Choosing Factors for the Vietnamese Stock Market 1

In this paper, we test the applicability of different Fama-French (FF) factor models in Vietnam, investigate the value factor redundancy and examine the choice of the profitability factor. Our empirical evidence shows that the FF five-factor model has more explanatory power than the FF three-factor model. The value factor remains important after inclusion of profitability and investment factors. Operating profitability performs better than cash and ROE profitability as a proxy for the profitability factor in the FF factor modeling. The value factor and operating profitability have the biggest marginal contribution to a maximum squared Sharpe ratio for the five-factor model’s factors, highlighting HML non-redundancy in describing the stock returns in Vietnam.


Introduction
Motivated by the recent Fama and French's (2018) analysis of a metric for ranking asset pricing models, our paper examines the Fama-French (FF hereafter) multifactor models (Fama andFrench, 1993, 2015) in asset pricing for the equity market of Vietnam.This new approach is supposed to overcome the challenge in choosing the best model among competing models with different factors in light of different anomalies previously discovered in international markets.This study adds to current literature further empirical evidence from a developing country that the FF five-factor model (Fama and French, 2015) outperforms the traditional FF three-factor model (Fama and French, 1993), which is consistent with Fama and French's (2017) findings in the stock markets of 25 developed countries.However, our findings are contrary to Fama andFrench's (2015, 2018) conclusion about the redundancy of the value factor (i.e. the book-to-market ratio) in the new five-factor model and the superiority of the cash profitability factor as the variable used to construct profitability factors.
This study aims to add to the international empirical literature on asset pricing tests with a detailed investigation of the Vietnamese stock market, the youngest in the ASEAN region, where the economy has gone through a massive privatization process over the past decade.Our paper entails a study of all major asset pricing models, both traditional and new, for the fast-growing market of Vietnam that features different financial market development conditions as well as a different political system.It is crucial to test this market as an example of the emerging stock market in order to come up with the conclusion of whether the FF (2015) five-factor model's superior performance is consistent regardless of the capital market development stage, economic conditions and political system.
Over the past 20 years of the FF three-factor model, it has become clear that there is a wide array of asset pricing anomalies that these models cannot explain.Among the anomalies -such as momentum (Jegadeesh and Titman, 1993), return reversal (Huang, Liu, Rhee and Zhang, 2010), liquidity risk (Pastor and Stambaugh, 2003) and idiosyncratic volatility (Ang, Hodrick, Xing, and Zhang, 2006) -there are profitability and investment patterns that burden different models from explaining the cross-sectional variation in expected returns (Hou, Xue & Zhang, 2015;Novy-Marx, 2013;Titman et al., 2004).Hou et al. (2015 and2019) provide evidence that the q-factor model (with profitability and investment factors) outperforms the FF three-factor (1993) and Carhart four-factor (1997) models in explaining the returns of a broad list of anomalies.
The new five-factor model (Fama and French, 2015) tries to explain the relationship between these new variables and stock expected returns from the dividend discount model perspective and the valuation theory.Fama and French (2015) suggest using profitability and investment factors, in addition to existing factors (market, size and value), to capture patterns in average stock returns.Fama and French's (2015) findings also suggest that the value factor (i.e. the bookto-market ratio) is redundant for explaining returns in the five-factor model that performs better in terms of describing the expected stock returns.
However, when testing on international markets, Fama and French (2017) find evidence that the five-factor model performs better in North America and Europe and for big stocks.Their findings also suggest that Japanese stock returns have little relation to new factors.Cakici (2015) reports similar results.Cakici compares the three-factor, four-factor and five-factor models on 23 developed stock markets and finds strong evidence for the five-factor model in North America, Europe and the global market.The author concludes that with the inclusion of the two new factors, the value factor becomes redundant in North American, European and global portfolios, but not in the Asia Pacific region.Hence, it is more appropriate to assess the performance of the FF five-factor model at the country or regional level . Fama French (2018) argue that the performance of the five-factor model is sensitive to the choice of the profitability factor, which improves the description of average portfolio returns.They provide evidence that cash profitability (Ball et al., 2015) would be more appropriate than operating profitability in the five-factor model.On the other hand, Hou, Mo, Xue and Zhang (2019) suggest that the qfactor model outperforms the FF five-factor model (2015).Fama and French (2018) using the maximum squared Sharpe ratio of intercepts and a model's factors (Barillas and Shanken, 2017) document the superiority of the cash profitability over operating profitability in the five-factor modeling.
Furthermore, their results provide evidence that the value factor adds no marginal contribution to the maximum squared Sharpe ratio of the five-factor model's model with the cash profitability factor.
Little, if any, has been published on the choice of the value and profitability factors for an emerging market and the explanatory power of the FF five-factor model.Heaney, Koh and Lan (2016) findings show that the correlation between asset returns and market-to-book firm characteristic is sensitive to an asset pricing model used in risk adjustment and this firm property is absorbed by the FF fivefactor model, suggesting the latter model might be a better choice for asset pricing tests for the Australian equity market.Yet, there is no research exploring the question of the choice of factors in FF multi-factor models over the traditional models for an emerging market; hence, this paper addresses this gap in the literature.
Despite the considerable literature on emerging asset pricing with CAPM, we know of limited study that has applied the three-factor model to emerging markets.
Notably, there is a study on ASEAN markets that uses Fama-French three-factor model in the analysis of five markets, namely Malaysia, Singapore, Thailand, Indonesia, and the Philippines (Nartea, Bert and Lee, 2011).By providing evidence of a positive relationship between idiosyncratic volatility and stock returns in Malaysia, Singapore, Thailand and Indonesia, the authors claim that generalizing empirical results obtained in developed stock markets to new and emerging markets could be potentially misleading.Nartea, Wu and Liu (2013) also suggest verifying the findings evident in developed countries for emerging markets at a country level due to distinctive features of each country when analysing idiosyncratic volatility for the Chinese stock market.There are other papers that deal with the asset pricing issue in Asian markets.Momentum and information uncertainty have been identified as a pricing factors (Cheema and Nartea, 2014).Volatility or MAX effect are also under the three-factor model's analysis for Hong Kong (Nartea, 2013) and South Korean markets (Nartea, 2014), respectively.There is no evidence of the superiority of the newly established fivefactor model (Fama and French, 2015) or any investigation on a factor modeling in a setting for a country in Asia.Our paper provides new evidence on the value factor non-redundancy, operating profitability (Novy-Max, 2013) supremacy and Fama-French five-factor model superiority for the region.
Literature studying Vietnam's stock market is sparse.Fang, Wu and Nguyen (2017) study the three-factor model for the stock market in Vietnam using idiosyncratic risk-sorted portfolios.Notably, they only test the three-factor model on portfolios formed on size and book-to-market.While their study finds support for the three-factor model, the methodology of creating three factors does not follow Fama and French's (1993) methodology.In addition, their model's test results suggest that size and value factors fail to explain the returns of valueweighted portfolios sorted on idiosyncratic risk.As with most findings in the finance literature, some studies also document other capital anomalies, such as liquidity, in Vietnam.Batten et al. (2014) show a positive relationship between liquidity and Vietnamese stock returns during the global financial crisis.
There also has not been much research in the context of state ownership and stock returns, which we consider as an important factor for a transitional economy, like Vietnam, that is not fully integrated with the global financial market.Empirical studies provide mixed or contradictory evidence from developed countries, developing markets or transitional economies. 2  Our research deals with the following questions: 1) Which multi-factor model (FF three-factor, FF four-factor or FF five-factor) best describes the behavior of the stock market of Vietnam? 2) Does the value factor become redundant for explaining the stock returns in a developing economy after including new factors into the asset pricing model?3) Is the new five-factor model (Fama and French, 2015) sensitive to the choice of the profitability factor in the context of the 2 Fama and Jensen (1983) show that an increase in managerial ownership would lead to increased entrenchment of managers.McConnell and Servaes (1990) and Cornet (2010) analyze the linkage between ownership structure and the performance of firms (measured by ROA, ROE).Lin and Zhang (2009) provide evidence that the "Big Four" state-owned commercial banks in China are less profitable and less efficient and have a lower quality of assets than other types of banks.
Vietnamese market?4) How do the asset pricing models perform under different ownership structures?
Our study makes four contributions to the current asset pricing literature.First, this study reveals new evidence on the forecasting power of the FF factor models in the context of an emerging stock market featuring state dominant role in the society.We present further evidence supporting Fama and French's (2017) claim about the superiority of the five-factor model for a liberalized market where a country is dominated by individual investors.
Second, the paper provides further evidence on the controversy regarding the redundancy of the value factor in the presence of profitability and investment factors in the model (Fama and French, 2015, 2017, 2018;Cakici, 2015, Chiah et al., 2016).Our results urge the need of developing market verification of results evident in developed countries.
Third, this paper provides new evidence on the controversy regarding the choice of a profitability proxy to construct the profitability factor in the five-factor model (Fama andFrench, 2017, 2018;Ball et al., 2015;Hou, Mo, Xue and Zhang, 2019;Novy-Max, 2013).
Lastly, this study reveals further findings on the performance of the asset pricing models using different profitability measures for state ownership of Vietnamese listed firms..The remainder of this paper is organized as follows.In Section 2, we provide an overview of the Vietnamese stock market, with a description of its distinctive features.Section 3 describes the data and methodology used in our analysis, including factor design and construction of test portfolios, with a detailed analysis of the state ownership-stock return relationship in Vietnam.Section 4 delivers empirical results on the FF five-factor model (2015) as compared with the threefactor framework (Fama and French, 1993), with a focus on the state ownership structure of listed firms.Section 5 verifies whether the value factor is redundant for explaining expected stock returns in Vietnam.Section 6 investigates different measures for a profitability factor in the five-factor model.Section 7 offers further results of the value factor non-redundancy and the choice of a profitability factor.Section 8 concludes our findings.

Vietnam's stock market and its unique features
The Hochiminh Stock Exchange, under a government initiative, was established on 28 July 2000.During the 2000-2005 period, the stock market had very few listings.In 2005, there were 44 listed companies with a total market capitalisation of VND 5 trillion.With the establishment of the Hanoi Stock Exchange in the same year and the country's favourable economic conditions, by the end of 2009 there were 541 listed companies with total market capitalisation of VND 620.5 trillion, equivalent to 40% GDP.During that year, Vietnam established a third stock market (UPCoM) to provide a pathway for small companies to trade their shares on an exchange, thus limiting the over-the-counter market and thereby increasing transparency and liquidity for Vietnamese firms.
After persistent and robust growth during the 2006-2007 period, the stock market of Vietnam was hit by the global financial crisis and affected by the government's tightening monetary policies to control inflation and stabilize the economy, leading to a continuous and significant drop in stock prices.The stock market of Vietnam has been gradually stabilizing since 2008.
The first listed companies were primarily state-owned enterprises (SOEs).
According to the Business Innovation and Development Committee, in August 2009 the country had more than 1500 enterprises fully owned by the state.With the goal to restructure Vietnam's economy and increase the efficiency of SOEs' performance through privatization of government-owned companies, 3 the state gradually sold its stake in SOEs through initial public offerings (IPOs) and listing on stock exchanges.However, the government still keeps the largest ownership proportion in many listed companies.Motivated by this idea, we pay special attention to SOEs and consider them as a separate group in our analysis.This paper presents new empirical evidence on the relationship between a stateownership structure and stock returns in a country with distinctive political and economic regimes.The effects of state ownership are important for policymakers who focus on stock market regulation and for investors who want to understand stock price behavior for portfolio management.

Data
The analysis in this study is conducted for all common stocks traded on the Hochiminh and Hanoi Stock Exchanges (inclusive of UPCoM) at a monthly frequency from August 2007 to July 2015. 4The source of data is the Thomson Reuters (Datastream) database, which includes daily data of adjusted closing prices, trading volume, market-to-book ratios, market capitalisation, total assets as well as annual information of revenue, administrative expense, interest 3 State-owned banks operated less profitably, held less core capital and had greater credit risk than private firms, but had more stable operations during unfavorable market conditions and survived better during the financial crisis (Cornet, 2010). 4For UPCoM, stocks prices are obtained as at the end of 2014.expense, cost of goods sold and state ownership.An interbank offer rate is also extracted monthly from Datastream and used as the risk-free rate in this study to be consistent with previous studies on Vietnam.
To be in the sample for the analysis, all stocks must have daily returns of no greater than 50% in absolute terms and monthly returns of no more than 200% to avoid stocks with abnormal trading or price errors on Datastream system.To reduce the impact of infrequent trading, all stocks with no return data for the previous 10 consecutive business days are excluded from the analysis in that specific month.In addition, stocks with no return data for more than 10 business days in a month are omitted from the sample during that month. 5We also exclude all stocks with negative book-to-market ratios from the sample to be consistent with Fama andFrench's (1993, 2015) methodology.To be in the sample on a specific date, in addition to having required accounting data 6 as prescribed by Fama andFrench (1993, 2015), companies must have a valid trade and not have been delisted prior to the formation period.
Table 1 presents the coverage of stocks used in our sample.Hence, we have 135 stocks in December 2007 and 438 stocks in 2015, accounting for 1,113,948 daily and 50,112 monthly observations in total.Our sample covers about 60% of the population of ordinary stocks in the Datastream database and represents 89% and 73% of the market in terms of total trading value and market capitalisation, respectively, over our sample period. 7On average, we have 56 state-owned 5 Angelides (2010) removes all the stocks that have fewer than five observations during a month. 6To reduce the noise in computing variables, we exclude several stocks with extreme values of book-to-market ratio (higher than 8.0), operating profitability ratio (more than 100%) and investment ratio (higher than 4.0). 7It is important to note that we do not exclude stocks out of the entire sample completely.We only omit them for the specific month that they have inadequate trading (no return data for the previous enterprises (SOEs) in a year, equivalent to 16.32% of average annual stock in our sample.
[Insert Table 1 here] By applying the Fama andFrench (1993, 2015) methodology, for inclusion in a portfolio in July of each year (annual rebalancing) a stock must have market equity data for December of the previous year and June of the current year; a nonmissing (positive) book-to-market ratio for December of the previous year; nonmissing revenues and at least one of the following: cost of goods sold, sales, general and administrative expenses, or interest expense at the end of the fiscal year (December) ending in the previous year; and total assets data at the end of the fiscal year ending in year t-1 and t-2.

Fama-French five factor construction
We follow the FF methodology in constructing risk factors (Fama andFrench, 1993, 2015).

Market factor (MKT)
MKT is the average excess return on a market portfolio constructed from our sample of stocks.MKT is value-weighted using market capitalisation as at the end of month t-1.The excess return of each stock is calculated as a monthly percentage change in a stock's price less the interbank offer rate in Vietnam.

Size factor (SMB)
To form a size portfolio in July of year t, stocks are sorted by the market equity as at the end of June of each year t.The stocks are allocated to two size portfolios 10 consecutive business days or no return data for more than 10 business days in total during a month) and include them again whenever they satisfy our criteria on trading activities.
(small and large), depending on whether their market equity is above or below the median.These two portfolios are annually rebalanced, with average returns calculated under a value-weighted approach.The size factor (SMB) is the return difference between the average returns on the small firms' portfolios and the average returns on big firms' portfolios.

Value factor (HML)
The book-to-market sort uses the book-to-market ratio for the fiscal year ending in calendar year t-1 (at the end of December of t-1).Three portfolios are formed using breakpoints at the 30th to 70th percentiles.These portfolios are annually rebalanced, with average returns calculated under a value-weighted approach.
From the independent sorting, we construct six portfolios from the intersection of two size and three book-to-market portfolios.The value factor (HML) is the return difference between the high book-to-market portfolios and the low book-to-market portfolios.

Operating, cash and ROE profitability factor (RMW, RWMC and RMWR)
RMW uses accounting data for the fiscal year ending in calendar year t-1.For portfolios formed in June of year t, operating profitability is defined as annual revenues minus cost of goods sold, interest expense, and selling, general and administrative expenses, all divided by book equity (Fama and French, 2015;Novy-Marx, 2013).Three portfolios are formed using the breakpoints of 30% and 70%.These portfolios are annually rebalanced, with average returns calculated using the value-weighted approach.We construct six portfolios from the intersection of two size and three profitability portfolios.The RMW factor is the return difference between the average returns on the high (robust) profitability portfolios and the average returns on the low (weak) profitability portfolios.
We also use cash profitability (RMWC) suggested by Fama and French (2018) and Ball et al. (2015) and the ROE profitability (RMWR) of Hou, Mo, Xue and Zhang (2019) in our factor testing to determine which profitability definition would be best to use in the FF five-factor model to describe the stock returns.However, to make the analysis on different profitability factors more comparable, we use oneyear-lagged book equity to calculate ROE profitability8 and conventional double (2x3) sorting on size and profitability.

Investment factor (CMA)
For portfolios formed in June of year t, CMA uses the change in total book equity in the fiscal year t-1 compared with the fiscal year t-2.Three portfolios are formed using the breakpoints of 30% and 70%.These portfolios are annually rebalanced, with average returns calculated using the value-weighted approach.We construct six portfolios from the intersection of two size and three investment portfolios.The CMA factor is the return difference between the average returns on the conservative (low) investment portfolios and the average returns on the aggressive (high) investment portfolios.
Table 2 presents the summary statistics of all factors.Panel A shows that the factors have a negative market premium, consistent with Fang et al. (2017).The market premium (mean MKT) for Vietnam is -0.65% per month, the size premium (mean SMB) and the value premium (mean SMB) is 0.38% and 0.61%, respectively.
The monthly premium for profitability and investment has the value of 0.34% and 0.095% during the 2008-2015 period.
[Insert Table 2 here] Panel B of Table 2 shows the correlations between the factors.Consistent with Fama and French (2015), profitability (RMW) is negatively correlated with all factors.There is a negative and high correlation between RMW with SMB and HML, suggesting smaller-sized companies tend to be high book-to-market (B/M) firms and they seem to be less profitable.There is a positive and high correlation between HML and CMA, indicating companies with high book-to-market (B/M) values tend to be low-investment firms.While RMW and CMA are each negatively correlated with MKT as Fama and French (2015) report, there is no correlation between SMB and MKT, similar to that of Australia (Chiah et al., 2016).

Factor model tests
Following Fama and French (2018), we apply two approaches to deal with our task of the factor choice.

Left-hand-side (LHS) approach for nested models
The first approach, LHS approach, is used to assess competing models with distinct factors (i.e., nested models) to capture excess returns of different sets of LHS stock portfolios.
Given it is imposible to make meaningful statistical inference of 316 factors (Harvey et al., 2015), Fama and French (2018) suggest using a limited number of factors in a model testing and a short list of model alternatives for comparison purposes.Hence, we investigate the performance of three multi-factor models of Fama andFrench (1993, 2015): Three-factor model: where  , is the returns of portfolio p in month t;   ,   ,   and   are the factor-mimicking portfolios for size, value, profitability and investment of Vietnamese equities; and   is the monthly excess returns on Vietnam's stock market portfolio.
We investigate the explanatory power of the new five-factor model on the variation of stock returns by looking at the average adjusted R 2 , GRS test statistics and its p-value (Gibbons, Ross and Shanken, 1989), the average value of absolute intercepts, A||, the Sharpe ratio for the intercept, Sh(), the maximum squared Sharpe ratio for intercepts, Sh 2 () (Fama and French, 2018), and the maximum squared Sharpe ratio for a model's factors, Sh 2 (f), (Barillas and Shanken, 2017).
GRS tests whether the regression intercepts are jointly equal to zero.As Merton (1973) suggests, the intercept is indistinguishable from zero if an asset pricing model completely captures expected returns.According to Lewellen et al. (2006), the smaller Sh(), the fewer unexplained average returns; hence, the better the model.In the same manner, we use average absolute intercepts, A||, of the portfolios under analysis to assess the performance of the models.The model that best describes the variation in stock returns across portfolios is the one that provides the lowest value of A||.Fama and French (2018) suggest to use the maximum squared Sharpe ratio of time-series regression's intercepts, Sh 2 (), and the maximum Sharpe ratio for a model's factors, Sh 2 (f) to overcome the limitation of other asset pricing tests when dealing with the issue of varying inferences across sets of LHS portfolios.Sh 2 () and Sh 2 (f) assist us in judging the competing factor models and can be used as ultimate metrics for ranking asset pricing models.
The best model is the one that provides the lowest Sh 2 () and whose factors have the highest Sh 2 (f).

Right-hand-side (RHS) approach for non-nested models
The second approach, RHS approach, is applied to spanning regressions to assess whether a specific factor should be added to a (non-nested) model by looking at its contribution to an explanation of the average portfolio excess returns provided by a model.The marginal contribution of a factor to a model,  2 /sd 2 (e), is calculated as the ratio of the squared intercepts in a spanning regression of the factor on the model's remaining factors and the residual variance of the same spanning regression (Fama and French, 2018).A factor that has high value of  2 /sd 2 (e) compared with other factors in a model is considered to have a significant contribution to the model in capturing stock returns.This approach assists us in estimating the role of a factor in a specified model and deciding on the relevancy or redundancy of a factor.
Since there has been controversy in the value factor role and the choice of the profitability measure, RHS approach (Barillas and Shanken, 2017) is particularly useful in investigating the value factor and proxies for the profitability factor.

Left-hand-side (LHS) portfolio characteristics
We form three sets of 3x3 portfolios to test asset pricing models.All stocks are allocated to three different portfolios at the end of December of each year based on market capitalisation using breakpoints at the 33rd and 67th percentiles.In the second sort, we further sort each size portfolio into three sub-portfolios based on book-to-market, profitability and investment.The average portfolio monthly returns are calculated from July of year t+1 using a value-weighted approach.The portfolios are rebalanced on an annual basis.
As we also want to investigate the return and other characteristics of state-owned equities (SOEs), we form two sub-portfolios for each size portfolio using an approach similar to the above, with one sub-portfolio containing all firms that have a government stake in company's shares and the other sub-portfolio where the firms are entirely private.
Table 3 reports the characteristics of the single-sorted portfolios.The highestearning portfolio is the one with average book-to-market.The loser portfolio over the sample period is the portfolio with an average investment ratio or with a weak profitability ratio.
[Insert Table 3 here] The results in Table 3 provide the 3x3 single-sorted portfolio characteristics consistent with factor characteristics in Panel B of Table 2. Firms with low bookto-market ratio have high profitability and invest more than those with low bookto-market values.
One interesting finding from our ownership structure analysis shows that SOEs have significantly higher average excess returns, though they invest less aggressively and have lower profitability and book-to-market ratios compared with private (non-SOE) firms.One potential explanation is that investors prefer SOEs that are backed by government and have more stable operations during unfavorable market conditions and survived better through the economic recession (Cornet, 2010).
Table 4 provides detailed summary statistics for three sets of nine double-sorted portfolios to be used in asset pricing tests.The two last columns show the sort on size and state-ownership structure of the firm.Panel A shows the monthly excess returns for each portfolio.Panel B reports the average B/M ratio for a portfolio, while Panels C and D show the profitability and investment ratios of each portfolio.

[Insert Table 4 here]
Panel A of Table 4 reports no obvious univariate relationship between the average excess returns and the B/M, profitability and investment of listed firms across all portfolios.Fama andFrench (2015, 2017) report that the five-factor model fails to capture the low average return on small stocks.
The size effect is found in all portfolios, except for the return characteristics of large-cap firms with an average book-to-market ratio, with an average profitability ratio and a high investment ratio (Panel A of Table 4) as well as the investment characteristics of portfolios sorted on size-profitability (Panel D of Table 4).Small firms have higher average returns and B/M values despite the evidence that they are, on average, less profitable and invest less than large-cap firms. 9The winner portfolio for each set of sorting would be all small-cap firms, either with average B/M, high profitability or low investment ratio or belong to the SOE group.However, the best performer among all portfolios is the small-cap SOEs with an average excess return of 1.23% per month.Multivariate regressions would provide a clearer picture on the average return behavior in the Vietnamese market.
9 Except for the cases when small-sized SOEs invest more than large-cap SOEs.
We also perform sorting on the state holdings of a firm and suggest that there is a return premium for state entities, with small-cap firms having the highest returns.
There is a size effect in all characteristics of portfolios sorted on size-non-SOEs.
The portfolio of private firms has the higher B/M, portfolio and investment ratios compared with that of state-owned entities (except the small-sized portfolio sorted on profitability and investment).
There is a strong evidence of the similar size patterns of different characteristics for SOEs and non-SOEs except for investment characteristics of portfolios based on ownership sorting.
Although the FF sort does not provide much information on the univariate characteristics of portfolios sorted on size and B/M, profitability and investment, our sort on ownership structure provides some interesting findings.Profitable private firms (non-SOEs) tend to provide lower returns to investors than their counterparts.Mid-and large-cap non-SOEs tend have higher profits and invest more aggressively than SOEs of the same size.

Empirical results on asset pricing tests
Table 5 reports the summary results of asset pricing tests.For brevity, we report the average adjusted R-squared, GRS test statistics and its p-values, the average values of absolute intercepts, Sharpe ratios for intercepts, the maximum squared Sharpe ratio for intercepts and model factors (Fama and French, 2018).The tests report the results of three asset pricing models, namely FF three-factor, FF fourfactor (i.e., FF five-factor without HML) and FF five-factor.
[Insert Table 5 here] Overall, the test statistics show that the new model can account for more asset pricing anomalies than the traditional asset pricing models of CAPM, the three- 10 In our unreported results of the maximum squared Sharpe ratio for intercepts with the cash profitability factor, we also find supporting evidence of the Fama-French five-factor model's superiority for all 6 portfolios sorted on size and state ownership as well as for 3 SOE portfolios sorted on size.Three-factor model is preferred over other models for non-SOE portfolios sorted on size.
Notably, Fama and French (2015) report that the five-factor model produces lower GRS statistics than the original three-factor model (the lowest GRS test statistic as compared with the three-factor model is produced by the five-factor model in the portfolio sorted on size and profitability).Our results in Table 5 show that the GRS test statistic is at its lowest of 0.78 for the portfolio sorted on size and investment (Inv) with the highest p-value of 0.64 for GRS.The average value of absolute intercepts also shows that the largest improvement of the five-factor model is produced for the size-invesment portfolios, consistent with GRS test values.Additional tests are conducted to decide on the explanatory power of Fama-French multi-factor models: the maximum squared Sharpe ratio for intercepts (Sh 2 ()) and the maximum squared Sharpe ratio for factors (Sh 2 (f)).Both tests show the superiority of the five-factor model consistent over all types of portfolio testing, with the exception for the SOE portfolios sorted on size.Overall, the results of Table 5 show that the five-factor model is the preferred model for all portfolios sorted on size and a combination of B/M, profitability and investment, taken together or standalone, and for the portfolios sorted on size-SOE.Fama and French (2015) report that HML is redundant for describing U.S.
average returns during the 1962-2013 period, but it is not redundant for explaining average returns in any region during the 1990-2014 period (Fama and French, 2017).They observe a strong positive relationship between the book-tomarket ratio and average returns of Japanese equities.Consistent with Fama and French's (2017) findings in Europe, Japan and the Asia Pacific region, we provide evidence that HML is not redundant in Vietnam.Our results on the Vietnamese stock market provide evidence that without the value factor (HML), the asset pricing model with only market, size, profitability and investment factors performs worse than the traditional three-factor model with market, size and value factors (Panels A, D, E and F).The value factor became even more important under the five-factor model (Panel D).The five-factor model minimizes the intercept effects for all portfolios through a large difference in average mean intercepts between the four-factor and five-factor models.Hence, we can suggest that some anomalies can be eliminated from previous versions of asset pricing models by including the value factor.There is only one portfolio, the SOE portfolio sorted on size, that has no obvious difference in average absolute intercepts between the four-and fivefactor models.However, the maximum squared Sharpe ratio provides evidence that the five-factor model is the best one to explain the SOE returns.Table 7 will provide further investigation of the value factor redundancy.
Overall, Table 5 shows that the five-factor model performs relatively well in explaining the expected returns of 27 portfolios with each 9 portfolios sorted on either book-to-market, profitability or investment.GRS fails to reject all of the models, providing the preference for the five-factor model as the best one among all tested.The maximum squared Sharpe ratio for intercepts gives a preference to the five-factor model with the exception of the non-SOE portfolios sorted on size.
The maximum squared Sharpe ratio for factors shows that the five-factor is superior to three-and four-factor models in explaining the stock returns.

Is the value factor (HML) redundant?
As our previous asset pricing tests suggest, the FF five-factor model works best and has superiority over the three-factor model when we include HML in the model.To further test our hypothesis of HML redundancy and to see the relationship of the factors, we run a regression of each factor on the other four remaining to find whether the explanatory variables can absorb the factor or not.  2 where the correlation between HML and CMA is found to be highest, the average HML returns are captured by the exposures of HML to CMA and MKT.However, unlike Fama and French's results that show CMA and RMW absorbing all the effects of HML, our test reports that the average CMA return is captured to a greater extent by its exposure to HML; RMW cannot absorb HML.
Notably, we find a similar controversy about the RMW and SMB with the largest negative correlation (Panel B of Table 2).Table 6 shows that in non-nested multivariate regression, RMW largely absorbs the SMB effect.Hence, the evidence suggests that in Vietnam, adding HML improves the mean-variance efficient tangency portfolio produced by combining the risk-free asset, the market, size, profitability and investment portfolios.One possible explanation for the value factor redundancy in Vietnam can be the strong correlation between the profitability and value factors (-0.49) as opposed to the US market (Fama and French, 2015).Cakici (2015) also highlights the similar evidence on the correlation of these two factors for Japan which is different from other regions in the world.

[Insert Table 6 here]
To further verify our findings on the HML redundancy, we follow Fama and French (2018) 5. Therefore, the value factor is confirmed to be non-redundant in the factor models for the Vietnamese stock market.

Operating, cash or ROE profitability?
Fama and French (2018) provide evidence that the five-factor model (Fama and French, 2015) is sensitive to the choice of the profitability factor.More specifically, the cash profitability suggested by Ball, Gerakos, Linnainmaa and Nikolaev (2015) improves the description of the average returns for portfolios of different sorts.
Cash profitability (RMWC) is the cash profits without accruals (i.e., before interest) scaled by total assets in the 2x3 portfolios sorted on size and profitability.
Using cash profitability (Ball et al., 2015), Fama and French (2018) try to explain small stocks with returns that behave like those of firms that invest a lot despite low profitability (Fama andFrench, 2015, 2017).Although we do not have a similar issue, we are interested in the choice of profitability factor that would be best for the five-factor model to explain the variation in the Vietnamese stock market.Table 7 shows the hypothesis that higher profitability leads to higher expected returns is only correct for large stocks with ROE profitability (Hou, Mo, Xue and Zhang, 2019).This hypothesis is also true for small and medium equities if we use cash profitability (Ball et al., 2015).The size effect is evident in returns of all double-sorted portfolios, except for portfolios with average operating profitability (Novy-Max, 2013), average cash profitability (Ball et al., 2015) and low profitability (Hou, Mo, Xue and Zhang, 2019).
[Insert Table 7 here] Panel B of Table 7 shows the identical patterns for B/M regardless of the choice for profitability factor, that is, smaller firms tend to have higher book-to-market ratios.Panel C of Table 7 shows an opposite size pattern for cash profitability as compared with portfolios calculated using operating and ROE profitability.One explanation would be that small firms rely more on equity capital and have lower access to borrowing.Hence, we observe such contradictory results.
Table 8 is the direct comparison of the FF multi-factor model performance when  8) and RMW is superior to all other models when it comes to explain the variation of each of the three sets of porfolios sorted on size and a combination of value, profitability and investment (Columns B/M, Profit and Inv of Sh 2 () in Table 8).
[Insert Table 8 here] Despite the results of the aforementioned tests give preference to the FF fivefactor model over all others under analysis, we find contradicting results in the choice of profitability factor when turning our attention to the comparison of the four-factor models.Sh 2 () indicates the superiority of cash profitability (RMWC) when testing all 27 portfolios but not for each set of double-sorted portfolios (the FF 4-factor model of Columns B/M, Profit and Inv in Table 8).
What is consistent across all tests is the results showing that regardless of the profitability factor choice, the superiority of the five-factor model in explaining the average returns as compared with the four-factor models in Table 8 across all profitability factors.
To further testify our results on profitability measures, we conduct a test of profitability factors similar to the test applied to the value factor for redundancy.
Given inconclusive results over the choice of profitability factors in Table 8, Table 9 with  2 /sd 2 (e) confirms the superiority of the operating profitability over the cash and ROE profitability factors, with the RMW intercepts having slightly more incremental information about the average returns under the tests.Operating profitability (RMW) is likely to perform better than cash profitability (RMWC) and ROE profitability (RMWR).
[Insert Table 9 here] Similar to Fama and French (2018), we provide evidence that changing the profitability from an operating one to cash profitability does not change the conclusion that all the factors have explanatory power.In addition, we provide evidence that the returns of RMWR are largely absorbed by SMB and HML.
Although we see strong negative slopes on SMB for RMW under both tests with RMWC and RMWR, as discussed earlier, SMB cannot absorb RMW as shown in the results of Table 6.

Robustness tests
By re-testing the five-factor model with cash profitability and ROE profitability as profitability proxies (Table 10), we reconfirm the HML non-redundancy.11Both panels of Table 10 report that the intercept in the spanning regression using cash profitability (RMWC) and ROE profitability (RMWR) to explain HML is 0.01% per month (t=1.63) and 0.01% per month (t=1.50), the highest value for the t-statistics among all the models under both profitability versions.
[Insert Table 10 here] The results of  2 /sd 2 (e) for Panel A provide evidence that the value factor contributes most to Sh 2 (f) of the five-factor model using cash profitability (0.034).
The returns of SMB and CMA are absorbed by strong positive slopes on HML.The cash profitability is another significant marginal contributor to Sh 2 (f) with  2 /sd 2 (e) of 0.029.The returns of MKT are absorbed by this factor.
Panel B provides persistent results for HML non-redundancy with the value factor having the highest marginal contribution to Sh 2 (f) of the five-factor model using ROE profitability (0.027).RMWR does not contribute much to Sh 2 (f), supporting the findings in Table 8.SMB can be well explained by RMWR.The returns of CMA and RMWR are absorbed by MKT.The MKT, RMWR and CMA returns are absorbed by strong slopes on HML.
The values of Sh 2 (f) as indicated in Tables 6 and 10 for the five-factor model with RMW, RMWC and RMWR are 0.073, 0.062 and 0.037, respectively.These results further indicate the preference for the operating profitability (RMW) when testing the maximum squared Sharpe ratio for the five-factor model's factors with different profitability proxies.

Conclusion
In this paper, we empirically examine three FF factor models for the Vietnamese stock market during the 2008-2015 period.Similar to Japan (Fama and French, 2017), the GRS test cannot reject all the asset pricing models in their power of capturing the average returns of Vietnamese equities.Test results point out the superiority of the FF five-factor model over the three-factor and four-factor models in explaining the returns of portfolios sorted on size and a combination of book-tomarket, profitability and investment.While the three-factor model is a preferred model in explaining the returns of non-SOEs sorted on size, the FF five-factor model is still superior for SOE sorted on size.Our study also reports evidence of the return premium on state-owned equities in Vietnam; that is, state-owned enterprises have significantly higher average returns than private firms, although the former invest less aggressively and have lower profitability and book-tomarket ratios than private (non-SOE) firms.Profitable private firms (non-SOEs) tend to provide lower returns to investors and invest more aggressively than SOEs.
We also show that investors holding the portfolio with small-cap SOEs during the sample period would bear highest returns during the sample period.The loser portfolio over the sample period is the one that contains large-sized stocks with an average investment ratio.
Our findings suggest that the value factor (HML) has a relationship with portfolio returns, and its effect is not absorbed by profitability and investment factors newly included in the traditional three-factor model (Fama and Fama, 2015).In contrast to Fama and French (2018) findings on HML value, it is not redundant in the Vietnamese stock market after considering different measures for the profitability factor.The value factor and operating profitability have the biggest marginal contribution to the maximum squared Sharpe ratio for the five-factor model's factors (Barillas and Shanken, 2017), implying HML is important in describing the stock returns in Vietnam.
The operating profitability (Novy-Max, 2013) used in the FF five-factor model is likely to perform better than cash profitability (Ball et al., 2015) and ROE profitability (Hou, Xue and Zhang, 2015;Hou, Mo, Xue and Zhang, 2019), indicating RMW intercepts have more incremental information about the average returns.All the tests provide consistent results on the superiority of the FF fivefactor model over other traditional asset pricing models, regardless of the profitability factor choice.In July of year t, we form two size portfolios based on market capitalisation as at the end of year t-1 and use the median as t h e breakpoint.These two portfolios are calculated using monthly returns and rebalanced annually.The size factor (SMB) is the return difference between the average returns on the small firm portfolios and the average returns on t h e portfolios containing large firms.We then construct six portfolios from the intersection of two size and three book-to-market portfolios (SL, SN, SH, BL, BN, BH) based on the 30th and 70th percentiles.The value factor (HML) is the return difference between the average returns on the high book-to-market portfolios and the average returns on the low book-tomarket portfolios.Similarly, we construct six portfolios from the intersection of two size and three profitability portfolios (SR, SN, SW, BR, BN and BW).Profitability factor (RMW) is the return difference between the average returns on the robust profitability portfolios and the average returns on the weak profitability portfolios.Six portfolios are from the intersection of two size and three investment portfolios (SC, SN, SA, BC, BN and BA).
Investment factor (CMA) factor is the return difference between the average returns on the conservative investment portfolios and the average returns on the aggressive investment portfolios.All portfolios are value-weighted and returns are in percentages.MKT is the value-weighted excess return on t h e market portfolio of all sample stocks minus the onemonth interbank offer rate.Statistics reported are the mean, median, standard deviation (st.dev), maximum (max), minimum (min), skewness and kurtosis.The sample is from September 2008 to July 2015.The factors are calculated as follows (Fama and French, 2015) with S and B denoting small-and big-sized portfolios, H, N and L for high, medium and low B/M, R, N and W for robust, medium and weak profitability, and C, N and A for conservative, medium and aggressive investment: The table provides time-series averages of average percentage monthly excess returns, book-tomarket (B/M), profitability (OP) and investment (Inv) ratios in July of year t to June of year t+1 for portfolios formed in December of year t-1 on a single sort of book-to-market, profitability or investment.Portfolio breakpoints are the 33rd and 67th percentiles.Each of the ratios for a portfolio in a given year is the value-weighted average of the ratios for the firms in the portfolios.Firms in the columns Ownership are sorted on (state) ownership structure.Column Low (under Book-to-market) is the characteristics for portfolios of stocks with low book-to-market ratio.
Column Ave shows the characteristics for portfolios of stocks with average book-to-market ratio.
Column High shows the characteristics for portfolios of stocks with high book-to-market ratio.The table provides time-series averages of average percentage monthly excess returns, bookto-market, profitability and investment ratios in July of year t to June of year t+1 for portfolios formed in December of year t-1 on double sort of size and a combination of bookto-market, profitability and investment.The portfolio formation and book-to-market, profitability and investment ratios follow Fama-French (2015) methodology.Each of the ratios for a portfolio in a given year is the value-weighted average of the ratios for the firms in the portfolios.Firms in the columns Ownership are sorted on size and ownership structure.Panel A provides time-series averages of monthly returns in excess of Vietnam's interbank offer rate (in percentages).Panel B, C a n d D show the book-to-market, profitability and investment times-series averages for a portfolio.Column Low (below Book-to-market) shows characteristics for portfolios of stocks sorted on size (Small, Medium and Large) and low book-to-market ratio.
Column Ave shows characteristics for portfolios of stocks sorted on size (Small, Medium and Large) and average book-to-market ratio.Column High shows the characteristics for portfolios of stocks sorted on size (Small, Medium and Large) and high book-to-market ratio.The table provides the summary results of the multivariate regressions for portfolios formed by size and a combination of book-to-market (B/M), profitability (OP), investment (Inv), SOE and non-SOEs.Portfolios are formed in July of year t to June of year t+1 from stock sorted in December of year t-1.The portfolio formation and book-to-market (HML), profitability (RMW) and investment (CMA) factor construction follows Fama-French's (1993, 2015) methodology.Summary results show the average value of all adjusted R-squared and the absolute intercepts (A |α|) of all portfolios from the respective regressions in Panels A to D of Table 6.GRS is the Gibbons, Ross and Shanken (1989) test statistic and its p-value, p(GRS).Sh(α), Sh 2 (α) and Sh 2 (f) are the Sharpe ratio for intercepts, its maximum squared value and the maximum squared Sharpe ratio for the model's factors, respectively.We apply these five tests to all portfolios (All) and portfolios formed by size and a combination of book-to-market (B/M), profitability (OP), investment (Inv).The tests also show the results for the portfolios sorted on size and a combination of SOEs and non-SOEs.The table reports the results of time-series regressions with each of the variables being regressed by the remaining of the five factors.MKT is the value-weighted excess return on the market portfolio, and SMB is average return on the portfolio sorted on size.HML is the value factor with size and book-to-market sort.RMW is the profitability factor.CMA is the investment factor.All factors are 2x3 portfolios constructed using Fama-French's (1993, 2015) methodology.Sh 2 (f) is the maximum squared Sharpe ratio for a model's factors from factor and the four-factor.Consistent withFama and French's results (2015), the five-factor model tested on the Vietnamese stock market performs best in relation to explaining the average returns of three sets of nine portfolios sorted by B/M, profitability and investment (Column All of each panel).The average of adjusted R-squared for all double-sorted portfolios (Column All of Panel A) improves from 89.58% (the three-factor model) to 90.49% (the five-factor model), with the lowest performing (four-factor) model at 89.49% average adjusted R-squared.Our result is consistent with average adjusted R-squared for the Asia Pacific region(Fama and French, 2017).Similar results of superiority of the five-factor model over the three-factor are found for the Australian stock market(Chiah et al., 2016).Looking at each set of portfolios, the five-factor model still outperforms all other models in explaining the expected returns of portfolios with each sorted on size and either book-to-market, profitability or investment.The average adjusted Rsquared for size-B/M sorted portfolios (Column B/M of Panel A), size-profitability portfolios (Column OP of Panel A) and size-investment portfolios (Column Inv of Panel A) is 91.0%, 90.9% amd 89.6% for the five-factor model, respectively.Table 5 shows consistent results of the Fama-French five-factor model's superiority as evidenced in the tests of Panels A to G for all 27 portfolios (Column A of all panels) and for three sets of 9 portfolios with each sorted on size and a combination of B/M (Column B/M of all Panels), operating profitability (Column OP of all Panels) and investment (Column Inv of all Panels).Despite there being different rankings for the three-and four-factor models among the portfolios, all results consistently show the superiority of the five-factor model (Columns All, B/M, OP and Inv of Panel D).In relation to portfolios sorted on state ownership, the obtained results of the average adjusted R-squared for SOEs (column SOE of Panel A) contradict with that of the remaining tests.Although the average value of absolute intercepts, GRS test statistics and its p-value extend the preference to the five-factor model for the size-SOE portfolios, the average adjusted R-squared shows the preference for the four-factor model.Referring to the results of the maximum squared Sharpe ratio for intercepts(Fama and French, 2018), we conclude that the five-factor is the best model to capture stock returns on SOE portfolio sorted on size (Column SOE of Panel F).Referring to the results of non-SOEs, we find that the average adjusted R-squared prefers the five-factor model, but GRS test statistics and the tests for intercepts (Column non-SOE in Panels B, D and E) point out the priority of the three-factor model.Based on the maximum squared Sharpe ratio for intercepts, Sh 2 (), we conclude that the three-factor still takes the place as the best model to explain the non-SOE portfolio sorted on size (Column non-SOE of Panel F).10 We came to the conclusion that the three-factor model best explains the variation in returns of non-SOEs and and the five-factor model is most preferred for all porfolios sorted on size and state ownership as well as SOE portfolios sorted on size from the results of the maximum squared Sharpe ratio for intercepts (Columns SOE and non-SOE of Panel F).
using different profitability ratios.The model withBall et al.'s (2015)  cash profitability factor, RMWC (Panel A), outperforms the model with RMW(Fama and French, 2015; Novy-Max, 2013) and the model with ROE profitability, RMWR(Hou, Xue and Zhang, 2015;Hou, Mo, Xue and Zhang, 2019), in the tests of the average adjusted R-squared performed on all portfolios (Columns All of Panels A, B and C).However Sh(), p-value of GRS, the average value of absolute intercepts, A||, show preference for RMW.The GRS test values for the five-factor model further complicate the analysis providing very low results for size-BM, size-Inv porfolios using operating profitability in Panel C and showing RMWC is the best model among four-factor models.Therefore, we rely on the maximum squared Sharpe ratio, Sh 2 (), to determine which profitability measure suits best for the four-factor and five-factor models.The results indicate RMWC is equally good when testing all 27 portfolios taken together (Column All of Sh 2 () in Table Four-factor model (Five-factor model without HML): , =   +     +     +     +     +  , ,  , =   +     +     + ℎ    +     +     +  ,

Table 6
shows the results of five spanning regressions (in columns) with MKT, SMB and HML, RMW and CMA as the dependent variable in each of the regressions.In the first model where the dependent variable is the return on to deconstruct the maximum squared Sharpe ratio for a model's factors, Sh 2 (f), in Table5by analyzing the extent of marginal contribution of a factor to Sh 2 (f),  2 /sd 2 (e), defined as the squared intercept over the variance of the regression residuals, and t-statisitics for the intercept (t()) in a factor-spanning regression.The factor's intercept () is close to zero and/or the residual standard error, s(e), is large if the factor's expected return is well explained by the remaining factors in a model.Hence, a factor is considered to be redundant if its marginal contribution to a model's maximum squared Sharpe ratio is small.The results of  2 /sd 2 (e) in Table6report that RMW and CML are by far the biggest marginal contributions to Sh 2 (f), which further supports our finding on the value factor in Table

Table 1 . Sample coverage for the Vietnamese stock market
Hou, Mo, Xue and Zhang (2019)mpanies during a year.MCap is market capitalisation in trillions of Vietnamese Dong (VND) as at the end of a year.Value and Volume are annual trading value (in trillions of VND) and trading volume (in millions of shares) of all stocks.OP, CP and RP are the average value of operating profitability ratio, cash profitability ratio and ROE profitability ratio per stock, respectively, usingFama and French (2015, 2018, 2019),Ball et al. (2015)andHou, Mo, Xue and Zhang (2019)profitability definition.INV is the average investment ratio per stock, respectively, as defined usingFama-French methodology (2015).BM is the average book-to-market ratio per stock.SOE is the number of listed companies that have state share of ownership.Data are obtained from Datastream from July 2007 to August 2015.

Table 2 . Summary statistics for Fama-French factors for Vietnamese stocks
Panel A reports the summary statistics for the Fama-French's monthly risk factors.Panel B reports the time-series correlation between the factors.

Table 4 . Characteristics of double-sorted portfolios
Column Weak (under Profitability) shows the characteristics for portfolios of stocks with low profitability ratio.Column Ave (under Profitability) shows characteristics for portfolios of stocks with average profitability ratio.Column Robust shows the characteristics for portfolios of stocks with high profitability ratio.Column Conserv (under Investment) shows the characteristics for portfolios of stocks with low investment ratio.Column Ave shows characteristics for portfolios of stocks with average investment ratio.Column Aggr shows characteristics for portfolios of stocks with high investment ratio.The sample is from September 2008 to July 2015.

Table 5 . Summary results of the factor models
Column Weak (below Profitability) shows characteristics for portfolios of stocks sorted on size (Small, Medium and Large) and low profitability ratio.Column Ave shows characteristics for portfolios of stocks sorted on size (Small, Medium and Large) and average profitability ratio.Column Robust shows characteristics for portfolios of stocks sorted on size (Small, Medium and Large) and high profitability ratio.Column Conserv (below Investment) shows characteristics for portfolios of stocks sorted on size (Small, Medium and Large) and low investment ratio.Column Ave shows characteristics for portfolios of stocks sorted on size (Small, Medium and Large) and average investment ratio.Column Aggr shows characteristics for portfolios of stocks sorted on size (Small, Medium and Large) and high investment ratio.The sample is from September 2008 to July 2015.

Adjusted R ¯ 2 Panel B: GRS Panel C: p(GRS)
Fama-French 3-factor model: R p,t = a p + b p M K T t + s p SM B t + h p H M L t + e i,t .Fama-French 4-factor model ( without HML): R p,t = a p + b p M K T t + s p SMB t + r p RM W t + c p C M A t + e i,t .Fama-French 5-factor model: R p,t = a p + b p M K T t + s p SM B t + h p H M L t + r p RM W t + c p C M A t + e i,t .The sample is from September 2008 to July 2015.

Table 6 . Testing a Fama-French factor by regressing the remaining variables of the five-factor model
Table5.α, s(e) and α 2 /sd 2 (e) are the factor's intercept, residual standard error from spanning regressions and the marginal contribution of a factor to a model's Sh 2 (f), respectively.The Newey-West tstatistic is given in parentheses.The sample is from September 2008 to July 2015.