients and t-statistics of the explanatory variables to a certain degree, indicating that a January seasonal effect is also present in international markets. However, removing January returns does not render investment-to-assets, size, or book-to-market equity insignificant. Thus, the general inference is similar to the baseline regressions in Panel A.

##### Robustness across size

Cross-section regressions are likely dominated by low capitalisation stocks. To clarify whether our findings also hold for mega-cap firms that constitute the majority of stock market equity, but are few in numbers, we estimate in Panel C cross-section regressions for two strongly different size-segmented subsamples. Therefore, we sort all stocks in our sample at the end of June of each year from 1982 to 2009 into two size groups (Big and Not Big) using the market capitalisation breakpoint between the smallest 80% and the largest 20% of firms at the end of June.36 For perspective, there are on average 1,466 mega-cap firms (Big) versus about four times (5,866) as many smaller firms (Not Big), but the mega-caps account for about 88% of the sample's total market equity.

The rationale for the absent investment premium based on the international DMI factor is that investment-to-assets owes much of its explanatory power to low capitalisation stocks (−0.64, t = −3.06). Mega-caps produce no reliable relation between investment and average returns (−0.16, t = −0.53). Regarding further the explanatory power of earnings-to-assets, it is neither detectable among high capitalisation firms nor among low capitalisation firms.

Similar to the investment-to-assets results, the average size slope for mega-caps is effectively zero (−0.01, t = −0.20), while the average slope for all smaller stocks is −0.23 with a *t*-statistic of −5.18. Thus, low capitalisation stocks are influential in the size effect observed in tests using all international stocks. The relation between average returns and B/M is more reliable across size. We identify in both size groups economically and statistically strong average regression slopes for book-to-market equity. Thus, the return-predictive ability of B/M is robust regardless of firm size.

##### Robustness across time

In Panel D, the sample is split roughly in half. We estimate split-sample regressions for the earlier subperiod which covers July 1982 to June 1996 (168 months) and the latter subperiod which covers July 1996 to December 2009 (162 months).

We observe that the explanatory power of investment-to-assets is less strong in the first half of the sample period (−0.55, *t* = −1.77) than in the second half (−0.68, *t* = −2.42). Similar to the overall period, the subperiods do not provide much basis that earnings-to-assets presents a key variable in international asset pricing. The average slope for E/A is negative for the 1982–1996 period (−2.41, *t* = −1.71) and it is positive for the 1996–2009 period (0.57, *t* = 1.01), however not statistically significant. For small firms, the 1980–82 recession turned into an enduring earnings depression. Small firms did not participate in the economic boom of the middle and late 1980s. The poor earnings of small stocks remained at low levels until the beginning of the 1990s (see Fama and French (1995)). Since low capitalisation stocks are influential in cross-section regressions, this provides a passable story for the change in the sign of the slope on E/A between the two subperiods.

The relation between average returns and size is weaker in the 1982–1996 period. However, in contrast to size, the return-predictive power of book-to-market equity shows up reliably in both the 1982–1996 and the 1996–2009 subperiods. Hence, the results from the subperiod regressions reinforce the evidence that among the variables considered here, book-to-market equity is consistently the most powerful for explaining the cross-section of international stock returns.

#### 8.4 Further Portfolio tests

In their paper, Chen *et al*. (2010) further test the alternative three-factor model on several other value-weighted portfolios formed on anomaly variables known to produce patterns in average US returns, e.g., short-term past returns (Jegadeesh and Titman, 1993), accruals (Sloan, 1996), net stock issues (Pontiff and Woodgate, 2008), and asset growth (Cooper *et al*. 2008). In (untabulated) tests, we find that except for momentum, value-weighted portfolios formed on the before mentioned variables do not produce strong differences in international returns. In the size-segmented test portfolios anomalous returns are only present among low capitalisation stocks, but absent for big stocks. Since portfolios formed on these variables do not exhibit much variation in the cross-section of international returns, they do not represent the same challenge for asset pricing models as in the USA.37 This critique notwithstanding, we are able to report from untabulated results that except for momentum the alternative factor model performs persistently worse (in terms of absolute magnitude and significance of regression intercepts) than the Fama-French model. For momentum, the explanatory power of the two competing models is similar due to the fact that the Fama-French model has problems to explain the continuation of short-term returns (see Fama and French, 1996a). The international test setting (ex US) cannot confirm the US evidence of Chen *et al*. (2010) that the alternative factor model is able to outperform the Fama-French model here.

We further test the explanatory power of the competing asset pricing models on 25 value-weighted size-I/A and size-E/A portfolios. These portfolios are formed in the same way as the 25 size-B/M portfolios, except we use I/A or E/A rather than B/M as the second variable on which the portfolios are sorted.

Though the alternative factor model owns in this test the benefit that the size-I/A and size-E/A portfolios are correlated with the underlying explanatory factors DMI and PMU, the Fama-French model again provides a better description of average returns than the alternative factor model and thus ultimately supports the inference of Table 6 that the alternative three-factor model is internationally a poor asset pricing model. Without showing all the details, the key results are summarised as follows.

##### Portfolios formed on Size-I/A

The alternative factor model leaves 13 portfolios unexplained. The average absolute pricing error based on the intercept estimates is 0.34% per month and the model is rejected by the GRS test (3.35, p-value = 0.000). The Fama-French model captures instead most of the size-I/A patterns in average returns. Only four portfolios produce intercepts that are more than two standard errors from zero. The average absolute intercept is 0.16% per month and the GRS test statistic is 2.42 (p-value = 0.000).

##### Portfolios formed on Size-E/A

The time-series factor regression results are similar to the size-I/A portfolios. The alternative factor model produces nine significant intercepts on the size-E/A portfolios, the Fama-French model just six. The average absolute intercepts and GRS statistics are, respectively, 0.32% per month and 3.14 (p-value = 0.000) for the alternative factor model and 0.15% per month and 2.20 (p-value = 0.001) for the Fama-French model.

#### 8.5 Two-Stage Cross-Section Regression (2SCSR) Approach

Finally, to examine whether DMI and PMU are important determinants of international returns in the presence of the Fama-French factors, we employ the two-stage cross-sectional regression (2SCSR) approach as proposed in Cochrane (2005) for determining whether a potential factor is priced and thus adds to the explanation of the cross-section of average returns. As in Section 7, we make use of the 25 size-B/M portfolios as test assets due to their strong cross-sectional return dispersion.38 We proceed as follows. In the first stage, we run time-series regressions of the portfolio excess returns on the full set of explanatory factors, i.e., MKT, DMI, PMU, SMB, and HML to obtain the respective factor loadings (betas).39 In the second stage, we estimate a cross-section regression in which the dependent variable is the mean excess return (over the sample period) on the 25 size-B/M portfolios and the independent variables are the factor loadings from the first stage. Our main interest is whether the average coefficient slopes on the DMI and/or PMU factor loadings are significantly positive and thus important determinants of international returns in the presence of the Fama-French factors.

Table 9 presents the results from the 2SCSR approach.40 The message from the test is easily summarised. The SMB and HML betas (s and h) are positive and statistically significant and thus represent priced factors in international returns, while the loadings on DMI and PMU (d and p) are not.41 Therefore, the hypothesis that DMI and PMU contain additional information beyond SMB and HML is rejected and thus we conclude that they are not rewarding alternative factors in international asset pricing.

Int | b | d | p | s | h | R^{2} | |
---|---|---|---|---|---|---|---|

Average | 1.29 | −0.64 | 0.03 | 0.55 | 0.16 | 0.80 | 0.80 |

t-statistic | 1.85 | −0.98 | 0.03 | 1.34 | 2.58 | 8.23 |

### 9. Conclusions

- Top of page
- Abstract
- 1. Introduction
- 2. Related Literature
- 3. Economic Framework
- 4. Data, Explanatory Variables, and Summary Statistics
- 5. Return Predictability
- 6. Explanatory Factors
- 7. Time-Series Factor Regression Tests
- 8. Robustness
- 9. Conclusions
- Appendix A
- Appendix B
- Appendix C
- References

Motivated by the important Chen *et al*. (2010) US results, we examine the performance of the alternative factor model against the classic Fama-French model in a large sample of 40 non-US stock markets during the time period 1982–2009. Our tests contribute to the international asset pricing literature and provide a useful out-of-sample test of the empirical robustness of the alternative three-factor model.

Our findings in this paper suggest that the alternative three-factor model is internationally not a serious alternative to the Fama-French model. First, cross-section regressions which investigate the joint return predictability of the explanatory variables on which the pricing models are built, in particular investment and profitability versus size and B/M, produce evidence acting as a counterpoint to the validity of the alternative three-factor model outside the USA: profitability seems to have no role in explaining the international cross-sectional variation in average returns.

Second, studying directly the return factor portfolios related to investment (DMI), profitability (PMU), size (SMB), and book-to-market equity (HML) further deteriorates the likelihood that the alternative factor model is able to describe international stock returns. As expected, the premium on PMU is small and insignificant. However, the DMI premium is also close to zero due to the value-weighting in the factor portfolios. The rationale for this is that investment is only able to price low capitalisation stocks, but not big stocks which account for about 90% of total market equity. In all fairness, the size premium of the popular three-factor model is not strong either.

Third and finally, we evaluate the explanatory power of the competing asset pricing models in time-series factor regression tests using the return patterns of the 25 size-B/M portfolios formed from the universe of international stocks. The alternative factor model performs basically like the CAPM (due to the absent DMI and PMU premiums) and leaves a large number of portfolios unexplained. In contrast, similar to previous evidence, the Fama-French model does a good job in pricing the set of international size-B/M portfolios.

The evidence against the alternative factor model outside the USA is supported by the results within the 40 individual markets, is robust across developed and emerging markets, is robust to alternative measures of investment and profitability, seasonality effects, size-segmented subsamples and subperiods, various test assets, and the two-stage cross-section regression (2SCSR) approach to test for priced factors.

### Appendix A

- Top of page
- Abstract
- 1. Introduction
- 2. Related Literature
- 3. Economic Framework
- 4. Data, Explanatory Variables, and Summary Statistics
- 5. Return Predictability
- 6. Explanatory Factors
- 7. Time-Series Factor Regression Tests
- 8. Robustness
- 9. Conclusions
- Appendix A
- Appendix B
- Appendix C
- References

This table describes the DataStream/Worldscope variables used in this paper.

Variable | Description | Data Item |
---|---|---|

Assets | This is the firm's book value of total assets. | WC02999 |

Book-to-Market Equity | This is book value of common equity for the fiscal year ending in the preceding calendar year divided by market equity at the end of that year. | WC03501/WC08001 |

Income Before Extraordinary Items | This is the firm's net income before extraordinary items. | WC01551 |

Inventories | This represents tangible items or merchandise net of advances and obsolescence acquired for either (1) resale directly or (2) included in the production of finished goods manufactured for sale in the normal course of operation. | WC02101 |

Market Equity | This is the stock price multiplied by the number of shares outstanding. | MV |

Property, Plant And Equipment Gross | This represents tangible assets with an expected useful life of over one year which are expected to be used to produce goods for sale or for distribution of services. | WC02301 |

### Appendix B

- Top of page
- Abstract
- 1. Introduction
- 2. Related Literature
- 3. Economic Framework
- 4. Data, Explanatory Variables, and Summary Statistics
- 5. Return Predictability
- 6. Explanatory Factors
- 7. Time-Series Factor Regression Tests
- 8. Robustness
- 9. Conclusions
- Appendix A
- Appendix B
- Appendix C
- References

This table presents summary statistics for the explanatory variables at the country level.

I/A | E/A | ME | B/M | |||||
---|---|---|---|---|---|---|---|---|

Mean | Median | Mean | Median | Mean | Median | Mean | Median | |

Argentina | 3.95 | 0.86 | 2.94 | 2.79 | 694 | 92 | 1.60 | 1.31 |

Australia | 12.51 | 5.75 | −3.34 | 1.79 | 558 | 135 | 0.82 | 0.68 |

Austria | 9.96 | 6.66 | 1.03 | 3.26 | 746 | 157 | 0.80 | 0.67 |

Belgium | 8.48 | 5.23 | 2.87 | 3.55 | 923 | 124 | 0.73 | 0.62 |

Brazil | 6.80 | 3.08 | 3.09 | 3.58 | 860 | 178 | 1.86 | 1.37 |

Canada | 16.90 | 8.27 | −1.63 | 2.55 | 657 | 138 | 0.82 | 0.65 |

Chile | 11.61 | 9.54 | 6.96 | 6.10 | 733 | 197 | 1.01 | 0.79 |

China | 10.58 | 7.46 | 4.30 | 3.95 | 192 | 79 | 1.03 | 0.84 |

Denmark | 8.72 | 6.38 | 2.97 | 4.13 | 546 | 73 | 0.81 | 0.72 |

Finland | 9.96 | 6.60 | 5.49 | 5.86 | 1,066 | 147 | 0.69 | 0.61 |

France | 7.25 | 5.10 | 3.30 | 3.47 | 1,163 | 151 | 0.89 | 0.68 |

Germany | 9.97 | 7.90 | 0.93 | 2.57 | 1,136 | 174 | 0.65 | 0.56 |

Greece | 12.15 | 8.06 | 5.20 | 4.26 | 269 | 65 | 0.79 | 0.64 |

Hong Kong | 11.28 | 6.97 | 5.57 | 6.13 | 688 | 127 | 1.15 | 0.89 |

India | 12.29 | 7.56 | 8.41 | 6.93 | 505 | 90 | 1.15 | 0.71 |

Indonesia | 9.46 | 4.05 | 5.14 | 4.13 | 320 | 47 | 1.22 | 0.90 |

Ireland | 11.06 | 7.02 | 2.77 | 5.55 | 805 | 183 | 0.71 | 0.57 |

Israel | 6.07 | 3.65 | 3.63 | 2.93 | 899 | 246 | 0.80 | 0.66 |

Italy | 9.63 | 6.37 | 2.01 | 2.56 | 1,146 | 203 | 0.93 | 0.79 |

Japan | 7.25 | 6.27 | 2.26 | 1.99 | 1,319 | 395 | 0.73 | 0.65 |

Korea | 9.15 | 6.29 | 1.85 | 2.09 | 517 | 108 | 1.72 | 1.43 |

Malaysia | 9.08 | 5.00 | 5.42 | 4.81 | 360 | 145 | 0.91 | 0.78 |

Mexico | 8.19 | 6.98 | 4.98 | 5.38 | 1,545 | 382 | 1.20 | 0.78 |

Netherlands | 7.80 | 5.08 | 4.81 | 5.92 | 1,896 | 232 | 0.70 | 0.58 |

New Zealand | 10.17 | 6.46 | 1.34 | 6.32 | 358 | 81 | 0.73 | 0.62 |

Norway | 12.70 | 6.84 | −0.29 | 2.78 | 581 | 109 | 0.81 | 0.63 |

Pakistan | 8.12 | 4.15 | 8.70 | 7.81 | 218 | 75 | 1.10 | 0.83 |

Peru | 13.22 | 9.51 | 8.00 | 5.29 | 386 | 66 | 1.73 | 1.21 |

Philippines | 7.75 | 5.12 | 3.51 | 3.14 | 252 | 47 | 1.76 | 1.21 |

Portugal | 12.42 | 8.73 | 2.67 | 2.87 | 708 | 108 | 1.25 | 0.91 |

Russia | 19.12 | 14.10 | 9.70 | 6.22 | 4,786 | 913 | 1.37 | 0.90 |

Singapore | 10.96 | 6.54 | 5.95 | 4.98 | 542 | 152 | 0.89 | 0.76 |

South Africa | 8.47 | 4.35 | 8.11 | 8.24 | 691 | 168 | 0.93 | 0.62 |

Spain | 11.52 | 6.77 | 4.49 | 4.33 | 2,288 | 480 | 0.83 | 0.68 |

Sweden | 8.38 | 4.72 | −1.14 | 3.82 | 704 | 86 | 0.68 | 0.58 |

Switzerland | 6.69 | 4.68 | 3.34 | 4.09 | 1,270 | 196 | 0.82 | 0.69 |

Taiwan | 7.74 | 4.34 | 5.39 | 4.55 | 760 | 254 | 0.87 | 0.73 |

Thailand | 10.21 | 6.97 | 5.48 | 5.56 | 223 | 36 | 1.23 | 0.98 |

Turkey | 18.47 | 10.25 | 8.90 | 7.18 | 336 | 98 | 0.72 | 0.62 |

United Kingdom | 10.58 | 5.88 | 1.27 | 5.48 | 812 | 95 | 0.78 | 0.61 |

### Appendix C

- Top of page
- Abstract
- 1. Introduction
- 2. Related Literature
- 3. Economic Framework
- 4. Data, Explanatory Variables, and Summary Statistics
- 5. Return Predictability
- 6. Explanatory Factors
- 7. Time-Series Factor Regression Tests
- 8. Robustness
- 9. Conclusions
- Appendix A
- Appendix B
- Appendix C
- References

This table displays the grouping of the sample countries in developed and emerging markets according to the classification of the International Monetary Fund (IMF).

Developed Markets (25) | Emerging Markets (15) |
---|---|

Australia | Argentina |

Austria | Brazil |

Belgium | Chile |

Canada | China |

Denmark | India |

Finland | Indonesia |

France | Malaysia |

Germany | Mexico |

Greece | Pakistan |

Hong Kong | Peru |

Ireland | Philippines |

Israel | Russia |

Italy | South Africa |

Japan | Thailand |

Korea | Turkey |

Netherlands | |

New Zealand | |

Norway | |

Portugal | |

Singapore | |

Spain | |

Sweden | |

Switzerland | |

Taiwan | |

United Kingdom |

- 1
Loughran and Wellman (2011) find that the enterprise multiple is related to but not totally explained by the alternative factor model. Hirshleifer

*et al*. (2011) show that innovative efficiency loads significantly on the profitability factor, but insignificantly on the investment factor as provided by the alternative factor model. - 2
A third interpretation is data snooping. However, arguments in that direction (Black, 1993; MacKinlay, 1995) have been refuted by further US and international out-of-sample evidence (Davis, 1994; Fama and French, 1998, 2011).

- 3
- 4
- 5
- 6
There are other sources for international data, i.e., Global Vantage and MSCI Indices, however, the coverage of these databases is not nearly as extensive as in DataStream. Global Vantage only goes back to 1993 and the target market representation of the MSCI stock universe is only 85% coverage, thus leaving out many small stocks in a country.

- 7
Our inferences do not change when using local currencies in our country level analyses.

- 8
This means preferred shares, investment trusts, and depository receipts are excluded.

- 9
In countries with multiple share classes, we select the most representative share class in terms of liquidity, ordinary voting rights, and accessibility to foreign investment.

- 10
The decision to winsorise in contrast to trim extreme observations does not affect the paper's general findings.

- 11
As shown by Ince and Porter (2006), possible data errors in DataStream are primarily concentrated among microcaps or stocks with very low prices.

- 12
Our inference throughout the paper is robust to a slightly modified definition of E/A in Chen,

*et al*. (2011). - 13
For a detailed description of the Datastream/Worldscope data items see Appendix A.

- 14
Since the fiscal year coincides for the majority of firms in the international sample with the calendar year, the portfolio formation date by the following June is justified. Things change, however, on the country level. We will take care of that issue in the next section.

- 15
For the domestic cross-section regressions, two adjustments are made to comply with country-specific conventions. First, for Japan and India, the explanatory variables are measured at the end of September since most firms in these two countries have the end of their fiscal year in March. Second, for Australia, New Zealand, Pakistan, and South Africa, the variables are updated in December of each year due to the fact the majority of firms have June as the end of their fiscal year. The regressions are then estimated analogously.

- 16
Robustness section 8.3. comes up with a story for this finding.

- 17
See Appendix C for the classification of the countries according to the International Monetary Fund (IMF).

- 18
For further details consult the fact sheet Worldscope Fundamentals at http://thomsonreuters.com/content/financial/pdf/i_and_a/Worldscope_Fundamentals.pdf.

- 19
Leuz

*et al*. (2003) cluster the following countries according to their pervasiveness of earnings management: low (Australia, Canada, Hong Kong, Malaysia, Norway, Singapore, UK), medium (Austria, Belgium, Denmark, Finland, France, Germany, Ireland, Japan, Netherlands, South Africa, Sweden, Switzerland, Taiwan), high (Greece, India, Indonesia, Italy, Korea, Pakistan, Philippines, Portugal, Spain, Thailand). As a further cross-check, we also repeat both tests (untabulated) later using the profitability country premiums instead of E/A, and obtain the same inference. - 20
However, the size results are statistically not significant in most countries. These weaker country-by-country results could be due to the relatively short sample period which weakens the power of the test for many countries.

- 21
Our inference throughout the paper does not change when applying a modified construction proposed by Chen

*et al*. (2011). - 22
Chen

*et al*. (2010) state on page 12: ‘We construct the investment factor,*r*, from a two-by-three sort on size and_{INV}*I/A*’. - 23
For countries with non-December fiscal year ends, the portfolio formation is adjusted as in the previous section.

- 24
Using the 80th percentile as the relevant size breakpoint at the country level instead of the median results in largely undiversified factor portfolios with only few stocks in the three big portfolios for many countries. Therefore, we use the median at the country level.

- 25
Chen

*et al*. (2010) state on page 14: ‘We form six portfolios from the intersections of the two size and three*ROA*groups’. - 26
Chen

*et al*. (2010) use quarterly US data for the construction of the PMU factor. Our data set did not permit us to employ a shorter interval because international reporting of quarterly accounting data is just emerging and not (yet) common practice in many non-US countries. However, this alteration does not affect our general inference about the alternative factor model since the return-predictive ability of a variable that is only present when measured with short lags is anyway not persistent (similar reasoning in Fama and French, 2008). - 27
Fama and French (2011) suggest a construction for the SMB and HML factors when used in regions. Griffin (2002) forms global versions of SMB and HML as weighted averages of the underlying country factors. We have tested both methodological approaches for our international versions with similar results in comparison to our pooling approach.

- 28
We discuss this issue later in Section 8 and provide more evidence for this finding.

- 29
See Davis

*et al*. (2000) for a similar result on the US market. - 30
For comparison, the average US premiums for the market, SMB, and HML factors during the same time period are 0.62% per month (t = 2.47), 0.10% per month (t = 0.57), and 0.36% per month (t = 2.06), respectively. We thank K. French for making the data publicly available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

- 31
Section 8.5. validates this finding with a more sophisticated 2SCSR approach.

- 32
For robustness, we also examine 25 value-weighted portfolios formed on size and earnings/price (E/P) or size and dividend/price (D/P) ratios. The inference does not change here in comparison to the tabulated results for the size-B/M portfolios.

- 33
The three-factor model is also rejected by the GRS test when used on the 25 US size-B/M portfolios. Although the model absorbs most of the variation in the returns on the 25 stock portfolios, even small abnormal average returns suffice to reject the hypothesis that all the estimated intercepts are zero (see, for instance, Fama and French, 1993, 1996a).

- 34
The same is true for I/A in developed markets (with a mean of 9.90 and a median of 6.20) and emerging markets (with a mean of 10.77 and a median of 6.42). However, the differences are noticeably less distinctive.

- 35
- 36
This size grouping is similar to the one used in Fama and French (2006b).

- 37
We are aware that these findings could be interpreted to stand in contrast to the recent international anomalies literature. McLean

*et al*. (2009) document a net stock issues effect, while Titman*et al*. (2010) and Watanabe*et al*. (2011) find an asset growth effect in international markets. However, these studies base their inferences mainly on cross-section regressions that are analogous to creating equal-weighed portfolios in which low capitalisation stocks are largely influential. Since we create value-weighted portfolios as in Chen*et al*. (2010), one should not be puzzled that we draw different conclusions about the existence of these anomalies in international markets. - 38
- 39
We apply full-period beta estimates in the analysis. However, the inference remains unchanged when using five-year rolling beta estimates.

- 40
We employ robust t-statistics as in Hirshleifer and Jiang (2010).

- 41

### References

- Top of page
- Abstract
- 1. Introduction
- 2. Related Literature
- 3. Economic Framework
- 4. Data, Explanatory Variables, and Summary Statistics
- 5. Return Predictability
- 6. Explanatory Factors
- 7. Time-Series Factor Regression Tests
- 8. Robustness
- 9. Conclusions
- Appendix A
- Appendix B
- Appendix C
- References

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