# Examination and Modification of Multi-Factor Model in Explaining Stock Excess Return with Hybrid Approach in Empirical Study of Chinese Stock Market

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

_{j}represents the factors and b represents the coefficients.

## 3. Methodology

#### 3.1. Hypotheses

**Hypothesis**

**1.**

**Hypothesis**

**2.**

**Hypothesis**

**3.**

**Hypothesis**

**4.**

**Hypothesis**

**5.**

**Hypothesis**

**6.**

**Hypothesis**

**7.**

#### 3.2. Research Design

#### Factor Selection

#### 3.3. Research Process

#### 3.3.1. Multi-Factor Model Examination with Single Stock Regression Analysis

**Stability Test**

- DV: Ri-Rf
- IV: Rm-Rf, SMB, RMW, HML, CMA, CRMHL, AMLH
- CV: Time, Time^2, Season

**OLS Regression**

**Ridge Regression**

**Robustness Test**

#### 3.3.2. Time-Series Analysis for Risk Factors

**Chi-Square Test**

**H0**:

**H1**:

**Back-Test for Trading Strategy**

#### 3.4. Assumptions for Multi-Factor Examination

- Perfect market: there are no tax and transaction costs.
- People are risk averse or rational.
- People can lend or borrow money at a risk-free rate freely.
- There is a trade-off between risk and return for all securities.
- Everyone can obtain market information equally and freely.
- Investors have the same expectations for this market.

#### 3.5. Models and Variable Definitions

## 4. Results

#### 4.1. Multi-Factor Model Examination with Single Stock Regression Analysis

#### 4.1.1. Stability Test

- DV: Ri-Rf
- IV: Rm-Rf, SMB, RMW, HML, CMA, CRMHL, AMLH
- CV: Time, Time^2, Season

#### 4.1.2. Regression Models

**OLS Regression**

**Model 1:**Five-factor model

- DV: Ri-Rf
- IV: Rm-Rf, SMB, RMW, HML, CMA

**Model 2:**Seven-factor model

- DV: Ri-Rf
- IV: Rm-Rf, SMB, RMW, HML, CMA, CRMHL, AMLH

**Model 3:**Modified optimal model

- DV: Ri-Rf
- IV: Rm-Rf, RMW, HML, CMA, CRMHL, AMLH

**Ridge Regression**

**Model 4:**Ridge regression model

- DV: Ri-Rf
- IV: Rm-Rf, SMB, RMW, HML, CMA, CRMHL, AMLH

#### 4.1.3. Robustness Test: Zero Mean Residual Testing

#### 4.1.4. Industry Analysis

- From analysis of factors’ changing pattern, can we find the reasons or elements to illustrate the fluctuation of seven factors? (if we find out the driving factor which stimulate the moving of other factors, we can explain the most essential ratio that investor may focus on.)
- Can we find an approach to forecast the moving of each factor and apply it to do the back test for trading strategies?

#### 4.2. Time-Series Analysis for Risk Factors

#### 4.2.1. Endogeneity and Exogeneity for Factors’ Cyclical Research

**Endogeneity**

**Exogeneity**

#### 4.2.2. Trading Strategy with Trend Analysis

#### 4.2.3. Back-Testing

## 5. Discussion

#### 5.1. Analysis of Multi-Factor Model

#### 5.2. Industry Analysis

#### 5.3. Factor Cyclical Research

#### 5.4. Trading Strategy and Back Test

#### 5.5. Significance and Limitations of Research

## 6. Conclusions and Further Study

## Funding

## Conflicts of Interest

## Appendix A. Intuition and Assumption Behind the Hypotheses

## Appendix B. Chi-Square Test of Industry in Different Factors

Factors | Chi-Square $\left({\mathbf{\chi}}^{2}\right)$ |
---|---|

SMB | 97.58155 |

RMW | 102.9963 |

HML | 134.683 |

CMA | 85.7257 |

Rm-Rf | 38.17769 |

CRMHL | 66.58794 |

AMLH | 179.6194 |

## Appendix C. Significance Level and Correlation Effect

Title | SMB | RMW | HML | CMA | CRMHL | AMLH | Rm-Rf |
---|---|---|---|---|---|---|---|

Extractive | 0 | −0.76 | −0.8 | −0.72 | 0.72 | −0.72 | 1 |

Media | 0 | −0.78571 | −1 | 0 | 0 | 0 | 1 |

Electrical equipment | 0.741935 | −0.80645 | −0.93548 | 0 | 0 | 0 | 1 |

Electronics | 0.833333 | 0 | −0.875 | 0 | 0.729167 | −0.70833 | 1 |

Housing | 0 | 0 | −0.72527 | 0 | 0.714286 | 0.791209 | 1 |

Textiles & garments | 0 | −0.70833 | −0.875 | 0.708333 | 0.916667 | 0 | 1 |

Non-bank finance | 0 | 0 | 0 | 0 | 0 | 0.714286 | 0.964286 |

Steel | −0.73684 | −0.94737 | 0.789474 | 0 | 1 | −0.89474 | 1 |

Utilities | 0 | 0 | 0 | 0.710526 | 0.828947 | 0 | 1 |

Defense | 0 | −0.8 | −0.72 | 0.8 | 0.8 | −0.84 | 1 |

Chemistry | 0 | −0.74699 | −0.78313 | 0 | 0.795181 | −0.84337 | 1 |

Mechanical equipment | 0 | −0.76667 | −0.76667 | 0 | 0.833333 | 0 | 1 |

Computer | 0.777778 | 0 | −0.92593 | 0 | 0.777778 | 0 | 1 |

Domestic appliance | 0 | 0 | 0 | 0 | 0.857143 | −0.7619 | 1 |

Construction material | 0.714286 | −0.7619 | 0 | 0 | 0.904762 | 0 | 1 |

Construction ornament | 0 | 0 | 0 | 0 | 0.933333 | 0 | 1 |

Transportation | 0 | −0.81633 | 0 | 0 | 0.857143 | 0 | 1 |

Animal husbandry and fishery | 0 | 0 | −0.71429 | 0 | 0 | 0 | 1 |

Automobile | 0 | −0.86364 | −0.75 | 0 | 0.818182 | −0.75 | 1 |

Light manufacturing | 0 | −0.73077 | −0.76923 | 0.730769 | 0.730769 | −0.80769 | 1 |

Commercial | 0 | 0 | −0.88525 | 0.754098 | 0 | 0 | 1 |

Food | 0.794118 | 0 | 0 | 0 | 0.794118 | −0.76471 | 1 |

Telecommunication | 0.727273 | 0 | −0.77273 | 0 | 0.772727 | −0.77273 | 1 |

Leisure service | 0.8125 | −0.875 | −0.8125 | 0 | 0.8125 | −0.8125 | 1 |

Medical | 0 | 0 | −0.80412 | 0 | 0.835052 | −0.74227 | 0.989691 |

Bank | 0 | 0.714286 | 1 | −0.71429 | 1 | 1 | 1 |

Nonferrous metal | 0 | −0.88372 | −0.74419 | −0.83721 | 0.790698 | −0.86047 | 1 |

Comprehensive | 0 | −0.92308 | −0.80769 | 0 | 0 | 0 | 1 |

## Appendix D. Forecasting the Direction of Factors

## Appendix E. Result of Stability Test

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Name | Label | Note |
---|---|---|

DV | ||

Excess return | ${R}_{i}$ − ${R}_{f}$ | The return of security mines risk-free rate of return |

IV | ||

Abnormal return | a | The constant term of formula |

Market premium | ${R}_{m}$ − ${R}_{f}$ | The return of market index (in this model, market index is Shanghai stock exchange market index) mines risk-free rate of return |

Size premium (Small minus Big) | SMB | The return on a diversified set of small stocks minus the return on a diversified set of big stocks. |

Book-to-market premium (High minus low) | HML | The difference between the returns on diversified portfolios of high and low B/M stocks. |

Profitability premium (Robust minus weak) | RMW | The difference between the returns on diversified portfolios of stocks with robust and weak profitability. |

Investment growth premium (Conservative minus aggressive) | CMA | The difference between the returns on diversified portfolios of the stocks of low and high investment firms, which we label as conservative and aggressive. |

Momentum premium (High momentum minus low momentum) | CRMHL | The difference between higher momentum (higher accumulated return) companies’ average return and lower momentum (lower accumulated return) companies’ average return in a diversified portfolio or in the market. |

Asset turnover premium (Low turnover rate minus high turnover rate) | AMLH | The difference between low asset turnover companies’ average return and higher turnover companies’ average return or in the market. |

OLS | Ridge Regression | ||||
---|---|---|---|---|---|

Model 1 | Model 2 | Model 3 | Model 4 | ||

Mean of R square | 0.5692 | 0.6078 | 0.5911 | 0.6048 | |

Mean of coefficient (p-level) | Rm-Rf | −0.29 (0.9535) | 0.29 (0.9991) | 0.82 (0.9991) | 0.21 (0.9991) |

SMB | −0.29 (0.8669) | 0.34 (0.1641) | 0.29 (0.8368) | ||

RMW | −0.74 (0.9189) | 0.24 (0.9891) | 0.40 (0.9763) | 0.22 (0.9298) | |

HML | 0.13 (0.3874) | 0.30 (0.9690) | −0.27 (0.9444) | 0.22 (0.9681) | |

CMA | −0.11 (0.9335) | 0.58 (0.9900) | −0.50 (0.9763) | 0.38 (0.9909) | |

CRMHL | −0.14 (0.9617) | 0.33 (0.9243) | 0.02 (0.9535) | ||

AMLH | −0.04 (0.9991) | −0.72 (0.9991) | 0.06 (0.9991) |

SMB | RMW | HML | CMA | AMLH | CRMHL | Rm-Rf | |
---|---|---|---|---|---|---|---|

Positive | 61.0% | 24.2% | 23.0% | 56.2% | 62.4% | 77.8% | 99.8% |

Negative | 22.7% | 68.7% | 73.8% | 42.8% | 37.5% | 17.6% | 0.1% |

Uncorrelated | 16.3% | 7.0% | 3.2% | 0.9% | 0.1% | 0.1% | 0.1% |

OLS t-Value | Ridge Regression t-Value | ||
---|---|---|---|

Model 1 | Model 2 | Model 3 | Model 4 |

0.5811 | 0.5393 | 0.5416 | 0.5387 |

Positive Relationships | Negative Relationships | |
---|---|---|

SMB | (Group A: 7) Electrical Equipment, Electronics, Computer, Construction Material, Food, Telecommunication, and Leisure Service | (Group B: 1) Steel |

RMW | (Group C: 1) Banking | (Group D: 16) Extractive, Media, Electrical Equipment, Textiles & Garments, Steel, Defense, Chemistry, Mechanical Equipment, Computer, Construction Material, Transportation, Automobile, Light Manufacturing, Leisure Service, Nonferrous Metal, and Comprehensive Industries. |

HML | (Group E: 1) Banking | (Group F: 19) Extractive, Media, Electrical Equipment, Electronics, Housing, Textiles & Garments, Steel, Defense, Chemistry, Mechanical equipment, Computer, Animal Husbandry and Fishery, Automobile, Light Manufacturing, Commercial, Telecommunication, Leisure Service, Medical, Nonferrous Metal, and Comprehensive Industries. |

CMA | (Group G: 5) Textiles & Garments, Utilities, Defense, Light Manufacturing, and Commercial | (Group H: 3) Extractive, Banking, and Nonferrous Metal |

CRMHL | (Group I: 20) Extractive, Electronics, Housing, Textiles & Garments, Steel, Utilities, Defense, Chemistry, Mechanical Equipment, Computer, Domestic Appliance, Construction material, Transportation, Automobile, Light Manufacturing, Telecommunication, Leisure Service, Medical, Banking, and Nonferrous Metal. | |

AMLH | (Group J: 3) Housing, Non-Bank Finance, and Banking. | (Group K: 14) Extractive, Electrical Equipment, Electronics, Steel, Defense, Chemistry, Domestic appliance, Automobile, Light Manufacturing, Food, Telecommunication, Leisure Service, Medical and Nonferrous Metal. |

Rm-Rf | (Group L: 28) All industries |

Condition | When Factor Is Positive | When Factor Is Negative | ||
---|---|---|---|---|

Strategies | BUY | SELL | BUY | SELL |

SMB | Small MV companies in Group A Big MV companies in Group B | Big MV companies in Group A Small MV companies in Group B | Big MV companies in Group A Small MV companies in Group B | Small MV companies in Group A Big MV companies in Group B |

RMW | Robust ROE companies in Group C Weak ROE companies in Group D | Weak ROE companies in Group C Robust ROE companies in Group D | Weak ROE companies in Group C Robust ROE companies in Group D | Robust ROE companies in Group C Weak ROE companies in Group D |

HML | High B/M companies in Group E Low B/M companies in Group F | Low B/M companies in Group E High B/M companies in Group F | Low B/M companies in Group E High B/M companies in Group F | High B/M companies in Group E Low B/M companies in Group F |

CMA | Conservative (low growth rate of assets) companies in Group G Aggressive (High growth rate of assets) companies in Group H | Aggressive companies in Group G Conservative companies in Group H | Aggressive companies in Group G Conservative companies in Group H | Conservative companies in Group G Aggressive companies in Group H |

CRMHL | High CR companies in Group I | High CR companies in Group I | ||

AMLH | Low Asset turnover companies in Group J High Asset turnover companies in Group K | High Asset turnover companies in Group J Low Asset turnover companies in Group K | High Asset turnover companies in Group J Low Asset turnover companies in Group K | Low Asset turnover companies in Group J High Asset turnover companies in Group K |

Rm-Rf | All companies (Group L) | All companies (Group L) |

Factors | Float Return | Expected Annual Return |
---|---|---|

SMB | 165.89% | 15.43% |

RMW | −6.525% | −0.61% |

HML | −22.29% | −2.07% |

CMA | 34.67% | 3.23% |

CRMHL | 313.09% | 29.13% |

AMLH | 90.26% | 8.40% |

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## Share and Cite

**MDPI and ACS Style**

Huang, J.; Liu, H.
Examination and Modification of Multi-Factor Model in Explaining Stock Excess Return with Hybrid Approach in Empirical Study of Chinese Stock Market. *J. Risk Financial Manag.* **2019**, *12*, 91.
https://doi.org/10.3390/jrfm12020091

**AMA Style**

Huang J, Liu H.
Examination and Modification of Multi-Factor Model in Explaining Stock Excess Return with Hybrid Approach in Empirical Study of Chinese Stock Market. *Journal of Risk and Financial Management*. 2019; 12(2):91.
https://doi.org/10.3390/jrfm12020091

**Chicago/Turabian Style**

Huang, Jian, and Huazhang Liu.
2019. "Examination and Modification of Multi-Factor Model in Explaining Stock Excess Return with Hybrid Approach in Empirical Study of Chinese Stock Market" *Journal of Risk and Financial Management* 12, no. 2: 91.
https://doi.org/10.3390/jrfm12020091