# Difference Between 5 Factor Model and Q Factor Model

Essay by Yunpeng Pan • August 22, 2019 • Essay • 2,023 Words (9 Pages) • 75 Views

**Page 1 of 9**

Introduction

This essay would compare two journals written by Fama and French (2015) and Hou, Xue, and Zhang (2015) who introduced two new asset pricing models. The main similarities and differences between five-factor asset pricing model and q-factor model would be investigated in part one and two respectively. Performance of two models on equity asset pricing would be assessed in part three. Furthermore, several limitations would be identified in part four. Part five would include a judgment that presents which model could be more appropriate for equity asset pricing based on the analysis of two journals and further research.

Part One Similarities

Firstly, the reasons to develop a new equity asset pricing model would be similar. The three-factor model was suggested by Fama and French in 1993 to discover the relationship between the average returns from market portfolios and other factors including the size of market capitalization and book to market ration. However, the past two decades’ evidence stated that the three-factor model could not minimise alpha in many cases (Sharma & Mehta, 2013).

Secondly, both expected profitability and investment factors were added to their new model. As Novy-Marx (2013) identified, there were significant impacts on average returns when expected profitability was examined. In addition, Aharoni, Grundy, and Zeng (2013) recorded a statistically significant relationship between investment and average returns. Thus, Fama and French introduced five-factor model in 2015. According to HZX, they derived that the expected returns would decrease with gradually increasing in investment-to-assets from historical documents such as Fisher (1930), Fama and Miller (1972), and Cochrane (1991). Furthermore, higher returns were expected for firms have high expected profitability depending on evidence from Berk (1995). Therefore, they constructed q-factor model to address the relationship.

Finally, the method of sorting anomalies was similar. Fama and French applied the independent sorts to divide the stocks into two group based on size, and two or three books to market ratio, operating profitability, and investment groups. 22, 23, 2222 sorts were utilised based on these groups to generate results. Meanwhile, HZX quantified q-factors through 233 sorts on size, investment and return on equity. Both sorts methods were similar and commonly used in analysing the anomaly factors (Fama and French, 2008). It should be noticed that the data of stocks from NYSE, Amex, and NASDAQ were exploited to generate the conclusion.[pic 1][pic 2][pic 3][pic 4][pic 5][pic 6][pic 7]

Part Two Differences

The key difference between five-factor model and q-factor model could be their different theoretical framework. As stated by Fama and French (2015), dividend discount model was used to explain how different variables could affect average returns. In addition, relationships between expected return, expected earning, and investment were found when divided it by book value of the asset. Dividend discount model has been tested that it could perform well on asset pricing (Forester and Sapp, 2005). Whereas, q-factor model was inspired by investment-based asset pricing (Net Present Value) as it could provide evidence that investments were related to the expected returns.

As profitability and investment were not considered in the three-factor model, Titman, Wei, and Xie (2004) suggested that the relation between average returns and these two factors should be added. Consequently, five-factor model was designed. In the q-factor model, returns on the difference between high and low b/m ratio were not included compared to the five-factor model. Furthermore, there was a slight difference in profitability factor's calculation. Although the returns on equity were selected by both model as the proxy for profitability, Fama and French selected one-year-lagged accounting data via using revenues minus related costs and expenses all divided by book equity. HZX selected announced earning divided by the book equity from the previous quarter to form the values of return on equity.

Additionally, the data period was different since Fama and French use data from July 1963 to December 2013, and HZX selected data from January 1972 to December 2012. Besides, HZX compared the performance of q-factor model to three-factor model and Carhart model.

Part Three Performance Compare

In conclusion of Fama and French’s journal, the cross-section variance of expected returns for factor size, investment, operation profitability, and book to market ratio was explained in the range between 71% and 94%. Meanwhile, almost one-half of 80 anomalies examined by HZX in the q-factor model could generate an insignificant average return. Thus, the existence of anomalies could be a consequence of the inaccurate asset pricing model. According to table 4 and 5 of HZX paper, the alpha in the q-factor model was closer to zero and the t-statistics of q-factor was lower among 80 tested anomalies compared to three-factor model and Carhart model. Furthermore, the average alpha for the q-factor model is 0.20% per month compared to 0.33% in the Carhart model and 0.55% in the three-factor model which could indicate that the performance of the q-factor model was better. From table 2 of Fama and French paper, average returns would be lower when there are lower profitability or higher investment. This was true for both big and small market capitalization groups which demonstrate the performance of the five-factor model is congruent with initial assumption. According to table 5 in the same paper, the same result could be derived from four approaches applied. Thus, regardless of different sorts, the performance of the five-factor model is greater than the three-factor model and four-factor model from these tables. It was also supported from table 7 to table 11 because from regression test would be closed to zero and statistically insignificant. [pic 8]

Part Four Limitation

Both models do have limitations when examining the impacts of variable factors on average returns. According to table 5 from Fama and French (2015), the results presented that the four-factor model without factor HML could perform well as the five-factor model does. The five-factor model could be a complete version of the four-factor model without factor HML since the five-factor model was developed from the three-factor model which include HML initially. Thus, it seems that HML is a redundant factor for explaining average returns from stocks data in the US between 1963 and 2013.

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