# Empirical Research on the Fama-French Three-Factor Model and a Sentiment-Related Four-Factor Model in the Chinese Blockchain Industry

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Fama-French Model Research

#### 2.2. Conventional Investor Sentiment Research

#### 2.3. Investor Sentiment Research Based on Internet Information

## 3. Data

#### 3.1. Stock and Financial Data

#### 3.1.1. Stock Returns

#### 3.1.2. Market Returns

#### 3.1.3. Risk-Free Rate

#### 3.1.4. Size

#### 3.1.5. Value

#### 3.1.6. Sentiment Data

## 4. Methodology

#### 4.1. Build Portfolios According to Size and Value

#### 4.1.1. Size

#### 4.1.2. Value

#### 4.1.3. Portfolios

- Portfolio S/L: Refers to those stocks which both belong to the small-size group and low book-to-market ratio group at the same time.
- Portfolio S/H: Refers to those stocks which both belong to the small-size group and high book-to-market ratio group at the same time.
- Portfolio B/L: Refers to those stocks which both belong to the big-size group and low book-to-market ratio group at the same time.
- Portfolio B/H: Refers to those stocks which both belong to the big-size group and high book-to-market ratio group at the same time.

#### 4.1.4. Construction of Independent Variables

#### Ri

#### Market Risk Premium Factor (Rm-Rf)

#### SMB

#### HML

#### Sentiment Factor

#### Fama-French Model

## 5. Analysis of the Model

#### 5.1. Descriptive Analysis

#### 5.2. Market Risk Factor

#### 5.3. Size Factor

#### 5.4. Related Test

#### ADF (Augmented Dickey–Fuller) Test

#### 5.5. Autocorrelation

#### 5.6. Multicollinearity

#### 5.7. Heteroscedasticity

#### 5.8. Regression Analysis of the FFTFM

#### 5.8.1. Goodness of Fit of the FFTFM

^{2}is usually used to determine the goodness of fit of the equation. The R

^{2}indicates what percent of the independent variable can explain the dependent variable. The value of R^2 is between 0 and 1. The closer R

^{2}is to 1, the better the model fits the sample data. If the R

^{2}is close to 0, the model fits the fact badly. The regression could be conducted in Python and the results of “goodness of fit” are shown below. Durbin–Watson statistics were also included in the table, indicating no autocorrelation.

#### 5.8.2. Significance Test of the Model

**Hypothesis**

**1 (H1).**

**Hypothesis**

**2 (H2).**

#### 5.8.3. Significance Test of Coefficients

#### 5.8.4. Book-to-Market Ratio Factor

#### 5.8.5. Size Factor

#### 5.8.6. An Improved Four-Factor Model Based on Fama-French Model

#### 5.8.7. Goodness of Fit and F Test

#### 5.8.8. Parameters’ Analysis

## 6. Conclusions

#### 6.1. Feasibility of FFTFM and an Improved Four-Factor Model

#### 6.2. Influence of Market Risk Premium Factor

#### 6.3. The Non-Existence of Size Effect and Book-to-Market Ratio Effect in the Chinese Blockchain Industry

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Test Focus | R_SL | R_SH | R_BL | R_BH | Rm-Rf | SMB | HML |
---|---|---|---|---|---|---|---|

count | 37 | 37 | 37 | 37 | 37 | 37 | 37 |

mean | 0.007166 | −0.01992 | 0.01505 | −0.01115 | −0.12047 | −0.00833 | −0.02664 |

std | 0.124866 | 0.091218 | 0.108523 | 0.081383 | 0.044723 | 0.049832 | 0.05708 |

min | −0.19904 | −0.14461 | −0.15265 | −0.12005 | −0.20996 | −0.11855 | −0.1435 |

25% | −0.06269 | −0.07561 | −0.07093 | −0.08007 | −0.14663 | −0.03881 | −0.06217 |

50% | −0.02073 | −0.04207 | 0.005983 | −0.01998 | −0.11772 | −0.00401 | −0.0235 |

75% | 0.035004 | 0.017523 | 0.081635 | 0.0212 | −0.09386 | 0.016986 | 0.013356 |

max | 0.395968 | 0.278853 | 0.327864 | 0.245898 | 0.024608 | 0.101769 | 0.089053 |

Test Variables- | rm-rf | SMB | HML | R_SL | R_SH | R_BL | R_BH |
---|---|---|---|---|---|---|---|

rm-rf | 1 | 0.19 | −0.1 | 0.56 | 0.68 | 0.54 | 0.67 |

SMB | 0.19 | 1 | −0.082 | 0.54 | 0.34 | −0.13 | 0.16 |

HML | −0.1 | −0.082 | 1 | −0.59 | −0.12 | −0.59 | −0.16 |

R_SL | 0.56 | 0.54 | −0.59 | 1 | 0.79 | 0.72 | 0.79 |

R_SH | 0.68 | 0.34 | −0.12 | 0.79 | 1 | 0.75 | 0.92 |

R_BL | 0.54 | −0.13 | −0.59 | 0.72 | 0.75 | 1 | 0.78 |

R_BH | 0.67 | 0.16 | −0.16 | 0.79 | 0.92 | 0.78 | 1 |

Portfolios | 1% Critical Value | 5% Critical Value | 10% Critical Value | t-Value | p-Value |
---|---|---|---|---|---|

S/L (S/L including sentiment) | −3.6267 | −2.9460 | −2.6117 | −5.4165 | 0.000 |

S/H (S/H including sentiment) | −3.6327 | −2.9485 | −2.6130 | −5.0223 | 0.000 |

B/L (B/L including sentiment) | −3.6392 | −2.9512 | −2.6144 | −4.3714 | 0.000 |

B/H (B/H including sentiment) | −3.6327 | −2.9485 | −2.6130 | −5.2175 | 0.000 |

Test Variables and Focus | Durbin-Watson Statistic | Durbin-Watson Critical Value (Upper) | chi2 | Prob > chi2 |
---|---|---|---|---|

S/L | 2.356 | 1.655 | 1.342 | 0.2467 |

S/H | 2.082 | 1.655 | 0.152 | 0.6970 |

B/L | 2.082 | 1.655 | 0.152 | 0.6970 |

B/H | 2.356 | 1.655 | 1.342 | 0.2467 |

S/L (add sentiment) | 2.330 | 1.723 | 1.164 | 0.2807 |

S/H (add sentiment) | 1.996 | 1.723 | 0.014 | 0.9057 |

B/L (add sentiment) | 2.108 | 1.723 | 0.180 | 0.6712 |

B/H (add sentiment) | 2.129 | 1.723 | 0.181 | 0.6703 |

Three-Factor Model | Collinearity Statistics | ||
---|---|---|---|

Tolerance | VIF | ||

S/L, S/H, B/L, B/H | (Constant) | ||

Rm-Rf | 0.889 | 1.124 | |

SMB | 0.95 | 1.053 | |

HML | 0.941 | 1.063 | |

Four-factor model | Collinearity Statistics | ||

Tolerance | VIF | ||

S/L | (Constant) | ||

VAR00002 | 0.889 | 1.124 | |

SMB | 0.95 | 1.053 | |

HML | 0.941 | 1.063 | |

S_SL | 0.882 | 1.133 | |

S/H | (Constant) | ||

VAR00002 | 0.951 | 1.052 | |

SMB | 0.946 | 1.058 | |

HML | 0.982 | 1.018 | |

S_SH | 0.973 | 1.027 | |

B/L | (Constant) | ||

VAR00002 | 0.957 | 1.045 | |

SMB | 0.902 | 1.109 | |

HML | 0.742 | 1.347 | |

S_BL | 0.727 | 1.375 | |

B/H | (Constant) | ||

VAR00002 | 0.956 | 1.046 | |

SMB | 0.933 | 1.072 | |

HML | 0.976 | 1.024 | |

S_BH | 0.96 | 1.041 |

Test Variables and Focus | chi2 | Prob > chi2 |
---|---|---|

S/L | 9.70 | 0.3751 |

S/H | 16.50 | 0.0572 |

B/L | 16.50 | 0.0572 |

B/H | 9.70 | 0.3751 |

S/L (add sentiment) | 12.78 | 0.5438 |

S/H (add sentiment) | 24.33 | 0.0518 |

B/L (add sentiment) | 21.67 | 0.0856 |

B/H (add sentiment) | 17.26 | 0.2426 |

S/L | S/H | B/L | B/H | |
---|---|---|---|---|

${R}^{2}$ | 0.770 | 0.509 | 0.653 | 0.458 |

${\overline{R}}^{2}$ | 0.749 | 0.464 | 0.621 | 0.409 |

Durbin-Watson statistic | 2.356 | 2.082 | 2.082 | 2.356 |

S/L | S/H | B/L | B/H | |
---|---|---|---|---|

F test (3,33) | 36.81 | 11.38 | 20.68 | 9.309 |

Prob (F) | 0.0000 | 0.0000 | 0.0000 | 0.000132 |

S/L | S/H | B/L | B/H | |
---|---|---|---|---|

${\beta}_{i}$ | 1.1939 | 1.2942 | 1.2942 | 1.1939 |

t-test | (−5.009) *** | (5.086) *** | (5.086) *** | (5.009) *** |

${\mathrm{s}}_{\mathrm{i}}$ | 1.0496 | 0.3943 | −0.6057 | 0.0496 |

t-test | (4.916) *** | (1.730) * | (−2.657) ** | (0.232) |

${h}_{i}$ | −1.1229 | −0.0612 | −1.0612 | −0.1229 |

t-test | (−6.102) *** | (−0.312) | (−5.402) *** | (−0.668) |

${\alpha}_{\mathrm{i}}$ | 0.0057 | 0.0136 | 0.0136 | 0.0057 |

t-test | (0.184) | (0.409) | (0.409) | (0.184) |

Test Focus | S/L | S/H | B/L | B/H |
---|---|---|---|---|

${R}^{2}$ | 0.771 | 0.529 | 0.689 | 0.514 |

${\overline{R}}^{2}$ | 0.743 | 0.47 | 0.65 | 0.453 |

F test(3,32) | 27 | 8.976 | 17.7 | 8.447 |

Prob(F) | 0.0000 | 0.0000 | 0.0000 | 0.0000 |

Test Focus | S/L | S/H | B/L | B/H |
---|---|---|---|---|

${\alpha}_{\mathrm{i}}$ | 0.006 | 0.0126 | 0.0075 | −0.012 |

t-test | 0.189 | 0.383 | 0.235 | −0.382 |

${\beta}_{i}$ | 1.2245 | 1.3174 | 1.289 | 1.1852 |

t-test | 4.894 *** | 5.19 *** | 5.267 *** | 5.166 *** |

${\mathrm{s}}_{\mathrm{i}}$ | 1.06 | 0.4275 | −0.4984 | 0.1167 |

t-test | 4.878 *** | 1.871 * | −2.203 ** | 0.56 |

${h}_{i}$ | −1.1042 | −0.0487 | −0.8535 | −0.155 |

t-test | −5.793 *** | −0.249 | −3.922 *** | −0.872 |

$sen{t}_{i}$ | 0.0351 | 0.1054 | 0.2469 | 0.1493 |

t-test | 0.461 | 1.172 | 1.922 * | 1.906 * |

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## Share and Cite

**MDPI and ACS Style**

Ji, Z.; Chang, V.; Lan, H.; Robert Hsu, C.-H.; Valverde, R.
Empirical Research on the Fama-French Three-Factor Model and a Sentiment-Related Four-Factor Model in the Chinese Blockchain Industry. *Sustainability* **2020**, *12*, 5170.
https://doi.org/10.3390/su12125170

**AMA Style**

Ji Z, Chang V, Lan H, Robert Hsu C-H, Valverde R.
Empirical Research on the Fama-French Three-Factor Model and a Sentiment-Related Four-Factor Model in the Chinese Blockchain Industry. *Sustainability*. 2020; 12(12):5170.
https://doi.org/10.3390/su12125170

**Chicago/Turabian Style**

Ji, Ziyang, Victor Chang, Hao Lan, Ching-Hsien Robert Hsu, and Raul Valverde.
2020. "Empirical Research on the Fama-French Three-Factor Model and a Sentiment-Related Four-Factor Model in the Chinese Blockchain Industry" *Sustainability* 12, no. 12: 5170.
https://doi.org/10.3390/su12125170