Analysis of the Modern Financial Regression Model: CAPM and

Fama-French

Yucheng Lin

College of Arts and Sciences, University of North Carolina at Chapel Hill, Chapel Hill, U.S.A.

Keywords: CAPM, FF3, FF5, Financial Pricing, Expected Returns.

Abstract: Contemporarily, financing pricing models are widely adopted in assets evaluations. This study will discuss

the development and empirical testing of the CAPM, Fama-French Three-Factor Model (FF3), and the Five-

Factor Model (FF5) in the context of modern asset pricing. The FF3 model improved upon the traditional

CAPM by introducing size and value factors to better capture variations in stock returns. However, its inability

to account for differences in profitability and investment behaviours led to the creation of the FF5 model,

which adds profitability and investment factors. Empirical evidence suggests that while the FF5 model

generally outperforms the FF3 model in explaining stock returns, particularly in the U.S. market, its

performance is less consistent in other markets, such as China and Japan, indicating its limitations in diverse

economic and regulatory environments. The review highlights the FF5 model's potential factor redundancy,

inconsistent results across markets, and limited ability to capture certain stock behaviours as areas requiring

further development. Future research directions include integrating artificial intelligence and behavioural

factors to enhance the model's predictive power and applicability. This research concludes that while the FF5

model represents a significant advancement in asset pricing.

1 INTRODUCTION

In broad terms, finance revolves around the study of

asset risk and return through mathematically lens. In

the early 1960s, American economist William Sharpe

and his colleagues revolutionized modern finance

through the Capital Asset Pricing Model, providing

foundation and framework for valuation of assets.

The pioneering financial model applied widely in the

20th century for and William Sharpe was awarded the

Nobel Price of Economic Science in 1990. In addition

to the Markowitz Model assumptions on risk aversion

of investor, the one-factor model added the

assumptions of complete agreement of investors and

risk-free rate borrow and lend (Fama & French, 2004).

CAPM asserted a linear relationship between asset

returns and market risk (Ross, 1978). Despite its

theoretical simplicity and strong explanatory power,

CAPM has faced criticism in practical applications,

particularly when dealing with real-world markets

characterized by incomplete information and

heterogeneous investors (Fama, 1970; Epps, 1976).

To address the limitations of CAPM, Fama and

French proposed FF3 model, introducing two

additional factors to explain anomalies in stock

returns that CAPM could not account for. The FF3

model demonstrated significant improvements in

various empirical studies, particularly in explaining

the excess returns of small-cap and value stocks

(Fama & French, 1993).

Fama and French later introduced the FF5 which

improves upon FF3, adding two additional factors to

the original three. FF5 aims to reflect the drivers of

stock returns, providing a more robust asset pricing

tool for both academic and practical use (Fama &

French, 2015). Empirical tests on developed global

markets suggest an improvement to FF3 and that the

regional models outperform global model (Cakici,

2015). This study will systematically review and

analyse the existing methodologies on the CAPM,

FF3, and FF5 models to explore their theoretical

foundations, applications, and performance across

different market environments.

This paper will first examine the history and

theoretical expansion of the modern financial models

and then assess their performance in empirical studies.

Then the paper will compare the application

outcomes of FF3 with FF5 across different markets.

Through this literature review, I hope to highlight the

limitations and prospects of these models in modern

314

Lin, Y.

Analysis of the Modern Financial Regression Model: CAPM and Fama-French.

DOI: 10.5220/0013224200004568

In Proceedings of the 1st International Conference on E-commerce and Artiﬁcial Intelligence (ECAI 2024), pages 314-318

ISBN: 978-989-758-726-9

financial markets, incorporating the models with new

emerging technologies of Artificial intelligence.

2 DEVELOPMENT FROM CAPM

TO FAMA-FRENCH MODEL

2.1 History of CAPM

In modern finance, CAPM remains as a simplistic yet

fundamental model for valuation of asset and

estimation of portfolio performance. CAPM,

introduced by Sharpe and Lintner, builds upon

Markowitz's mean-variance optimization theory

developed in the 1950s. Markowitz’s model assume

investors to minimize the variance and maximize the

return rate of a portfolio. The model indicates prices

of all assets reflect their market risk, represented by

their beta coefficients. It distinguishes between

systematic risk and unsystematic risk (risk specific to

an individual asset), assuming that investors

concerned with systematic risk primarily. It assumes

every investor's portfolio follows the mean-variance

optimization strategy and can borrow or lend

unlimited amounts at the risk-free rate (Ross, 1978).

Based on the assumptions, CAPM concludes on a

linear relationship between the expected return and

beta:

𝐸



𝑅





= 𝑅



+ 𝛽



(𝐸

(

𝑅





− 𝑅



) (1)

Beta represents the systematic risk of the market and

depends on historical returns and market returns,

𝛽



(



,



)





(

)

(2)

Beta also represents the slope of linear regression

between the expected return and market return which

provides information on sensitivity of individual

stock given the fluctuating market return. Under the

assumption of CAPM, the beta of riskless asset equals

zero and the expected return of the portfolio must

equal to the risk-free rate.

While CAPM provides a simplistic algebraic

method to valuate asset, it has limitations due to

assumptions on investors behaviors. It assumes an

efficient market where all investors behave rationally,

and they can borrow or lend at the risk-free rate.

Contrary to this idealized assumption, market

information is not fully transparent, transaction costs

exist, and borrowing is not always possible at the risk-

free rate, thereby weakening CAPM's effectiveness in

real-world applications (Ross, 1978; Bartholdy &

Peare, 2005). The assumption of investors caring only

about mean-variance also reflects the flaw of CAPM.

It is likely for investors to care for income in addition

to the mean-variance analysis, thus undermining the

portfolio’s return variance as it misses such variables

(Fama & French 2004).

2.2 CAPM TO FF3

Academia recognized the limitations to a single-

factor model in valuating asset. Eugene Fama and

Kenneth French introduced the FF3 in 1993, which

added two additional factors—firm sizeand book-to-

market ratio—to capture the effects of size and value

on stock returns:

𝐸

(

𝑅



)

= 𝑅



+ 𝛽



𝐸

(

𝑅



)

− 𝑅



 + 𝛽



(

𝑆𝑀𝐵

)

𝛽



(

𝐻𝑀𝐿

)

(3)

Intuitively, higher expected returns for small-cap

stocks represented by the size factor will compensate

investors for the additional risks associated with

smaller firms, which may include higher volatility,

less liquidity, and higher default risks. Small firms

often have less access to capital, fewer resources to

weather economic downturns, and are generally

considered riskier investments compared to their

larger counterparts. Investors demand a risk premium

for holding that stocks, leading to higher expected

returns relative to large-cap stocks (Fama & French

1992). FF3’s logic builds on the premise that stock

returns are influenced not only by their sensitivity to

overall market risk but also by their exposure to these

additional risk factors. By including these two

additional factors, FF3 provides a more nuanced

explanation of stock returns, reflecting the risk

premiums investors demand for holding small-cap

and value stocks due to their perceived higher risk.

2.3 Development of FF5

In 2014, Eugene Fama and Kenneth French extends

the original model again with additional factors of

profitability and investment. FF5 extends on logic of

FF3 using factors of RMW and CMA,

𝐸

(

𝑅



)

= 𝑅



+ 𝛽



𝐸

(

𝑅



)

− 𝑅



 + 𝛽



(

𝑆𝑀𝐵

)

𝛽



(

𝐻𝑀𝐿

)

+ 𝛽



(

𝑅𝑀𝑊

)

+ 𝛽



(

𝐶𝑀𝐴

)

+ 𝛽



(4)

Here, RMW calculates the difference in returns

between a portfolio of stocks with robust and weak

portfolio. Profitability is typically measured by

operating profitability. Research shows that firms

Analysis of the Modern Financial Regression Model: CAPM and Fama-French

315

with higher profitability tend to have higher stock

returns, as they are often perceived as more stable and

less risky investments. Profitable companies generate

stronger cash flows and are better able to weather

economic downturns, which justifies a risk premium

on their returns (Fama & French, 2015). CMA

calculates the difference in returns between firms that

follow low asset growth and those that adopt high

asset growth. The CMA factor captures the

observation that firms with lower levels of asset

growth tend to have higher future returns comparing

to those with higher levels of asset growth. This can

be attributed to the tendency of firms that invest

aggressively to undertake riskier or less profitable

projects, which may lead to lower future profitability

and hence lower expected returns. Conversely, firms

with conservative investment policies are generally

viewed as more disciplined and less risky, resulting

in relatively higher expected returns. If the Betas

explain all cross-sectional variation of the portfolio,

then 𝛽



, or the intercept, equals zero (Fama & French,

2015).

FF5 bases in Dividend Discount Model (DDM)

which suggests that expected returns are linked to

profitability and investment patterns. DDM states

that given the expected dividend 𝐸(𝑑



), the stock

price:

𝑚



∑

𝐸(𝑑



)/(1 + 𝑟)







(5)

The relation given by DDM has implications on

the expected return of an individual stock and CMA

and RMW aim to explain cross-sectional variation

under this model. Despite its broader scope, the FF5

model has faced several criticisms. One key criticism

is the potential redundancy of the value factor (HML).

Fama and French found that the HML factor's

significance diminished with the inclusion of FF5

factors, raising questions about its necessity in the

model (Cakici, 2015). Furthermore, the FF5 model's

performance varies across different markets and

portfolio constructions, suggesting that its

applicability might be context dependent (Fama &

French, 2015). The limitations suggest a need for

empirical examination of the FF3 and FF5 Model

performance.

3 APPLICATION AND

DEVELOPMENT OF FAMA-

FRENCH MODEL

3.1 Empirical Stuies

In the study on performance of FF3 and FF5 on

portfolio of ten US sectors, researchers point out that

FF5 explains the variability of sector portfolio better

than FF3 (Sarwar et al., 2017). While both FF3 and

FF5 outperform the benchmark of S&P 500, the result

reveals a higher cumulative return and adjusted R

than that of CAPM and FF3. According to the

research, FF5 alpha has higher adjust R

than that of

FF3 alpha across all ten US sectors. The return of FF5

portfolio also have 7% higher return and 2% lower

standard deviation compared to the buy-and-hold

S&P 500. With trading on sector ETFs, long-only

FF5 trading strategy has 5.53% of mean return while

buy-and-hold S&P500 only has 2.05%. The

researchers suggest that the factors of RMW and

CMA betas of FF5 likely decrease alpha estimate in

most sectors (Sarwar et al., 2017).

Research on the U.S. market sectors suggests that

the FF5 better explains the variation compared to the

FF3 model, particularly in small-cap, high-

investment portfolios and among highly profitable

companies. However, the FF5 model also shows that

the role of the HML is reduced in certain contexts,

reflecting the ability of the new factors to account for

market anomalies and partially replace traditional

factors.

The valuation model applies significantly

different in global markets and regional markets.

Study shows that RMW and CMA factors in FF5 do

not have significant explanatory power on expected

return in the Chinese A-share stock market (Jiao &

Lilti, 2017). In tracking the performance of FF3 and

FF5 from July 2010 to May 2015, the paper indicates

the distinguishable difference of the Size-B/P

portfolio intercept from zero (Jiao & Lilti, 2017).

Under the assumption where the coefficients (betas)

of the factors explaining the cross-sectional expected

return, the intercept β should equal zero. The non-

zero intercept thus reveals that FF5 Model do not

fully account for the expected return. The researchers

also indicated that coefficient of RMW only have

statistically significant in Size-OP portfolio and that

the coefficient of CMA negatively correlate with

small size-aggressive investment portfolio (Jiao &

Lilti, 2017). Noticeably, the adjusted R

of FF5 and

FF3 after running time-series regression on the same

portfolio do not differ dramatically. Probability and

ECAI 2024 - International Conference on E-commerce and Artiﬁcial Intelligence

316

investment thus do not have explanatory effect on the

expected return and the two models’ performance do

not have huge difference. The result diverges from the

empirical study of FF3 and FF5 on the US market

where FF5 have higher cumulative return and R

The difference between the two empirical study

results on FF3 and FF5 performance reveal the

limitation of Fama-French Model in specific regions

or context. Whereas the additional two factors of

CMA and RMW have improved performance in

North America, CMA seems redundant in Europe and

Japan (Fama & French, 2016). The studies highlight

the importance of market-specific empirical testing

and suggest that asset pricing models may require

customization or adjustments when applied to

different economic and regulatory environments.

3.2 Limitations and Prospects

As an empirical model, FF5 has limitations to

measurement of expected return. FF5 model has

shown inconsistent performance across different

markets, highlighting its limitations in capturing local

market dynamics. While the model performs well in

the U.S. market, where it significantly improves upon

the FF3 model, its effectiveness is less pronounced in

other markets, such as the Chinese A-share market

and Japanese markets.

Recent research has begun to explore the

integration of the FF5 model with advanced

technologies and additional factors to improve its

predictive capacity. For example, Mita and Takahashi

(2023) propose a new approach that combines the

FF5 model with artificial intelligence techniques,

such as Gradient Boosting Machine (GBM) and state-

space models, to enhance the accuracy of return

predictions. By using AI-driven predictions in

conjunction with the FF5 factors, this approach can

dynamically adjust to changing market conditions

and better forecast future returns, outperforming

traditional strategies like buy-and-hold or typical

mutual fund approaches for Japanese equities. The

study demonstrates that an AI-enhanced FF5 model

not only retains the strengths of the traditional model

but also provides superior performance, suggesting a

promising future direction for integrating machine

learning techniques into asset pricing models to

handle large datasets and capture complex patterns in

financial markets (Mita & Takahashi, 2024).

As AI and machine learning techniques continue

to advance, there is a significant opportunity to

enhance the FF5 model’s predictive power and

applicability across diverse markets. AI-based

models have the advantage of processing vast

amounts of data more efficiently and identifying

complex, non-linear relationships that traditional

econometric models may miss. By leveraging these

technologies, the FF5 model can potentially evolve

into a more flexible and adaptive tool for predicting

returns in real-time, accounting for rapid changes in

market conditions and investor behavior (Mita &

Takahashi, 2024).

Other researchers have explored the addition of

new factors to the FF5 model to address its current

limitations. Dhaoui and Bensalah expanded the FF5

model by incorporating momentum and investor

sentiment factors, arguing that these additions could

improve the model's ability to capture certain market

behaviors that the standard FF5 model misses. The

inclusion of a momentum factor helps account for the

tendency of stocks to continue moving in their current

direction, while the investor sentiment factor reflects

the impact of psychological biases on asset prices.

Their findings suggest that this enhanced model can

better predict expected returns and explain anomalies

related to small stocks with high investment and low

profitability, i.e., an area where the original FF5

model often falls short. This approach underscores

the potential for further developments that

incorporate behavioral and sentiment-based factors,

offering a more holistic view of asset pricing that

includes both traditional financial variables and

behavioral elements (Dhaoui & Bensalah, 2016).

4 CONCLUSIONS

To sum up, FF3 model marked a significant departure

from the traditional CAPM by additional factors,

which allowed for a more nuanced understanding of

stock returns by accounting for systematic risks

beyond market exposure. FF5 model represents a

further evolution in asset pricing by adding two

additional factors to provide a more comprehensive

model for understanding the variations in stock

returns. Empirical evidence suggests that FF5

generally performs better than FF3 in explaining

returns, particularly in markets like the United States.

The model's performance varies significantly across

different markets. This study recognizes the

explanatory limitation of FF5 as empirical model and

suggest that the emergence of AI or factor that

customized to local financial market will improve the

performance of factors. In conclusion, while FF5

represents a substantial step forward in asset pricing

theory, its mixed empirical results and inherent

limitations indicate that it is not yet the final word on

modelling stock returns. Future developments should

Analysis of the Modern Financial Regression Model: CAPM and Fama-French

317

focus on refining the model by integrating new

techniques and data sources to enhance its robustness,

flexibility, and applicability across global financial

markets.

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