#
Choosing Factors for the Vietnamese Stock Market^{ †}

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Data and Methodology

#### 3.1. Data

#### 3.2. Fama–French Five Factor Construction

#### 3.2.1. Market Factor (MKT)

#### 3.2.2. Size Factor (SMB)

#### 3.2.3. Value Factor (HML)

#### 3.2.4. Operating, Cash and ROE Profitability Factor (RMW, RWMC and RMWR)

#### 3.2.5. Investment Factor (CMA)

**A**) reports the summary statistics for the Fama–French’s monthly risk factors. Panel (

**B**) reports the time-series correlation between the factors. In July of year t, we form two size portfolios based on market capitalization as at the end of year t − 1 and use the median as the 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 the 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-to-market 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 the two size and three investment portfolios (SC, SN, SA, BC, BN and BA). The 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 the returns are in percentages. MKT is the value-weighted excess return on the market portfolio of all sample stocks minus the one-month 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:

#### 3.3. Factor Model Tests

#### 3.3.1. Left-Hand-Side (LHS) Approach for Nested Models

^{2}, GRS (Gibbons et al. 1989) test statistics and its p-value (Gibbons et al. 1989), the average value of absolute intercepts, A|$\alpha $|, the Sharpe ratio for the intercept, Sh($\alpha $), the maximum squared Sharpe ratio for intercepts, Sh

^{2}($\alpha $) (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 and Nagel (2006), the smaller Sh($\alpha $), the fewer unexplained average returns; hence, the better the model. In the same manner, we used average absolute intercepts, A|$\alpha $|, of the portfolios under analysis to assess the performance of the models. The model that best describes the variation in stock returns across portfolios is the one that provides the lowest value of A|$\alpha $|. Fama and French (2018) suggest to use the maximum squared Sharpe ratio of time-series regression’s intercepts, Sh

^{2}($\alpha $), 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}($\alpha $) 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}($\alpha $) and whose factors have the highest Sh

^{2}(f).

#### 3.3.2. Right-Hand-Side (RHS) Approach for Non-Nested Models

^{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 $\alpha $

^{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.

#### 3.4. Left-Hand-Side (LHS) Portfolio Characteristics

^{rd}and 67

^{th}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.

## 4. Empirical Results on Asset Pricing Tests

^{2}($\alpha $), we conclude that the three-factor still takes the place as the best model to explain the non-SOE portfolio sorted by size (column non-SOE of panel F) (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 six portfolios sorted by size and state ownership as well as for three SOE portfolios sorted by size. Three-factor model is preferred over other models for non-SOE portfolios sorted by size). We came to the conclusion that the three-factor model best explains the variation in returns of non-SOEs and the five-factor model is most preferred for all portfolios sorted by size and state ownership as well as SOE portfolios sorted by size from the results of the maximum squared Sharpe ratio for intercepts (columns SOE and non-SOE of panel F).

^{2}($\alpha $)) 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 by size. Overall, the results of Table 5 show that the five-factor model is the preferred model for all portfolios sorted by size and a combination of B/M, profitability and investment, taken together or standalone, and for the portfolios of SOEs sorted by size.

## 5. Is the Value Factor (HML) Redundant?

^{2}(f), in Table 5 by analyzing the extent of the marginal contribution of a factor to Sh

^{2}(f), $\alpha $

^{2}/sd

^{2}(e), defined as the squared intercept over the variance of the regression residuals, and t-statistics for the intercept (t($\alpha $)) in a factor-spanning regression. The factor’s intercept ($\alpha $) 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 $\alpha $

^{2}/sd

^{2}(e) in Table 6 report 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 5. Therefore, the value factor is confirmed to be non-redundant in the factor models for the Vietnamese stock market.

## 6. Operating, Cash or ROE Profitability?

^{2}($\alpha $), to determine which profitability measure suits best the four-factor and five-factor models. The results indicate that RMWC is equally good when testing all 27 portfolios taken together (column All of Sh

^{2}($\alpha $) in Table 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 by size and a combination of value, profitability and investment (columns B/M, Profit and Inv of Sh

^{2}($\alpha $) in Table 8).

^{2}($\alpha $) 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).

^{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).

## 7. Robustness Tests

^{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 $\alpha $

^{2}/sd

^{2}(e) of 0.029. The returns of MKT are absorbed by this factor.

^{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.

^{2}(f) as indicated in Table 6 and Table 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.

## 8. Discussion

## 9. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Vietnam’s Stock Market and Its Unique Features

## References

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**Table 1.**Sample coverage for the Vietnamese stock market. Co is the number of listed companies during a year. MCap is market capitalization in trillions of Vietnamese Dong (VND) as at the end of a year. Value and Volume are the 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, using Fama and French (2015, 2018, 2020), Ball et al. (2015) and Hou et al. (2019) profitability definitions. INV is the average investment ratio per stock, respectively, as defined using Fama and French (2015) methodology. BM is the average book-to-market ratio per stock. SOE is the number of listed companies that have state share of ownership. Data were obtained from Datastream from July 2007 to August 2015.

Year | Co | MCap | Value | Volume | OP | CP | RP | INV | BM | SOE |
---|---|---|---|---|---|---|---|---|---|---|

2007 | 135 | 334.5 | 267.6 | 2.610 | 0.0523 | 0.102 | 0.157 | 0.689 | 0.442 | 31 |

2008 | 189 | 148.3 | 120.5 | 5.261 | 0.0563 | 0.100 | 0.051 | 0.278 | 0.885 | 44 |

2009 | 279 | 371.0 | 445.9 | 18.79 | 0.0579 | 0.088 | 0.094 | 0.331 | 0.928 | 54 |

2010 | 400 | 453.1 | 408.0 | 19.12 | 0.0655 | 0.089 | 0.100 | 0.342 | 0.813 | 64 |

2011 | 421 | 308.9 | 137.6 | 11.27 | 0.0709 | 0.092 | 0.069 | 0.151 | 1.488 | 67 |

2012 | 442 | 383.4 | 193.2 | 18.77 | 0.0770 | 0.090 | 0.049 | 0.046 | 1.879 | 70 |

2013 | 425 | 446.9 | 229.7 | 22.09 | 0.0747 | 0.086 | 0.049 | 0.069 | 1.939 | 62 |

2014 | 460 | 542.2 | 523.1 | 40.16 | 0.0783 | 0.087 | 0.066 | 0.125 | 1.416 | 62 |

2015 | 438 | 623.1 | 255.8 | 18.83 | n/a | n/a | n/a | n/a | 1.319 | 47 |

Panel A: Summary statistics | ||||||

Factor | Mean | Std. dev. | Skewness | Kurtosis | Min. | Max. |

MKT | −0.0065 | 0.0843 | −0.0244 | 3.7537 | −0.2457 | 0.2390 |

SMB | 0.0038 | 0.0540 | 0.0002 | 3.9358 | −0.1388 | 0.1704 |

HML | 0.0061 | 0.0464 | 0.9480 | 5.9929 | −0.0978 | 0.1774 |

RMW | 0.0034 | 0.0378 | −0.1730 | 5.3969 | −0.1249 | 0.1277 |

CMA | 0.0010 | 0.0349 | −0.4653 | 3.5054 | −0.1004 | 0.0792 |

Panel B: Correlation | ||||||

Factor | MKT | SMB | HML | RMW | CMA | |

MKT | 1 | |||||

SMB | −0.0640 | 1 | ||||

HML | 0.1287 | 0.3821 | 1 | |||

RMW | −0.0844 | −0.5832 | −0.4928 | 1 | ||

CMA | −0.2159 | 0.1076 | 0.4888 | −0.2730 | 1 |

**Table 3.**Characteristics of value-weighted single-sorted portfolios. The table provides time-series averages of average percentage monthly excess returns, book-to-market (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) shows the characteristics of the portfolios of stocks with low book-to-market ratio. Column Ave shows the characteristics of portfolios of stocks with an average book-to-market ratio. Column High shows the characteristics of portfolios of stocks with a high book-to-market ratio. Column weak (under profitability) shows the characteristics of the portfolios of stocks with a low profitability ratio. Column Ave (under Profitability) shows the characteristics of portfolios of stocks with an average profitability ratio. Column Robust shows the characteristics of portfolios of stocks with high profitability ratio. Column Conserv (under Investment) shows the characteristics of portfolios of stocks with a low investment ratio. Column Ave shows the characteristics of portfolios of stocks with average investment ratio. Column Aggr shows characteristics of portfolios of stocks with high investment ratio. The sample is from September 2008 to July 2015.

Book-to-Market | Profitability | Investment | Ownership | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Low | Ave | High | Weak | Ave | Robust | Conserv | Ave | Aggr | SOE | Non-SOE | |

Excess returns | −0.66 | −0.09 | −0.14 | −0.99 | −0.53 | −0.55 | −0.69 | −1.00 | −0.22 | −0.21 | −0.59 |

B/M | 0.57 | 1.18 | 1.64 | 1.23 | 1.07 | 0.66 | 1.01 | 0.88 | 0.65 | 0.67 | 0.78 |

OP | 0.29 | 0.15 | 0.08 | 0.02 | 0.04 | 0.31 | 0.18 | 0.21 | 0.27 | 0.22 | 0.25 |

Inv | 0.24 | 0.19 | 0.11 | 0.13 | 0.18 | 0.23 | 0.13 | 0.16 | 0.27 | 0.14 | 0.23 |

**Table 4.**Characteristics of double-sorted portfolios. The table provides time-series averages of average percentage monthly excess returns, book-to-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 book-to-market, profitability and investment. The portfolio formation and book-to-market, profitability and investment ratios follow Fama and 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 by 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**–

**D**) show the book-to-market, profitability and investment times-series averages for a portfolio. Column Low (below Book-to-market) shows the characteristics of portfolios of stocks sorted by size (small, medium and large) and low book-to-market ratio. Column Ave shows the characteristics of the portfolios of stocks sorted by size (small, medium and large) and average book-to-market ratio. Column High shows the characteristics of the portfolios of stocks sorted by size (small, medium and large) and high book-to-market ratio. Column Weak (below profitability) shows the characteristics of portfolios of stocks sorted by size (small, medium and large) and low profitability ratio. Column Ave shows the characteristics of portfolios of stocks sorted by size (small, medium and large) and average profitability ratio. Column Robust shows characteristics of portfolios of stocks sorted by size (small, medium and large) and high profitability ratio. Column Conserv (below investment) shows characteristics of portfolios of stocks sorted by size (small, medium and large) and low investment ratio. Column Ave shows characteristics of portfolios of stocks sorted by size (small, medium and large) and average investment ratio. Column Aggr shows characteristics of portfolios of stocks sorted by size (small, medium and large) and high investment ratio. The sample is from September 2008 to July 2015.

Book-to-Market | Profitability | Investment | Ownership | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Low | Ave | High | Weak | Ave | Robust | Conserv | Ave | Aggr | SOE | Non-SOE | |

Panel A: Excess returns | |||||||||||

Small | 0.29 | 0.43 | 0.28 | 0.27 | −0.22 | 0.65 | 0.68 | −0.10 | 0.36 | 1.23 | 0.13 |

Medium | −0.83 | −0.20 | −0.18 | −0.17 | −0.63 | −0.31 | −0.01 | −0.56 | −0.43 | −0.34 | −0.43 |

Large | −0.88 | 0.24 | −0.38 | −0.87 | −0.37 | −0.53 | −0.80 | −0.91 | −0.33 | −0.24 | −0.62 |

Panel B: Book-to-market | |||||||||||

Small | 1.16 | 1.52 | 1.98 | 1.55 | 1.54 | 1.51 | 1.52 | 1.61 | 1.48 | 1.44 | 1.50 |

Medium | 0.89 | 1.23 | 1.69 | 1.28 | 1.28 | 1.27 | 1.36 | 1.31 | 1.16 | 1.19 | 1.26 |

Large | 0.49 | 0.85 | 1.37 | 1.09 | 0.86 | 0.59 | 0.92 | 0.75 | 0.61 | 0.63 | 0.71 |

Panel C: Profitability | |||||||||||

Small | 0.03 | 0.03 | 0.04 | 0.01 | 0.02 | 0.06 | 0.04 | 0.02 | 0.04 | 0.05 | 0.03 |

Medium | 0.08 | 0.09 | 0.08 | 0.01 | 0.04 | 0.17 | 0.08 | 0.08 | 0.09 | 0.06 | 0.09 |

Large | 0.32 | 0.23 | 0.13 | 0.03 | 0.08 | 0.37 | 0.21 | 0.26 | 0.28 | 0.23 | 0.27 |

Panel D: Investment | |||||||||||

Small | 0.20 | 0.20 | 0.10 | 0.18 | 0.14 | 0.18 | 0.11 | 0.19 | 0.21 | 0.19 | 0.16 |

Medium | 0.26 | 0.17 | 0.12 | 0.12 | 0.22 | 0.19 | 0.11 | 0.20 | 0.23 | 0.15 | 0.18 |

Large | 0.27 | 0.18 | 0.15 | 0.16 | 0.20 | 0.24 | 0.14 | 0.18 | 0.27 | 0.13 | 0.24 |

**Table 5.**Characteristics of double-sorted portfolios. 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 the stock sorted in December of year t − 1. The portfolio formation and book-to-market (HML), profitability (RMW) and investment (CMA) factor construction follow Fama and French’s (1993, 2015) methodology. Summary results show the average value of all adjusted R-squared (Panel (

**A**)) and the absolute intercepts (A |

**α**|) (Panel (

**D**)) of all portfolios from the respective regressions (Eq. (

**1**), (

**2**) and (

**3**)). GRS in Panel (

**B**) is the Gibbons et al. (1989) test statistic and its p-value, p(GRS), is shown in Panel (

**C**). Sh($\alpha $ ) in Panel (

**E**), Sh

^{2}($\alpha $ ) in Panel (

**F**) and Sh

^{2}(f) in Panel (

**G**) 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 by size and a combination of SOEs and non-SOEs. The sample is from September 2008 to July 2015.

Panel A: Adjusted${\overline{R}}^{2}$ | All | B/M | OP | Inv | SOE | non-SOE |

Fama–French 3-factor | 0.8958 | 0.9080 | 0.8969 | 0.8825 | 0.6721 | 0.9618 |

Fama–French 4-factor | 0.8949 | 0.8969 | 0.9044 | 0.9091 | 0.6755 | 0.9570 |

Fama–French 5-factor | 0.9049 | 0.8825 | 0.8898 | 0.8960 | 0.6715 | 0.9630 |

Panel B: GRS | All | B/M | OP | Inv | SOE | non-SOE |

Fama–French 3-factor | 1.5629 | 1.0278 | 1.1892 | 0.9157 | 4.2280 | 9.9838 |

Fama–French 4-factor | 1.5403 | 1.4262 | 1.3022 | 1.0259 | 3.9507 | 11.7091 |

Fama–French 5-factor | 1.4003 | 0.9739 | 1.0858 | 0.7789 | 3.7389 | 10.8280 |

Panel C:p(GRS) | All | B/M | OP | Inv | SOE | non-SOE |

Fama–French 3-factor | 0.0822 | 0.4268 | 0.3157 | 0.5170 | 0.0080 | 0.0000 |

Fama–French 4-factor | 0.0902 | 0.1935 | 0.2516 | 0.4286 | 0.0113 | 0.0000 |

Fama–French 5-factor | 0.1484 | 0.4689 | 0.3843 | 0.6363 | 0.0146 | 0.0000 |

Panel D:A|$\alpha $| | All | B/M | OP | Inv | SOE | non-SOE |

Fama–French 3-factor | 0.0033 | 0.0032 | 0.0051 | 0.0030 | 0.0137 | 0.0072 |

Fama–French 4-factor | 0.0043 | 0.0032 | 0.0039 | 0.0031 | 0.0135 | 0.0086 |

Fama–French 5-factor | 0.0029 | 0.0034 | 0.0038 | 0.0026 | 0.0135 | 0.0073 |

Panel E:Sh|$\alpha $| | All | B/M | OP | Inv | SOE | non-SOE |

Fama–French 3-factor | 0.9040 | 0.3657 | 0.3980 | 0.3578 | 0.4112 | 0.6318 |

Fama–French 4-factor | 0.9102 | 0.4307 | 0.4165 | 0.3787 | 0.4019 | 0.6920 |

Fama–French 5-factor | 0.8913 | 0.3559 | 0.3803 | 0.3300 | 0.4003 | 0.6813 |

Panel F:Sh^{2}|$\alpha $| | All | B/M | OP | Inv | SOE | non-SOE |

Fama–French 3-factor | 0.8171 | 0.1337 | 0.1584 | 0.1280 | 0.1691 | 0.3992 |

Fama–French 4-factor | 0.8285 | 0.1855 | 0.1734 | 0.1434 | 0.1616 | 0.4788 |

Fama–French 5-factor | 0.7944 | 0.1267 | 0.1446 | 0.1088 | 0.1603 | 0.4642 |

Panel G:Sh^{2}|$f$| | All | |||||

Fama–French 3-factor | 0.0266 | |||||

Fama–French 4-factor | 0.0363 | |||||

Fama–French 5-factor | 0.0725 |

**Table 6.**Testing a Fama–French factor by regressing the remaining variables of the five-factor model. 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 by 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 2 × 3 portfolios constructed using Fama and French’s (1993, 2015) methodology. Sh

^{2}(f) is the maximum squared Sharpe ratio for a model’s factors from Table 5. $\alpha $, s(e) and $\alpha $

^{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 t-statistic is given in parentheses. The sample is from September 2008 to July 2015.

MKT | SMB | HML | RMW | CMA | |
---|---|---|---|---|---|

MKT | −0.12 | 0.12 ** | −0.05 | −0.13 ** | |

(−1.63) | (2.06) | (−0.96) | (−2.29) | ||

SMB | −0.39 | 0.19 * | −0.34 *** | −0.13 | |

(−1.39) | (1.67) | (−3.73) | (−1.18) | ||

HML | 0.61 ** | 0.27 * | −0.18 | 0.40 *** | |

(2.34) | (1.84) | (−1.30) | (4.56) | ||

RMW | −0.39 | −0.76 *** | −0.28 | −0.15 | |

(−0.99) | (−5.14) | (−1.25) | (−0.94) | ||

CMA | −0.97 ** | −0.30 | 0.60 *** | −0.15 | |

(−2.24) | (−1.22) | (4.25) | (−0.89) | ||

$\alpha $ | −0.01 | 0.00 | 0.01 | 0.01 * | −0.00 |

(−0.66) | (0.92) | (1.57) | (1.84) | (−0.36) | |

Adj.R^{2} | 0.117 | 0.362 | 0.414 | 0.415 | 0.314 |

Sh^{2}(f) | 0.073 | 0.073 | 0.073 | 0.073 | 0.073 |

s(e) | 0.008 | 0.005 | 0.004 | 0.006 | 0.003 |

$\alpha $^{2}/sd^{2}(e) | 0.006 | 0.010 | 0.036 | 0.040 | 0.000 |

**Table 7.**Characteristics of portfolios sorted on a combination of size and operating profitability, cash profitability or return-on-equity (ROE) profitability. The table provides time-series averages of excess returns, book-to-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 the double sort of size and a combination of cash profitability (Ball et al. 2015; Fama and French 2018), ROE profitability (Hou et al. 2015, 2019) and operating profitability (from Table 4). The portfolio formation and book-to-market, profitability and investment ratios follow the Fama and French (2015) methodology. Each of the ratios for a portfolio in a given year is a value-weighted average of the ratios for the firms in the portfolios. Panel (

**A**) provides time-series averages of the monthly returns in excess of Vietnam’s interbank offer rate (in percentages). Panels (

**B**–

**D**) show the book-to-market, profitability and investment times-series averages for a portfolio. Column Weak shows the characteristics of portfolios of stocks sorted by size (small, medium and large) and low profitability ratio. Column Average shows the characteristics of portfolios of stocks sorted by size (small, medium and large) and average profitability ratio. Column Robust shows characteristics of portfolios of stocks sorted by size (small, medium and large) and high profitability ratio. The sample is from September 2008 to July 2015.

Operating Profitability | Cash Profitability | ROE Profitability | |||||||
---|---|---|---|---|---|---|---|---|---|

Weak | Average | Robust | Weak | Average | Robust | Weak | Average | Robust | |

Panel A: Excess returns | |||||||||

Small | 0.27 | −0.22 | 0.65 | 0.14 | 0.15 | 0.53 | 0.22 | 0.20 | 0.45 |

Medium | −0.17 | −0.63 | −0.31 | −0.42 | −0.35 | −0.30 | −0.36 | −0.26 | −0.48 |

Large | −0.87 | −0.37 | −0.53 | −0.79 | −0.22 | −0.43 | 0.54 | −0.63 | −0.79 |

Panel B: Book-to-market | |||||||||

Small | 1.55 | 1.54 | 1.51 | 1.66 | 1.62 | 1.33 | 1.81 | 1.61 | 1.32 |

Medium | 1.28 | 1.28 | 1.27 | 1.40 | 1.34 | 1.11 | 1.60 | 1.30 | 1.06 |

Large | 1.09 | 0.86 | 0.59 | 0.74 | 0.70 | 0.71 | 1.19 | 1.02 | 0.59 |

Panel C: Profitability | |||||||||

Small | 0.01 | 0.02 | 0.06 | 0.04 | 0.08 | 0.18 | 0.00 | 0.01 | 0.02 |

Medium | 0.01 | 0.04 | 0.17 | 0.03 | 0.08 | 0.19 | 0.02 | 0.03 | 0.09 |

Large | 0.03 | 0.08 | 0.37 | 0.01 | 0.04 | 0.12 | 0.28 | 0.43 | 0.81 |

Panel D: Investment | |||||||||

Small | 0.18 | 0.14 | 0.18 | 0.19 | 0.17 | 0.16 | 0.07 | 0.19 | 0.21 |

Medium | 0.12 | 0.22 | 0.19 | 0.14 | 0.19 | 0.20 | 0.12 | 0.16 | 0.23 |

Large | 0.16 | 0.20 | 0.24 | 0.17 | 0.27 | 0.22 | 0.23 | 0.21 | 0.21 |

**Table 8.**Summary of the regression results using cash profitability and ROE profitability factors. Panel (

**A**) of this table describes the average adjusted R-squared of all portfolios sorted by size and a combination of B/M, profitability, investment and the average adjusted R-squared of size-All (All), size-SOE (SOE) and size-non-SOE sorted (non-SOE) portfolios. The portfolio formation and book-to-market (HML), cash profitability (RMWC) and investment (CMA) factor construction follow Fama and French’s (1993, 2015, 2018) methodology. Summary results show the average value of all adjusted R-squared (Adj.R

^{2}) and the absolute intercepts (A|$\alpha $ |) of all portfolios from the respective regressions in panels A to D of Table 6. GRS is the Gibbons et al. (1989) test statistic and its p-value, p(GRS). Sh($\alpha $ ) and Sh

^{2}($\alpha $ ) are the Sharpe ratio for intercepts and its maximum squared value, respectively. We apply these five tests to all portfolios (All) and the portfolios formed by size and a combination of book-to-market (B/M), profitability (OP), investment (Inv). Column “SOE” shows the results for companies classified as state-owned and “non-SOE” column reports the results on the privately owned group of listed firms. Fama–French five-factor model with RMWC: ${R}_{p,t}={\alpha}_{p}+{b}_{p}MK{T}_{t}+{s}_{p}SM{B}_{t}+{h}_{p}HM{L}_{t}+{r}_{p}RMW{C}_{t}+{c}_{p}CM{A}_{t}+{\epsilon}_{p,t}$. Fama–French four-factor model (without HML): ${R}_{p,t}={\alpha}_{p}+{b}_{p}MK{T}_{t}+{s}_{p}SM{B}_{t}+{r}_{p}RMW{C}_{t}+{c}_{p}CM{A}_{t}+{\epsilon}_{p,t}.$ The sample is from September 2008 to July 2015. Panel (

**B**) follows the same data and methodology as in panel A with the ROE profitability, RMWR, (Hou et al. 2015, 2019) as the proxy for a profitability factor. The Fama–French five-factor model with RMWR: ${R}_{p,t}={\alpha}_{p}+{b}_{p}MK{T}_{t}+{s}_{p}SM{B}_{t}+{h}_{p}HM{L}_{t}+{r}_{p}RMW{R}_{t}+{c}_{p}CM{A}_{t}+{\epsilon}_{p,t}$. Fama–French four-factor model (without HML): ${R}_{p,t}={\alpha}_{p}+{b}_{p}MK{T}_{t}+{s}_{p}SM{B}_{t}+{r}_{p}RMW{R}_{t}+{c}_{p}CM{A}_{t}+{\epsilon}_{p,t}.$ The sample is from September 2008 to July 2015. Panel (

**C**) displays the summary results of Table 5 with operating profitability (RMW) in the models.

Adjusted${\overline{R}}^{2}$ | GRS | Sh(α) | |||||||||

Summary results | All | SOE | non-SOE | All | B/M | Profit | Inv | All | B/M | Profit | Inv |

Panel A: Using RMWC as profitability factor | |||||||||||

Fama–French 4-factor | 0.8952 | 0.6943 | 0.959 | 1.53 | 1.22 | 1.42 | 1.37 | 0.9 | 0.4 | 0.43 | 0.42 |

Fama–French 5-factor | 0.9096 | 0.6946 | 0.9678 | 1.41 | 1.04 | 1.22 | 1.09 | 0.89 | 0.38 | 0.42 | 0.39 |

Panel B: Using RMWR as profitability factor | |||||||||||

Fama–French 4-factor | 0.8929 | 0.6809 | 0.9566 | 1.76 | 1.19 | 1.52 | 1.37 | 0.96 | 0.39 | 0.44 | 0.42 |

Fama–French 5-factor | 0.9061 | 0.6837 | 0.9649 | 1.65 | 1.02 | 1.32 | 1.14 | 0.95 | 0.37 | 0.42 | 0.39 |

Panel C: Using RMW as profitability factor | |||||||||||

Fama–French 4-factor | 0.8949 | 0.6755 | 0.957 | 1.54 | 1.19 | 1.3 | 1.09 | 0.67 | 0.4 | 0.42 | 0.38 |

Fama–French 5-factor | 0.9049 | 0.6715 | 0.963 | 1.4 | 0.92 | 1.03 | 0.78 | 0.66 | 0.36 | 0.38 | 0.33 |

A|α| | p(GRS) | Sh^{2}(α) | |||||||||

Summary results | All | SOE | non-SOE | All | B/M | Profit | Inv | All | B/M | Profit | Inv |

Panel A: Using RMWC as profitability factor | |||||||||||

Fama–French 4-factor | 0.0038 | 0.0129 | 0.0061 | 0.09 | 0.3 | 0.28 | 0.22 | 0.82 | 0.16 | 0.19 | 0.18 |

Fama–French 5-factor | 0.0034 | 0.0126 | 0.0076 | 0.14 | 0.42 | 0.29 | 0.38 | 0.79 | 0.14 | 0.17 | 0.15 |

Panel B: Using RMWR as profitability factor | |||||||||||

Fama–French 4-factor | 0.0039 | 0.0139 | 0.008 | 0.04 | 0.31 | 0.16 | 0.22 | 0.92 | 0.15 | 0.19 | 0.18 |

Fama–French 5-factor | 0.0031 | 0.0133 | 0.0067 | 0.06 | 0.43 | 0.24 | 0.35 | 0.9 | 0.14 | 0.18 | 0.15 |

Panel C: Using RMW as profitability factor | |||||||||||

Fama–French 4-factor | 0.0043 | 0.0135 | 0.0086 | 0.09 | 0.32 | 0.25 | 0.38 | 0.83 | 0.16 | 0.17 | 0.14 |

Fama–French 5-factor | 0.0029 | 0.0135 | 0.0073 | 0.15 | 0.52 | 0.43 | 0.64 | 0.79 | 0.13 | 0.14 | 0.11 |

**Table 9.**Testing the profitability factors. The table reports the results of time-series regressions with each of the profitability variables (operating profitability (RMW), cash profitability (RMWC) and ROE profitability (RMWR)) being regressed by the remaining five factors. MKT is the value-weighted excess return on the market portfolio, and SMB is the average return on the portfolio sorted by size. HML is the value factor sorted by size and book-to-market ratio. RMW is the operating profitability factor (Fama and French 2015). RMWC is the cash profitability factor (Fama and French 2018; Ball et al. 2015). RMWR is the ROE profitability factor (Hou et al. 2015, 2019). CMA is the investment factor. All factors are 2 × 3 portfolios constructed using the Fama and French (1993, 2015) methodology. Sh

^{2}(f) is the maximum squared Sharpe ratio for a model’s all 6 factors. $\alpha $, s(e) and $\alpha $

^{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. Newey–West t-statistic is given in parentheses. The sample is from September 2008 to July 2015.

Results of Spanning Regressions | RMW | RMWC | RMW | RMWR |
---|---|---|---|---|

MKT | −0.03 | −0.11 * | −0.05 | 0.08 * |

(−0.47) | (−1.84) | (−1.00) | (1.94) | |

SMB | −0.35 *** | 0.16 | −0.35 *** | −0.28 *** |

(−3.78) | (1.31) | (−3.10) | (−3.28) | |

HML | −0.13 | −0.17 | −0.19 | −0.37 *** |

(−1.10) | (−1.58) | (−1.35) | (−3.56) | |

RMW | 0.33 *** | −0.01 | ||

(2.87) | (−0.09) | |||

RMWC/RMWR | 0.21 *** | −0.01 | ||

(2.67) | (−0.09) | |||

CMA | −0.13 | −0.05 | −0.15 | −0.09 |

(−0.81) | (−0.34) | (−0.87) | (−0.61) | |

$\alpha $ | 0.00 | 0.00 | 0.01 * | 0.00 |

(1.33) | (1.10) | (1.84) | (0.70) | |

Adj.R^{2} | 0.448 | 0.188 | 0.407 | 0.509 |

Sh^{2}(f) | 0.085 | 0.085 | 0.063 | 0.063 |

s(e) | 0.003 | 0.004 | 0.003 | 0.003 |

$\alpha $^{2}/sd^{2}(e) | 0.025 | 0.015 | 0.040 | 00.005 |

**Table 10.**Testing the redundancy of the value factor using cash profitability (Fama and French 2018; Ball et al. 2015) and ROE profitability (Hou et al. 2019). This 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 by size. HML is the value factor with size and book-to-market sort. CMA is the investment factor. All factors are 2 × 3 portfolios constructed using the Fama and French (1993, 2015) methodology. Sh

^{2}(f) is the maximum squared Sharpe ratio for a model’s factors. $\alpha $ and $\alpha $

^{2}/sd

^{2}(e) are the factor’s intercept from spanning regressions and the marginal contribution of a factor to a model’s Sh

^{2}(f), respectively. The Newey–West t-statistic is given in parentheses. The sample is from September 2008 to July 2015. Panel (

**A**) shows the analysis with respect to the cash profitability factor (RMWC) by Fama and French (2018) and Ball et al. (2015). Panel (

**B**) describes the ROE profitability factor (RMWR) calculated using Hou et al.’s (2019) definition.

Panel A: Cash Profitability (RMWC) | |||||

MKT | SMB | HML | RMWC | CMA | |

MKT | −0.09 | 0.11 * | −0.13 ** | −0.13 ** | |

(−0.97) | (1.89) | (−2.12) | (−2.20) | ||

SMB | −0.22 | 0.29 *** | 0.05 | −0.08 | |

(−0.93) | (3.59) | (0.47) | (−0.90) | ||

HML | 0.51 * | 0.58 *** | −0.23 * | 0.42 *** | |

(1.86) | (4.30) | (−1.74) | (4.85) | ||

RMWC | −0.56 * | 0.09 | −0.22 | −0.06 | |

(−1.90) | (0.50) | (−1.50) | (−0.61) | ||

CMA | −0.92 ** | −0.24 | 0.62 *** | −0.10 | |

(−2.13) | (−0.90) | (4.76) | (−0.58) | ||

$\alpha $ | −0.00 | −0.00 | 0.01 | 0.01 | −0.00 |

(−0.49) | (−0.10) | (1.63) | (1.50) | (−0.49) | |

Adj. R^{2} | 0.162 | 0.138 | 0.415 | 0.139 | 0.303 |

Sh^{2}(f) | 0.062 | 0.062 | 0.062 | 0.062 | 0.062 |

$\alpha $^{2}/sd^{2}(e) | 0.004 | 0.000 | 0.034 | 0.029 | 0.004 |

Panel B: ROE Profitability (RMWR) | |||||

MKT | SMB | HML | RMWC | CMA | |

MKT | −0.02 | 0.16 *** | 0.08 ** | −0.11 ** | |

(−0.31) | (2.92) | (1.98) | (−2.05) | ||

SMB | −0.06 | 0.09 | −0.28 *** | −0.11 | |

(−0.31) | (0.81) | (−3.01) | (−0.90) | ||

HML | 0.90 *** | 0.17 | −0.37 *** | 0.39 *** | |

(3.36) | (0.73) | (−3.68) | (3.02) | ||

RMWR | 0.67 * | −0.75 ** | −0.53 *** | −0.10 | |

(1.93) | (−2.41) | (−2.70) | (−0.51) | ||

CMA | −0.82 ** | −0.27 | 0.50 *** | −0.09 | |

(−2.24) | (−0.97) | (3.28) | (−0.56) | ||

$\alpha $ | −0.01 | 0.00 | 0.01 | 0.00 | −0.00 |

(−1.01) | (0.25) | (1.50) | (0.63) | (−0.55) | |

Adj. R^{2} | 0.147 | 0.315 | 0.503 | 0.515 | 0.305 |

Sh^{2}(f) | 0.037 | 0.037 | 0.037 | 0.037 | 0.037 |

$\alpha $^{2}/sd^{2}(e) | 0.016 | 0.001 | 0.027 | 0.005 | 0.005 |

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## Share and Cite

**MDPI and ACS Style**

Ryan, N.; Ruan, X.; Zhang, J.E.; Zhang, J.A.
Choosing Factors for the Vietnamese Stock Market. *J. Risk Financial Manag.* **2021**, *14*, 96.
https://doi.org/10.3390/jrfm14030096

**AMA Style**

Ryan N, Ruan X, Zhang JE, Zhang JA.
Choosing Factors for the Vietnamese Stock Market. *Journal of Risk and Financial Management*. 2021; 14(3):96.
https://doi.org/10.3390/jrfm14030096

**Chicago/Turabian Style**

Ryan, Nina, Xinfeng Ruan, Jin E. Zhang, and Jing A. Zhang.
2021. "Choosing Factors for the Vietnamese Stock Market" *Journal of Risk and Financial Management* 14, no. 3: 96.
https://doi.org/10.3390/jrfm14030096