Empirical study of Fama-French Five-Factor Asset Pricing Model in Asia Pacific ex Japan area

Empirical Study of Fama-French Five-Factor Asset

Pricing Model in Asia Pacific ex Japan area

Abstract Fama and French (2015) recently introduced a five-factor model to explain more pricing anomalies in excess stock returns than other asset pricing models. This study uses an extensive sample of monthly stock returns over the period January 1991-December 2017 in the Asia Pacific ex Japan area to analyze the performance of the five-factor model. The regression results show that the five-factor model outperforms the CAPM and three-factor model in the 25 Size-B/M portfolios and the 25 Size-OP portfolios. But the five-factor model is not able to explain more pricing anomalies in the 25 Size-INV portfolios than the three-factor model. The regressions also show that all models have problems pricing small high value stocks, small high profitability stocks and small low investment stocks. This indicates respectively a significant value effect in Size-B/M portfolios, a significant size effect in Size-OP portfolios and a significant investment effect in Size-INV portfolios. Key words: CAPM, Fama-French Three Factor Asset Pricing Model, Fama-French Five-Factor Asset Pricing Model Statement of Originality This document is written by Mitchell Huisman who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

1. Introduction In 2015 Fama and French published a paper explaining the Fama-French Five- Factor Model. In this model they included two new factors compared to the Fama-French Three-Factor Model, profitability and investment. The five-factor model should estimate expected returns on stocks better than three-factor model. Following this new model small companies with a high market-to-book value and a high profitability and investment ratio should have the highest expected returns. Asset pricing models are used by investors and investment companies to determine an appropriate rate of return on assets. If the asset pricing model performance improves then investors and investment companies can better estimate this rate of return of the asset. Therefore the effect of profitability and investment should be well researched. This study will provide new insights in model performances of different asset pricing models in the Asia Pacific area. As stated in the literature review later on, the five-factor model has been tested in the US, Japan, China, Norway, India and Australia. Therefore this study on the Asia Pacific ex Japan area adds to the already existing literature provided. The dataset used is recent and is therefore valuable for investors in the decision making process of asset and portfolio selection in the Asia Pacific area. And the findings of this study show a comparison between the US stock market returns and portfolio returns in the Asia Pacific area. The empirical study by Fama and French (2015) showed that the five-factor model improves explaining of excess average returns compared to the three-factor model on US stock returns between July 1963 and December 2013. This study tests the excess average returns of different portfolios by comparing the five-factor model to the three-factor model and the Capital Asset Pricing Model (CAPM) in the Asia Pacific ex Japan area. The Asia Pacific ex Japan area consists of Australia, Hong Kong, New Zealand and Singapore. Comparing the different capital asset pricing models by analyzing regression intercepts of expected returns of diversified portfolios should provide clear results on which model should be used to provide a better estimate of expected returns in the Asia Pacific area. These results should provide an answer to the central research question stated in this paper: ‘Does the Fama-French Five-Factor Asset Pricing Model provide

better estimates on expected returns of portfolios in the Asia Pacific ex Japan Area between 1991 and 2017 than the Fama-French Three-Factor Asset Pricing Model and the CAPM?’ The framework of this paper is as follows. In the next section the literature review of asset pricing models will be discussed. Section 3 describes the research methodology, data collection and portfolio construction. Section 4 shows the average excess returns on portfolios and correlations between factors. Section 5 reports and analyzes the regression results of the CAPM, the three-factor model and the five-factor model on different portfolios. Sections 6 and 7 conclude the regression results and discusses limitations of this study. Section 8 describes future research possibilities. 2. Literature Review 2.1. Markowitz portfolio selection theory In 1952 Markowitz introduced a theory of selecting a portfolio by investors. This theory was the foundation for Modern Portfolio Theory. The theory included observations of expected returns, investor’s beliefs about future performance and the choice of a portfolio. A mean-variance analysis was shown where the expected return was described as the mean of the expected returns and the risk as the variance of expected returns. The mean-variance analysis showed the optimal allocation of the risk and return trade-off for different levels of means and variances. Diversifying across industries for large number of assets lead to efficient portfolios. The optimal allocation of different efficient portfolios resulted in an efficient frontier of risky assets. It was stated that investors desired the largest expected returns for the least variance in the assets. The frontier showed the results of minimization of variance for different levels of expected returns of assets. Depending on the investor’s preferences, investors could increase expected return levels by increasing the variance of the assets. Later Tobin (1958) showed that the selection of portfolios by investors in the model of Markowitz depended on investor’s preferences of combining risky assets and allocating funds between a combination of assets and risk-free assets.

2.2. The Single Index model The portfolio selection model of Markowitz (1952) was limited because it did not provide an explanation of the risk premiums of risky assets and analysis required a high number of observations. In 1963, Sharpe introduced the Single Index Model to provide new insight into portfolio diversification by allocating risk premiums of risky assets in systematic risk and unsystematic risk (Bodie, Kane, Marcus, 2014, pp. 256). 2.3. Capital Asset Pricing Model (CAPM) In 1964 Sharpe introduced a theory of market equilibrium under risk conditions based on the portfolio selection approach of Markowitz. The theory showed the relationship between prices and the risk components of assets by adding microeconomic theory of capital markets behavior to the portfolio selection model. If investors followed rational expectations and diversified their portfolios, they could obtain higher expected returns by increasing the risk on the asset. The systematic component of the risk on the asset could be diversified away since this is risk for the entire market. But they could not diversify away unsystematic risk since this risk is specific to the firm or industry. The Capital Asset Pricing Model was introduced in articles of Sharpe (1964), Litner (1965) and Mossin (1966). The CAPM explains the relationship between expected returns and the different risk components of an asset or portfolios. Despite having problems in empirical tests the model is generally used as a benchmark for calculating the expected rate of returns on investments for a certain level of risk. The beta in the CAPM model shows the correlation between the stock return and the market. The formula is as follows: 𝑅!"− 𝑅!"= 𝛼!+ 𝛽!"#$(𝑅!"#− 𝑅!")+ 𝑒!"

The dependent variable, 𝑅!"− 𝑅!", is the expected excess rate of return. 𝑅!"# is

the explanatory variable, 𝛼_! is the return of the portfolio above expectation 𝑒_!" is the

error term for observation i. (Bodie, Kane, Marcus, 2014, pp. 291)

2.4. Multifactor models

Multifactor models were introduced since there were anomalies in expected returns that could not be entirely empirically explained by the market factor in the

CAPM. The risk premiums of assets should illustrate the correlation between changes in the market or in asset prices and the different systematic risk factors. It showed the relationship of multiple factors and their performance in identifying anomalies. By adding factors a multifactor model could improve estimations and better explain differences between the expected returns and risk factors such as business-cycle risk, interest rate risk or inflation risk (Bodie, Kane, Marcus, 2014, pp. 324-325). 2.4.1. Arbitrage Pricing theory In 1976 Ross introduced the arbitrage pricing theory (APT). The APT assumes that asset returns can be described by an asset pricing model, that there are sufficient assets available to diversify away non-systematic risk and efficient markets do not allow for arbitrage opportunities (Bodie, Kane, Marcus, 2014, pp. 327). The APT model uses more risk factors compared to the CAPM but investors must determine the number and identity of the risk factors that could affect the asset returns themselves. 2.4.2. The Fama-French Three-Factor Asset Pricing Model In 1993 Fama and French introduced the Fama-French Three Factor Asset Pricing Model. This model added the factors size (SMB) and value (HML) to the CAPM. These two factors were added since empirical research showed patterns in expected returns that a corporate size factor and a book-to-market ratio factor could better explain anomalies of expected returns than the CAPM model. The formula is as follows: 𝑅!"− 𝑅!"= 𝛼!+ 𝛽!"#$(𝑅!"#− 𝑅!")+ 𝛽!"#$ 𝑆𝑀𝐵!+ 𝛽!"#$𝐻𝑀𝐿!+ 𝑒!" The dependent variable, 𝑅_!"− 𝑅_!", is the portfolio’s expected excess rate of

return. 𝑅_!"#, Size and Value are the explanatory variables, 𝛼_! is the return of the

portfolios above expectation and 𝑒!" is the error term for observation i (Bodie, Kane, Marcus, 2014, pp. 340) Empirical research by Fama and French (1996) confirmed that the three-factor model reduces anomalies in expected returns of assets compared to the CAPM model for stock data of the NYSE, AMEX and NASDAQ in the period 1963-1990 except for small growth portfolios.

2.4.3. Fama-French Five-Factor Asset Pricing Model Empirical evidence by Novy-Marx (2013) and Aharoni, Grundy and Zheng (2013) showed that anomalies in average returns of the three-factor model could be reduced by the factors profitability and investment. Therefore Fama and French (2015) introduced the Fama-French Five-Factor Asset Pricing Model by adding the factors profitability and investment to the three-factor model. The formula is as follows: 𝑅!"− 𝑅!"= 𝛼!+ 𝛽!"#$(𝑅!"#− 𝑅!")+ 𝛽!"#$ 𝑆𝑀𝐵!+ 𝛽!"#$𝐻𝑀𝐿!+ 𝛽!"#$𝑅𝑀𝑊!+ 𝛽!"#$𝐶𝑀𝐴!+ 𝑒!" The dependent variable, 𝑅!"− 𝑅!", is the portfolio’s expected excess rate of

return. 𝑅_!"#, Size, Value, Profitability and Investment are the explanatory variables, 𝛼_! is

the return of the portfolios above expectation and 𝑒_! is the error term for observation i. Following Fama and French (2015) the explanatory variable 𝑆𝑀𝐵! is the Small-versus-Big factor (size effect), 𝐻𝑀𝐿_! is the High minus Low book-to-market ratio factor (value effect), 𝑅𝑀𝑊_! is the return of profitable companies versus less profitable companies factor (profitability effect) and 𝐶𝑀𝐴! is the return on diversified portfolios which invest conservative versus aggressive factor (investment effect). 2.5. Five-factor model empirical study results The results on scientific research of the five-factor model differ across countries. Fama and French (2015) empirically tested the five-factor model on US stock data and found that the five-factor model provided better estimates on average stocks returns than the three-factor model. And by adding the factors profitability and investment the value factor became redundant in their sample. The main problem of the five-factor model was to explain average returns of small stocks with high investments and low profitability. Kubota and Takehara (2018) found no statistically significant evidence for the factors profitability and investment in the French Five-Factor Model in Japan. Lin (2017) found that the French Five-Factor Model consistently outperformed the Chinese equity markets but the explanatory variable investment was redundant. Mustafa and Ali (2016) used the five-factor model to test Norwegian mutual fund returns over the period 2002-2011. They found that the five-factor model improved estimations on mutual fund returns compared to the three-factor model.

Balakrishnan, Maiti and Panda (2018) empirically tested stock returns in India and found that average returns were strongly influenced by the factors size, value, profitability and investment. But the three-factor model outperformed the five-factor model for the Indian stock market over the period 1999-2015. Chiah et al. (2016) tested the five-factor model in Australia and found that the five-factor model better explained asset price anomalies than the three-factor model. 2.6. Conclusion In conclusion, the five-factor model has been shown to outperform the three- factor model in the US, China, Norway and Australia. One would expect that the five-factor model should outperform the three-factor model and the CAPM in explaining excess average returns of the Asia Pacific area. But empirical studies showed that the five-factor model does not outperform the three-factor model in the stock markets of India and Japan. To outperform the three-factor model and the CAPM, the intercept of the five-factor model should be closer to zero compared to the intercepts of the other asset pricing models. 3. Data collection and analysis 3.1. Data source and selection The portfolio and factor dataset used in this paper is from the data library of French. The dataset contains monthly stock returns of Australia, Hong Kong, New Zealand and Singapore for the period January 1991 until December 2017 in US dollars. The monthly returns on these stocks are constructed by including dividends and capital gains. 3.2. Factor construction The CAPM, three-and five-factor models contain the explanatory factors 𝑅!"#−

𝑅_!", 𝑆𝑀𝐵_!, 𝐻𝑀𝐿_!, 𝑅𝑀𝑊_! and 𝐶𝑀𝐴_!. As in Fama and French (2015) the factor 𝑅_!"#− 𝑅_!" is

constructed by using value-weighted market portfolios of the countries in the Asia Pacific ex Japan area and the risk free rate is the one-month US T-bill rate. The factor

𝑆𝑀𝐵_! is the market capitalization at the end of June in year t. The HML factor is the

t-1 divided by the market equity at the end of December of the year t-1. The RMW factor is measured as revenue minus the cost of goods sold, selling expenses, general expenses, administrative expenses and interest expenses all divided by book equity for the year ending in year t-1. The CMA factor is measured as the difference in total assets from the fiscal year ending in year t-2 and the year ending in t-1 divided by the total assets ending in year t-2. 3.3. Portfolio construction In this study different asset pricing models will be tested against average returns on 25 Size-B/M portfolios, 25 Size-OP portfolios and 25 Size-INV portfolios. These portfolios, factor values and average returns are downloaded from the data library of French for the Asia Pacific ex Japan area. The 25 Size-B/M portfolios are constructed by sorting the stocks into five groups and five book-to-market ratio groups. The size factor groups are classified from small to big. The groups are divided by breakpoints in the market capitalization values of the

companies at the 3rd_{, 7}th_{, 13}th_{, and 25}th _{percentile. The value factor is constructed by}

classifying the book-to-market ratios into groups from low to high. The breakpoints are at the 20th_{, 40}th_{, 60}th _{and 80}th _percentiles.

The 25 Size-OP portfolios consist of five size groups and five operating profitability groups. The size groups are classified in the same way as in the 25 Size-B/M portfolios. The operating profitability groups are classified from robust to weak. The breakpoints in the operating profitability ratios are at the 20th_{, 40}th_{, 60}th _{and 80}th percentiles. The 25 Size-INV portfolios are sorted into five size groups and five investment groups. The size groups are classified in the same way as the other portfolios. The investment groups are sorted from conservative to aggressive. The breakpoints in the investment ratios are at the 20th_{, 40}th_{, 60}th _{and 80}th _percentiles.

4. Empirical results 4.1. Methodology This study tests the performance of the five-factor model to respectively the three-factor model and the CAPM for 25 different portfolios based on the factors market,

size, value, profitability and investment. To find an answer to the research question in this study I will run regressions of the average returns of different portfolios as dependent variable and the factor variables as independent variables. If the model performs well, alpha should be zero since it is the regression intercept and represents the pricing error of the model. At first I will analyze average returns on the different portfolios based on the factors size, B/M, profitability and investment to find patterns in excess returns that need to be explained. After that I will look at factor correlations to see if factor effects on average returns are isolated in the five-factor model. Later I will run regressions on different portfolios and analyze the different intercepts to gain more insight into model performance. First, I will run a regression on the different portfolios and the market factor to find the intercepts of the CAPM. Second, I will run regressions on the different portfolios and the factors market, size and value to find the intercepts of the three-factor model. Third, I will run a regression on the different portfolios and the factors market, size, value, profitability and investment to find the intercepts of the five-factor model. The following regression formulas will be used: (1) 𝑅!"− 𝑅!"= 𝛼!+ 𝛽!"#$(𝑅!"#− 𝑅!")+ 𝑒!" (2) 𝑅_!"− 𝑅_!"= 𝛼_!+ 𝛽_!"#$(𝑅_!"#− 𝑅_!")+ 𝛽_!"#$ 𝑆𝑀𝐵_!+ 𝛽_!"#$𝐻𝑀𝐿_!+ 𝑒_!" (3) 𝑅_!"− 𝑅_!"= 𝛼_!+ 𝛽_!"#$(𝑅_!"#− 𝑅_!")+ 𝛽_!"#$ 𝑆𝑀𝐵_!+ 𝛽_!"#$𝐻𝑀𝐿_!+ 𝛽_!"#$𝑅𝑀𝑊_!+ 𝛽_!"#$𝐶𝑀𝐴_!+ 𝑒_!" The intercept results from the regressions will provide an answer to the research question: ‘Does the Fama-French Five-Factor Asset Pricing Model provide better estimates on expected returns of portfolios in the Asia Pacific ex Japan Area between 1991 and 2017 than the Fama-French Three-Factor Asset Pricing Model and the CAPM?’ If all intercepts are zero then the portfolio return is equal to the expected return of the stocks. Therefore I will look at the number of significant alphas and the average absolute alphas to analyze if the five-factor model provides better estimates of expected returns on portfolios in the Asia Pacific ex Japan area.

4.2. Average excess returns for different portfolios First I will look at the average excess returns of the different portfolios for patterns that need to be explained. Table 1 reports the average excess returns of the different portfolios. Panel A shows the average excess returns for 25 Size-B/M portfolios. Looking at the B/M quintiles, the average returns increase from small to big stocks for the lower three B/M quintiles. This indicates a negative size effect for these portfolios. For the highest two B/M quintiles the average returns decrease from small to big stocks, hence a positive size effect. By analyzing the size levels, average returns for all size quintiles increase from low B/M to high B/M quintiles, the value effect. It is known from Fama and French (2015) that the value effect is stronger among small stocks. The table shows that small stock average returns increases from 0,595% for low B/M stocks to 1,547% for high B/M stocks, and for big stocks from 0,627% to 1,081%. Panel B shows the average excess returns for 25 Size-OP portfolios. Average returns of small stocks are larger than for big stocks for all profitability levels, indicating positive size effects. For small low OP stocks the average returns are 0,924% and for big low OP stocks 0,624%. This difference is in contrast to the small high OP stock returns of 1,273% and big high OP returns of 0,733%. By analyzing profitability levels, all high OP quintiles have higher average excess returns than low OP quintiles. This is in line with the profitability effect of Novy-Marx (2013) and Fama and French (2015), which showed that for all stock sizes high profitability results in higher average returns than low profitability. Panel C shows the average excess returns for 25 Size-INV portfolios. Average returns decrease from small to big stocks in all investment quintiles, indicating positive size effects. For all size quintiles the average returns decrease when moving from the lowest INV quintile to the highest INV quintile, this is the investment effect. As can be seen from the table this investment effect is largely due to the fact that the average returns in the highest INV quintile are low compared to the average returns in the lower four INV quintiles. This effect will be discussed later on in analyzing the five-factor regression.

Table 1 Average monthly excess returns minus US one-month T-bill rate for the 25 portfolios based on Size, Value, Operating Profitability and Investment. The portfolios are from the Asia Pacific ex Japan area for January 1991-December 2017, 324 months 4.3. Five-factor correlations Table 2 shows the correlations in the five-factor model since factor correlations could have effect on the estimates of the average returns. The factors value and profitability are significant moderately correlated (-0,608) at 1%. And value is very low significantly correlated to the factors market (0,111) at 5% and investment (0,181) at 1%. This indicates that high value stocks tend to have high betas, low profitability and low investments. This is in line with Fama and French (1993, 2015) since they found that the factors value, profitability and investment are correlated and that high B/M stocks have low profitability and low investments. The market is significant moderately correlated to the factors profitability (-0,385) and investment (-0,487) at 1%. This indicates that high beta stocks have low profitability and high investments. The very low correlation (0,157) between the factors Small 2 3 4 Big S-B Panel A: 25 Size-B/M portfolios Low B/M 0,595 -0,042 0,220 0,704 0,627 -0,032 2 0,463 0,312 0,460 0,853 0,847 -0,384 3 0,789 0,445 0,836 0,675 0,869 -0,080 4 1,140 0,666 0,809 1,002 0,859 0,281 High B/M 1,547 0,978 0,862 1,115 1,081 0,466 H-L 0,952 1,021 0,642 0,411 0,454 Panel B: 25 Size-OP portfolios Weak 0,924 0,348 0,212 0,685 0,624 0,300 2 1,366 0,535 0,883 0,813 0,918 0,448 3 1,170 0,773 0,853 0,808 0,963 0,207 4 1,424 0,885 0,928 1,003 0,889 0,535 Robust 1,273 0,729 0,878 1,016 0,733 0,540 R-W 0,349 0,381 0,666 0,332 0,109 Panel C: Size-INV portfolios Conservative 1,204 0,666 0,675 0,707 0,912 0,291 2 1,345 0,937 1,102 0,841 0,784 0,561 3 1,361 0,672 0,735 1,078 0,860 0,501 4 1,234 0,706 0,887 0,989 0,852 0,383 Aggressive 0,651 0,128 0,265 0,618 0,571 0,080 C-A 0,553 0,538 0,409 0,089 0,342

profitability and investment is significant at 1%. This indicates that high profitable companies tend to have low investments. These correlation results show that the Size-B/M, Size-OP and Size-INV portfolios do not isolate value, profitability and investment effects in average returns since the factors are correlated. Table 2 Factor correlations and p-values for the five-factor model. The factors are from the Asia Pacific ex Japan area for January 1991-December 2017, 324 months. In parentheses the p-values are shown. *** Significant at 1%. ** Significant at 5%. * Significant at 10%. 5. Regression results To analyze the patterns described in the average returns I will perform regressions of the different factors on the portfolios. These regression intercepts of the different models and the factor slopes will provide more insight into model performance of the different portfolios. I will analyze the number of significant alphas and compare the average absolute size of the alphas of the models. 5.1. 25 Size-Book-to-Market portfolio regressions Table 3 reports the intercepts of the regressions on 25 Size-B/M portfolios. Following Fama and French (2015) the three-and five-factor models have problems explaining the portfolios of low extreme growth stocks in the US stock markets. They are negative for small stocks and positive for big stocks. Analyzing the number of significant alphas at 5% show that in panel A, 5 out of 25 portfolio intercepts are significant. The table shows there are no significant size effects

Mkt-rf Size Value Profitability Investment

Mkt-rf 1,000 0,000 0,111 -0,385 -0,487 (0,998) (0,045)** (0,000)*** (0,000)*** Size 0,000 1,000 0,082 -0,215 -0,073 (0,998) (0,142) (0,000)*** (0,189) Value 0,111 0,082 1,000 -0,608 0,181 (0,045)** (0,142) (0,000)*** (0,001)*** Profitability -0,385 -0,215 -0,608 1,000 0,157 (0,000)*** (0,000)*** (0,000)*** (0,005)*** Investment -0,487 -0,073 0,181 0,157 1,000 (0,000)*** (0,189) (0,001)*** (0,005)***

at 5% but there are significant value effects for the lowest three size quintiles, the largest for small high B/M stocks (1,033%). Panel B shows that 6 out of 25 portfolio intercepts are significant. There are significant size effects for higher B/M quintiles in the three-factor model, the largest for small high B/M stocks (1,134%). The three-factor model has more difficulties explaining size effects and fewer difficulties explaining value effects since the value effects reduce in size but size effects increase in significance compared to the CAPM. In panel C there are 3 out of 25 portfolio intercepts significantly different from zero. This indicates that the five-factor model can explain excess returns better than the three-factor model and the CAPM on Size-B/M portfolios. The five-factor model shows significant size effects for higher B/M values but reduces the size compared to the three-factor model. And the model reduces value effects on the 2nd, ₃rd and 4th _{quintiles compared to the CAPM and three-factor model.} To analyze the size of the alpha’s I look at the average absolute value of the 25 portfolios. This shows that the CAPM has an average absolute value of alpha of 0,237%, the three-factor model of 0,224% and the five-factor model of 0,168%. These results indicate that the five-factor model performs better on these portfolios than the three-factor model and the CAPM since it reduces the average absolute size of the alphas closer to zero. Analyzing the average absolute size effects of the models show that the average effect for CAPM is 0,310%, for the three-factor model is 0,444% and for the five-factor model is 0,361%. This is odd since the three- and five-factor model should have lower absolute alphas than the CAPM. But the average absolute value effect for the five-factor model (0,300%) shows that the value effects are reduced compared to the three-factor model (0,384%) and the CAPM (0,634%). The intercept values for small and big extreme growth stocks are moving from a negative value in the CAPM towards positive values in the three-and five factor models. Since these intercepts are not significant in any model this indicates that in the sample used there is no difficulty in explaining these anomalies compared to the US stock market research (Fama and French, 2015). The problems in the 25 Size-B/M portfolios for the CAPM model are in the small growth quintiles and as can be seen from the table the five-factor model can reduce the significance level and lower the intercept values towards zero. The intercepts represent

the excess average returns that could not be explained by the model factors. The five-factor model has the lowest number of significant alphas and the lowest average absolute value of alphas. This indicates that the five-factor model can explain excess average returns better than the CAPM and three-factor model in 25 Size-B/M portfolios. This is consistent with the findings of Fama and French (1993, 2012, 2015).

Table 3 Pricing errors in percentages for empirical tests of CAPM, three- and five factor model regressed on 5x5 Size-B/M portfolios in the Asia Pacific area; January 1991-December 2017, 324 months. Column S-B shows average excess returns on small stock portfolios minus big stock portfolios, the size effect. And column H-L shows average excess returns of value stocks minus growth stocks, the value effect. In parentheses the p-values are shown. *** Significant at 1%. ** Significant at 5%. * Significant at 10%. Panel A: CAPM alphas Small 2 3 4 Big S-B Low B/M -0,235 -0,849 -0,606 -0,067 -0,155 -0,080 (0,438) (0,000)*** (0,003)*** (0,675) (0,249) (0,815) 2 -0,389 -0,561 -0,338 0,089 0,072 -0,460 (0,097)* (0,003)*** (0,046)** (0,558) (0,461) (0,086)* 3 -0,025 -0,336 0,022 -0,086 0,066 -0,091 (0,909) (0,054)* (0,895) (0,537) (0,529) (0,716) 4 0,354 -0,144 0,000 0,191 0,073 0,281 (0,099)* (0,417) (0,999) (0,159) (0,580) (0,303) High B/M 0,798 0,132 -0,001 0,171 0,156 0,641 (0,001)*** (0,557) (0,996) (0,364) (0,472) (0,057)* H-L 1,033 0,981 0,605 0,237 0,312 (0,000)*** (0,000)*** (0,027)** (0,323) (0,294) Panel B: three-factor model alphas Small 2 3 4 Big S-B Low B/M 0,166 -0,567 -0,251 0,141 0,110 0,056 (0,444) (0,000)*** (0,127) (0,321) (0,315) (0,827) 2 -0,100 -0,328 -0,128 0,216 0,158 -0,258 (0,502) (0,007)*** (0,365) (0,148) (0,079)* (0,134) 3 0,167 -0,172 0,174 0,024 0,039 0,129 (0,183) (0,145) (0,195) (0,861) (0,713) (0,400) 4 0,439 -0,164 -0,029 0,163 -0,204 0,643 (0,000)*** (0,150) (0,833) (0,216) (0,061)* (0,000)*** High B/M 0,704 -0,174 -0,330 -0,231 -0,430 1,134 (0,000)*** (0,101) (0,023)** (0,108) (0,005)*** (0,000)*** H-L 0,538 0,393 -0,079 -0,372 -0,540 (0,014)** (0,038)** (0,692) (0,040)** (0,005)*** Panel C: five-factor model alphas Small 2 3 4 Big S-B Low B/M 0,249 -0,370 0,038 0,125 0,163 0,086 (0,255) (0,016)** (0,818) (0,404) (0,158) (0,739) 2 -0,029 -0,195 -0,194 0,068 0,070 -0,099 (0,848) (0,125) (0,195) (0,661) (0,453) (0,562) 3 0,140 -0,163 -0,031 -0,193 -0,049 0,189 (0,286) (0,194) (0,823) (0,163) (0,656) (0,241) 4 0,451 -0,180 -0,086 -0,026 -0,169 0,620 (0,000)*** (0,129) (0,550) (0,850) (0,128) (0,000)*** High B/M 0,722 -0,073 -0,220 -0,096 -0,089 0,810 (0,000)*** (0,513) (0,144) (0,524) (0,558) (0,000)*** H-L 0,473 0,297 -0,259 -0,221 -0,252 (0,036)** (0,135) (0,220) (0,242) (0,203)

5.2. 25 Size-Operating Profitability portfolio regressions Table 4 reports the intercepts of the regressions on 25 Size-OP portfolios. Analyzing the number of significant alphas at 5% show that in panel A, 6 out of 25 portfolio intercepts are significant. There are multiple size effects and profitability effects that are significant for smaller stocks with higher profitability in CAPM. In panel B, 13 out of 25 portfolio intercepts are significantly different from zero. The table shows that in the three-factor model the significance level is increasing for smaller high OP stocks and there are more significant size and profitability effects compared to the CAPM. This indicates that the three-factor model has more difficulties explaining the excess average returns. In panel C, 7 out of 25 portfolio intercepts are significant. The five-factor model shows multiple size effects and one significant profitability effect at the middle OP quintile of 0,440%. To analyze the size of the alphas the table shows that the CAPM has an average absolute value of alpha of 0,242%, the three-factor model of 0,324% and the five-factor model of 0,183%. This indicates that the five-factor model reduces pricing anomalies better on 25 Size-OP portfolios than the other models. There is an interesting asset pricing problem in the excess average returns on profitability and small stocks for all models. They have difficulties explaining the highest OP quintiles for small portfolios. The three-factor model also shows intercepts deviating far from zero for big stocks. This shows that the three-factor model has more problems explaining portfolios with a low and a high profitability portfolio than the other models. This is in line with the US research for the three-factor model (Fama and French, 2015). Comparing the average absolute size effects show that the CAPM has an average absolute size effect of 0,482%, the three-factor model of 0,57% and the five-factor model of 0,440%. Analyzing the average absolute profitability effects show that the CAPM has an average value effect of 0,517%, the three-factor model of 0,762% and the five-factor of 0,228%. The five-factor model outperforms the other models in reducing average absolute size and profitability effects. But the three-factor model is outperformed by the CAPM based on the number and the average absolute value of the size and profitability effects on 25 Size-OP portfolios. This shows that the three-factor model has more difficulties explaining average returns on these portfolios than the CAPM. This is interesting since one would expect it to be the other way around.

The CAPM model outperforms the three-and five-factor model based on the number of significant alphas but the five-factor model outperforms the other models based on the average absolute alphas. Since this study is interested in reducing pricing errors to zero and the five-factor shows the lowest average absolute alphas, the five-factor model better explains excess average returns on these 25 Size-OP portfolios than the three- factor model and the CAPM. This is in line with the empirical results on US stock data.

Table 4 Pricing errors in percentages for empirical tests of CAPM, three- and five factor model regressed on 5x5 Size-OP portfolios in the Asia Pacific area; January 1991-December 2017, 324 months. Column S-B shows average excess returns on small stock portfolios minus big stock portfolios, the size effect. And column R-W shows average excess returns of robust stocks minus weak stocks, the profitability effect. In parentheses the p-values are shown. *** Significant at 1%. ** Significant at 5%. * Significant at 10%. Panel A: CAPM alphas Small 2 3 4 Big S-B Weak 0,063 -0,534 -0,669 -0,272 -0,353 0,415 (0,814) (0,023)** (0,001)*** (0,130) (0,056)* (0,215) 2 0,657 -0,296 0,050 -0,007 0,022 0,635 (0,005)*** (0,130) (0,776) (0,955) (0,883) (0,030)** 3 0,468 0,002 0,055 0,045 0,190 0,278 (0,018)** (0,990) (0,707) (0,771) (0,059)* (0,223) 4 0,719 0,110 0,151 0,224 0,167 0,553 (0,002)*** (0,538) (0,289) (0,100)* (0,132) (0,046)** Robust 0,547 -0,090 0,070 0,270 0,019 0,528 (0,005)*** (0,604) (0,650) (0,060)* (0,886) (0,037)** R-W 0,485 0,445 0,739 0,542 0,372 (0,012)** (0,042)** (0,001)*** (0,016)** (0,171) Panel B: three-factor model alphas Small 2 3 4 Big S-B Weak 0,239 -0,586 -0,691 -0,406 -0,692 0,931 (0,094)* (0,000)*** (0,000)*** (0,012)** (0,000)*** (0,000)*** 2 0,669 -0,494 -0,082 -0,087 -0,243 0,912 (0,000)*** (0,000)*** (0,562) (0,490) (0,059)* (0,000)*** 3 0,404 -0,010 0,051 0,080 0,125 0,280 (0,000)*** (0,934) (0,668) (0,609) (0,213) (0,052)* 4 0,652 0,121 0,246 0,256 0,294 0,358 (0,000)*** (0,334) (0,058)* (0,050)** (0,004)*** (0,023)** Robust 0,638 0,130 0,234 0,404 0,269 0,369 (0,000)*** (0,270) (0,079)* (0,003)*** (0,018)** (0,031)** R-W 0,399 0,716 0,924 0,810 0,961 (0,026)** (0,000)*** (0,000)*** (0,000)*** (0,000)*** Panel C: five-factor model alphas Small 2 3 4 Big S-B Weak 0,417 -0,228 -0,347 -0,139 -0,060 0,477 (0,003)*** (0,072)* (0,013)** (0,398) (0,658) (0,016)** 2 0,668 -0,357 -0,068 -0,035 0,159 0,508 (0,000)*** (0,005)*** (0,649) (0,797) (0,169) (0,002)*** 3 0,315 -0,118 -0,076 -0,096 0,058 0,257 (0,006)*** (0,338) (0,543) (0,554) (0,583) (0,093)* 4 0,490 -0,065 -0,024 -0,063 -0,015 0,505 (0,000)*** (0,610) (0,855) (0,620) (0,871) (0,002)*** Robust 0,465 0,011 0,093 0,203 0,010 0,455 (0,000)*** (0,927) (0,475) (0,145) (0,928) (0,012)** R-W 0,049 0,239 0,440 0,342 0,070 (0,773) (0,200) (0,019)** (0,104) (0,700)

5.3. 25 Size-Investment portfolio regressions Table 5 reports the intercepts of the regressions on 25 Size-INV portfolios. Analyzing the number of significant alphas at 5% show that in panel A, 8 out of 25 portfolios are significant for the CAPM model. It shows a significant size effect of 0,626% at the 2nd _{investment quintile and multiple investment effects. In panel B, 9 out of 25} portfolios are significant for the three-factor model. The table shows significant size effects for the four lowest investment quintiles and significant investment effects for smaller stocks. Compared to the CAPM results there are more size effects and less investment effects. In panel C, 8 out of 25 portfolio intercepts are significantly different from zero. The five-factor model shows a significant size effect for the three lowest investments quintiles and a significant investment effect for small stocks (0,658%). Analyzing the size of the alphas, the table shows that the CAPM has an average absolute value of 0,260%, the three-factor model of 0,245% and the five-factor model of 0,249%. These results indicate that the three-factor model performs better than the five-factor model and the CAPM on these 25 Size-INV portfolios. Comparing the average absolute value of the size effects of the different models show that the CAPM has an average size effect of 0,396%, the three-factor model of 0,474% and the five-factor model of 0,527%. This shows that the size effect increases when moving to the three- and five-factor model. The average absolute investment effects show that the CAPM has an average effect of 0,555%, the three-factor model of 0,409% and the five-factor model of 0,332%. This is interesting since the pricing anomalies should move closer to zero when moving to a model with more explanatory factors. This is the case for average investment effects but not for average size effects. The problems in the Size-INV portfolios of the CAPM are for small stocks and high INV stocks. The small stock excess returns cannot be explained by using the three or the five-factor model. The intercepts of high INV stocks are moving to zero in the three-factor model. And in the five-factor model the intercepts move even further to zero compared to the three-factor model. But for smallest stocks the three-and five-factor model increase the significance level and alphas. This study does not have a problem explaining excess average returns on small high INV stocks as in US research was shown. The results of this study show that based on the number of significant alphas the CAPM and five-factor model outperform the

three-factor model. But the three-factor model outperforms the CAPM and the five-factor model based on the average absolute value of alpha. Since this study is interested in reducing pricing errors, the three-factor model better explains excess average returns on these 25 Size-INV portfolios. The fact that the five-factor model does not outperform the other models is not in line with US stock research by Fama and French (2015) and should therefore be further analyzed by factor slopes in the next part.

Table 5 Pricing errors in percentages for empirical tests of CAPM, three- and five factor model regressed on 5x5 Size-INV portfolios in the Asia Pacific area; January 1991-December 2017, 324 months. Column S-B shows average excess returns on small stock portfolios minus big stock portfolios, the size effect. And column C-A shows average excess returns of conservative stocks minus aggressive stocks, the profitability effect. In parentheses the p-values are shown. *** Significant at 1%. ** Significant at 5%. * Significant at 10%. Panel A: CAPM alphas Small 2 3 4 Big S-B Conservative 0,431 -0,123 -0,115 -0,023 0,250 0,181 (0,092)* (0,518) (0,493) (0,864) (0,090)* (0,556) 2 0,650 0,182 0,356 0,089 0,025 0,626 (0,001)*** (0,318) (0,027)** (0,515) (0,844) (0,012)** 3 0,635 -0,058 -0,066 0,288 0,085 0,550 (0,008)*** (0,738) (0,657) (0,033)** (0,360) (0,052)* 4 0,454 -0,173 0,035 0,112 0,005 0,449 (0,039)** (0,411) (0,833) (0,515) (0,969) (0,113) Aggressive -0,222 -0,787 -0,642 -0,308 -0,396 0,174 (0,399) (0,000)*** (0,001)*** (0,096)* (0,023)** (0,600) C-A 0,653 0,664 0,526 0,285 0,646 (0,000)*** (0,000)*** (0,011)** (0,202) (0,013)** Panel B: three-factor model alphas Small 2 3 4 Big S-B Conservative 0,564 -0,150 -0,180 -0,049 0,139 0,425 (0,000)*** (0,183) (0,194) (0,717) (0,340) (0,028)** 2 0,708 0,119 0,317 -0,027 -0,008 0,715 (0,000)*** (0,327) (0,023)** (0,837) (0,952) (0,000)*** 3 0,601 -0,138 -0,131 0,288 0,093 0,508 (0,000)*** (0,281) (0,317) (0,028)** (0,291) (0,003)*** 4 0,464 -0,296 0,041 0,080 -0,019 0,483 (0,000)*** (0,027)** (0,771) (0,617) (0,880) (0,007)*** Aggressive -0,089 -0,650 -0,467 -0,191 -0,325 0,236 (0,531) (0,000)*** (0,000)*** (0,272) (0,065)* (0,315) C-A 0,653 0,500 0,286 0,142 0,464 (0,000)*** (0,004)*** (0,149) (0,521) (0,077)* Panel C: five-factor model alphas Small 2 3 4 Big S-B Conservative 0,600 -0,106 -0,361 -0,361 -0,199 0,799 (0,000)*** (0,362) (0,011)** (0,005)*** (0,106) (0,000)*** 2 0,675 0,068 0,209 -0,201 -0,173 0,848 (0,000)*** (0,586) (0,150) (0,145) (0,137) (0,000)*** 3 0,575 -0,219 -0,221 0,178 0,093 0,482 (0,000)*** (0,105) (0,105) (0,196) (0,325) (0,007)*** 4 0,463 -0,243 0,092 0,120 0,154 0,309 (0,000)*** (0,077)* (0,527) (0,468) (0,192) (0,078)* Aggressive -0,058 -0,376 -0,319 -0,009 0,140 -0,198 (0,696) (0,003)*** (0,015)** (0,958) (0,341) (0,367) C-A 0,658 0,271 -0,042 -0,352 -0,338 (0,000)*** (0,109) (0,827) (0,095)* (0,066)*

5.4. Five-factor coefficients In this study I focus on the 25 Size-INV portfolios to further analyze the regression intercept results. Table 6 shows the different factor regression slopes of the five-factor model. The slopes for the three-factor model and CAPM are shown in the appendix. Table 6 and A1 show that the market, size and value slopes are similar for the CAPM, three-factor model and five-factor model. If the five-factor model performs well the slopes of the factors investment and profitability should reduce the regression intercept to zero. Problems in the 25 Size-INV portfolios are for small stocks and highest INV stocks. For small stocks the negative profitability slopes show that it reduces alpha towards zero for the 25 Size-INV portfolios. The largest significant effect at 1% is for small low OP portfolios (-0,360; t=-5,310). But the positive investment slopes for small stocks show that it moves alpha further away from zero, the largest significant effect at 1% for small low INV portfolios (0,458; t=7,311). For high INV stocks the negative profitability slopes moves alpha further away from zero, except for the significant 3th size and highest INV quintile slope (0,032; t=0,509). But all negative investment slopes move alpha further away from zero for high INV quintiles, the largest significant effect at 1% for big high INV stocks (-0,871; t=-13,257). Therefore the five-factor slopes reduce pricing errors in small stocks but do not reduce pricing errors in high INV stocks for 25 Size-INV portfolios.

Table 6 Five-factor betas and t-statistics for 25 Size-Inv portfolios in the Asia Pacific area; January 1991-December 2017, 324 months. Column S-B shows average excess returns on small stock portfolios minus big stock portfolios, the size effect. And column C-A shows average excess returns of conservative stocks minus aggressive stocks, the profitability effect. The regression formula of the five-factor model is: 𝑅!"− 𝑅!"= 𝛼!+ 𝛽!"#$(𝑅!"#− 𝑅!")+ 𝛽!"#$ 𝑆𝑀𝐵!+ 𝛽!"#$𝐻𝑀𝐿!+ 𝛽!"#$𝑅𝑀𝑊!+ 𝛽!"#$𝐶𝑀𝐴!+ 𝑒!" 6. Conclusion In this study, different asset pricing models were compared to analyze if the five-factor model outperformed the CAPM and three-factor model in the Asia Pacific area. The excess average returns of portfolios based on the factors size, book-to-market ratio,

Small 2 3 4 Big S-B Small 2 3 4 Big S-B

𝛽!"# 𝑡(𝛽!"#) Conservative 1,014 0,988 1,055 1,035 0,989 0,026 37,627 44,107 38,458 41,603 41,731 0,688 2 0,911 0,973 0,974 0,989 1,051 -0,140 39,833 40,150 34,748 37,148 46,878 -4,289 3 0,913 0,918 1,001 1,011 0,975 -0,061 31,297 35,222 38,040 38,108 53,701 -1,778 4 0,975 1,034 1,023 1,050 0,958 0,017 38,841 39,059 36,336 32,834 42,125 0,512 Aggressive 1,092 1,034 1,061 1,085 1,002 0,090 37,779 41,817 42,128 31,281 35,423 2,110 C-A -0,077 -0,046 -0,005 -0,050 -0,014 -2,360 -1,415 -0,149 -1,235 -0,390 𝛽!"#$ 𝑡(𝛽!"#$) Conservative 1,273 0,900 0,598 0,208 -0,120 1,393 28,159 23,953 13,012 4,997 -3,028 22,075 2 1,006 0,798 0,515 0,174 -0,120 1,125 26,226 19,647 10,970 3,903 -3,182 20,572 3 1,146 0,702 0,448 0,284 -0,205 1,351 23,423 16,059 10,165 6,385 -6,746 23,303 4 1,099 0,911 0,541 0,414 -0,273 1,372 26,119 20,543 11,468 7,721 -7,172 24,218 Aggressive 1,352 0,995 0,803 0,392 -0,186 1,538 27,917 23,990 19,016 6,746 -3,913 21,635 C-A -0,080 -0,095 -0,204 -0,184 0,065 -1,453 -1,742 -3,304 -2,703 1,099 𝛽!"#$ 𝑡(𝛽!"#$) Conservative -0,306 0,045 0,182 0,088 0,036 -0,342 -5,322 0,942 3,106 1,656 0,715 -4,262 2 -0,088 0,132 0,122 0,270 -0,119 0,031 -1,805 2,559 2,048 4,759 -2,490 0,446 3 0,191 0,305 0,301 0,134 -0,056 0,247 3,063 5,480 5,363 2,374 -1,458 3,349 4 0,114 0,445 0,154 0,222 0,135 -0,021 2,132 7,895 2,568 3,262 2,785 -0,290 Aggressive -0,073 -0,072 -0,069 -0,110 -0,041 -0,032 -1,178 -1,361 -1,281 -1,490 -0,672 -0,354 C-A -0,233 0,117 0,250 0,198 0,077 -3,336 1,683 3,187 2,290 1,013 𝛽!"#$ 𝑡(𝛽!"#$) Conservative -0,360 -0,188 0,104 0,222 0,059 -0,419 -5,310 -3,348 1,510 3,554 0,998 -4,431 2 -0,151 -0,073 0,050 0,180 -0,085 -0,066 -2,630 -1,201 0,712 2,700 -1,511 -0,806 3 -0,020 0,143 0,220 0,188 -0,016 -0,004 -0,276 2,180 3,334 2,821 -0,356 -0,046 4 -0,034 0,106 0,074 0,111 0,055 -0,089 -0,539 1,591 1,048 1,378 0,968 -1,051 Aggressive -0,080 -0,166 0,032 -0,087 -0,174 0,093 -1,103 -2,679 0,509 -0,995 -2,442 0,877 C-A -0,279 -0,022 0,072 0,309 0,233 -3,391 -0,269 0,776 3,029 2,614 𝛽!"#$ 𝑡(𝛽!"#$) Conservative 0,458 0,178 0,284 0,426 0,735 -0,277 7,311 3,412 4,458 7,378 13,362 -3,173 2 0,309 0,235 0,188 0,151 0,533 -0,224 5,822 4,168 2,886 2,436 10,240 -2,955 3 0,094 -0,019 -0,113 -0,015 0,027 0,068 1,391 -0,307 -1,857 -0,238 0,632 0,842 4 0,055 -0,290 -0,238 -0,267 -0,506 0,561 0,943 -4,723 -3,635 -3,597 -9,586 7,147 Aggressive 0,048 -0,417 -0,409 -0,312 -0,871 0,919 0,715 -7,262 -6,988 -3,874 -13,257 9,333 C-A 0,410 0,595 0,693 0,738 1,606 5,378 7,869 8,091 7,836 19,494

operating profitability and investment were tested by comparing the CAPM, the three-factor and the five-factor model. The average excess returns of portfolios showed strong value effects for small stocks, positive size effects for high B/M stocks and negative size effects for low B/M stocks in 25 Size-B/M portfolios. In 25 Size-OP portfolios there are positive size and profitability effects for all profitability and size quintiles. In 25 Size-INV portfolios there are positive size effects, positive investment effects and the average returns in the highest INV quintile are low compared to the four lowest INV quintiles. The regression results showed that the five-factor model outperforms the CAPM and three-factor model based on number of significant alphas and the average absolute value of alphas in 25 Size-B/M portfolios. In 25 Size-OP portfolios the five-factor model outperforms the three-factor model and CAPM based on average absolute value of alphas but is outperformed by the CAPM based on the number of significant alphas. Since this study is interested in reducing pricing anomalies to zero and the five-factor model has the lowest average absolute alphas, the five-factor model outperforms the three-factor model and the CAPM on 25 Size-OP portfolios. In 25 Size-INV portfolios the five-factor model and CAPM outperformed the three-factor model based on the number of significant alphas. But the three-factor model outperformed the other models based on the average absolute value of alphas. Therefore the three-factor model explained pricing anomalies on these 25 Size-INV portfolios better than the other models. Since this is not in line with the results of Fama and French (2015) on US stocks, the five-factor slopes of these portfolios were further analyzed. These results showed that the factors profitability and investment reduced pricing errors for small stocks but had difficulties explaining excess returns for high INV stocks. The five-factor model outperforming the three-factor model is consistent with empirical research of Fama and French (2015), Lin (2017), Chiah et al. (2016) and Mustafa and Ali (2016). But the three-factor outperforming the five-factor model is not consistent with the literature of the multifactor model. This model stated that adding factors should improve the estimates of the excess average returns. Therefore the answer on the central research question in this study is; the five-factor model outperforms the CAPM and three-factor model in the Asia Pacific ex Japan area between January 1991 and December 2017 for 25 Size-B/M and 25 Size-OP portfolios. But is outperformed by the three-factor model for 25 Size-INV portfolios. The results show

that the five-factor model can explain excess average returns on some portfolios better than the other models but the five-factor model can be improved to fully explain excess average returns. The regressions also show that all models have problems pricing small high value stocks, small high profitability stocks and small low investment stocks. This indicates respectively a significant value effect in Size-B/M portfolios, a significant size effect in Size-OP portfolios and a significant investment effect in Size-INV portfolios. These results are in line with the findings in the average excess returns of portfolios. The results in this study are important since it offers new insights in the asset pricing model performances in the Asia Pacific area. It is showed that the five-factor model is significantly better in estimating excess returns on some portfolios than other asset pricing models. These findings are valuable since investors and investment companies use these asset pricing models for choosing assets or portfolios to invest in. And these findings compare the US stock market returns to stocks of the countries in the Asia Pacific area. 7. Limitations A limitation in this study is that this study does not include country-specific factors. This study focuses on the Asia pacific ex Japan area as if it is one country. By using cross-country analysis it is assumed that the countries in the Asia Pacific ex Japan area perform as integrated markets. But the countries could have country specific market, size, value, profitability and investment factors if the markets are not integrated. A second limitation in this study is the economic mechanism data mining. Data mining is used to find patterns in historical data. This is a problem for asset pricing models because when this technique is used it could not be clear if there are anomalies in the asset pricing models or that these deviations from the models are due to data mining. (Bodie, Kane, Marcus, 2014, pp. 373, 930) A third limitation is the robustness test used. This study focuses on three sets of 5x5 portfolios of different factors used by Fama and French (2015). By analyzing alternative methods of calculating portfolios returns, factor definitions and the formation of the test assets the conclusion on model performances of the asset pricing models used in this study could differ.

A fourth limitation in this study is described by Black (1993). When researches are data-snooping to search for explanatory variables they could find asset return patterns that are purely based on luck. This is a problem for empirical models such as the CAPM, three-factor model and five-factor model. 8. Future study The models used in this study could not explain some anomalies in average excess returns. Future study could include country-specific factors in the Asia Pacific ex Japan area to compare the five-factor model results of cross-country analysis to country-specific analysis. Another interesting subject for future research is the model performance of the three-factor model on the 25 Size-OP and 25 Size-INV portfolios. As shown in this study, the three-factor model is outperformed by the CAPM in 25 Size-OP portfolios but outperformed the five-factor model in 25 Size-INV portfolios based on average absolute alphas. Following the literature of the multifactor model, one would expect that adding factors should reduce pricing anomalies compared to other asset pricing models. Adding other factors to the CAPM or testing different asset pricing models could also improve the model performance in the Asia Pacific area. The four-factor model by Carhart (1997) could be tested to analyze if this model outperforms the CAPM, three-factor model and the five-factor model in the Asia Pacific area. Since the four-factor model adds the factor momentum to the three-factor model instead of profitability and investment. 9. Appendix Table A1 shows the CAPM and three-factor model slopes and t-statistics for 25 Size-INV portfolios.

Table A1 CAPM and three-factor betas and t-statistics for 25 Size-Inv portfolios in the Asia Pacific area; January 1991-December 2017, 324 months. Column S-B shows average excess returns on small stock portfolios minus big stock portfolios, the size effect. And column C-A shows average excess returns of conservative stocks minus aggressive stocks, the profitability effect. 10. References Aharoni, G., Grundy, B., & Zeng, Q. (2013). Stock returns and the Miller Modigliani valuation formula: Revisiting the Fama French analysis. Journal of Financial Economics, 110(2), 347-357. Balakrishnan, A., Maiti, M., & Panda, P. (2018). Test of Five-factor Asset Pricing Model in India. The Journal of Business Perspective, 22(2), 153-162. Panel A: CAPM coefficients

Small 2 3 4 Big S-B Small 2 3 4 Big S-B

𝛽!"# 𝑡(𝛽!"#) Conservative 0,967 0,988 0,989 0,913 0,829 0,138 22,389 30,653 34,775 40,204 33,312 2,646 2 0,869 0,945 0,933 0,941 0,950 -0,081 25,442 30,755 34,446 40,767 44,816 -1,929 3 0,908 0,914 1,002 0,988 0,969 -0,061 22,475 31,045 39,755 43,376 61,494 -1,272 4 0,976 1,100 1,067 1,098 1,060 -0,083 26,263 30,912 38,337 37,870 48,571 -1,744 Aggressive 1,092 1,145 1,135 1,158 1,210 -0,118 24,586 31,382 35,709 37,189 41,326 -2,098 C-A -0,125 -0,158 -0,146 -0,245 -0,381 -4,495 -5,318 -4,198 -6,516 -8,659 Panel B: three-factor coefficients 𝛽!"# 𝑡(𝛽!"#) Conservative 0,969 0,978 0,978 0,910 0,820 0,148 39,997 52,173 42,317 40,443 33,836 4,614 2 0,866 0,933 0,926 0,929 0,948 -0,082 44,181 46,175 40,098 42,010 45,187 -3,030 3 0,896 0,901 0,993 0,986 0,972 -0,076 37,718 42,279 45,575 45,247 65,902 -2,689 4 0,968 1,081 1,063 1,091 1,059 -0,091 47,451 48,602 45,599 41,188 50,565 -3,086 Aggressive 1,093 1,150 1,145 1,166 1,217 -0,124 46,511 52,042 52,142 40,317 41,709 -3,169 C-A -0,125 -0,172 -0,167 -0,256 -0,397 -4,444 -5,947 -5,043 -6,963 -9,108 𝛽!"#$ 𝑡(𝛽!"#$) Conservative 1,293 0,915 0,560 0,140 -0,188 1,480 26,723 24,444 12,125 3,118 -3,872 23,038 2 1,005 0,791 0,493 0,134 -0,148 1,153 25,648 19,599 10,685 3,034 -3,540 21,459 3 1,142 0,681 0,423 0,256 -0,205 1,346 24,060 15,996 9,718 5,874 -6,957 23,988 4 1,100 0,918 0,548 0,418 -0,242 1,342 26,992 20,656 11,770 7,891 -5,783 22,735 Aggressive 1,361 1,054 0,830 0,430 -0,090 1,451 28,988 23,877 18,923 7,452 -1,539 18,580 C-A -0,069 -0,139 -0,270 -0,290 -0,098 -1,222 -2,400 -4,094 -3,949 -1,123 𝛽!"#$ 𝑡(𝛽!"#$) Conservative -0,032 0,176 0,187 0,063 0,155 -0,188 -0,682 4,775 4,121 1,418 3,263 -2,973 2 0,051 0,216 0,135 0,210 0,032 0,019 1,315 5,458 2,985 4,834 0,772 0,357 3 0,220 0,229 0,167 0,037 -0,043 0,263 4,715 5,475 3,908 0,860 -1,481 4,763 4 0,142 0,333 0,069 0,113 0,005 0,138 3,553 7,639 1,501 2,165 0,113 2,373 Aggressive -0,023 -0,073 -0,168 -0,130 -0,130 0,107 -0,489 -1,675 -3,893 -2,289 -2,266 1,397 C-A -0,010 0,248 0,355 0,192 0,285 -0,179 4,378 5,472 2,665 3,331

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