Fama-French Three-Factor Model

An asset pricing model that factors in market risk, company size, and the book-to-market ratio to explain variations in stock returns and assess a portfolio's performance

Author: Christopher Haynes
Christopher Haynes
Christopher Haynes
Asset Management | Investment Banking

Chris currently works as an investment associate with Ascension Ventures, a strategic healthcare venture fund that invests on behalf of thirteen of the nation's leading health systems with $88 billion in combined operating revenue. Previously, Chris served as an investment analyst with New Holland Capital, a hedge fund-of-funds asset management firm with $20 billion under management, and as an investment banking analyst in SunTrust Robinson Humphrey's Financial Sponsor Group.

Chris graduated Magna Cum Laude from the University of Florida with a Bachelor of Arts in Economics and earned a Master of Finance (MSF) from the Olin School of Business at Washington University in St. Louis.

Reviewed By: Adin Lykken
Adin Lykken
Adin Lykken
Consulting | Private Equity

Currently, Adin is an associate at Berkshire Partners, an $16B middle-market private equity fund. Prior to joining Berkshire Partners, Adin worked for just over three years at The Boston Consulting Group as an associate and consultant and previously interned for the Federal Reserve Board and the U.S. Senate.

Adin graduated from Yale University, Magna Cum Claude, with a Bachelor of Arts Degree in Economics.

Last Updated:October 29, 2023

What is the Fama-French Three-factor Model?

The Fama French Three factor model is an Asset pricing model developed in 1992 that collectively emphasizes the Capital Asset Pricing Model (CAPM), considering size, value, and market risk factors.

This statistical analysis model comprises three elements: the outperformance ratio of low versus big enterprises, Market excess return rate, and out-performing high market versus low.

Well, the first and last are the current academic debate subjects. Researchers and experienced marketers have claimed that the Model's application has skyrocketed results when applied to growth and value-based markets.

 Though some researchers and economists have urged over the fact that applying the Fama French Factor boards the book-to-market ratio explanation, performing the equity ratio is not considerable.

They also believed that the five-factor Model is more compliant as it considers more factors, thus offering better accountability.

Different sections are accustomed to a different perspective of the French Fama Factor. Still, all have one aspect in common: the risks can get reduced with the application of the French Fama Factor, and thus the explanation of returns will rise.

Key Takeaways

  • The Fama-French Three-Factor Model, developed in 1992, is an asset pricing model that goes beyond the Capital Asset Pricing Model (CAPM) by considering size, value, and market risk factors to explain stock returns.

  • The model's factors highlight that value stocks perform better than growth stocks and that small-capital stocks tend to outperform large-capital stocks in the long term. It aids in crafting investment strategies based on these insights.

  • The Fama-French Three-Factor Model is crucial for investors seeking to understand the risk and return trade-offs in their portfolios. By accounting for various factors, the model helps investors anticipate volatility and potential underperformance in the short term while aiming for long-term returns.

Understanding the Fama and French Three Factor Model

The researchers and former professors at the University of Chicago Booth School of Business, Eugene Fama and Kenneth French, came up with this ideology to scale market returns. Their studies have shown that value stocks perform better than growth stocks.

Also, it stated that small-capital stocks had surpassed large-capitalized stores. An analysis model shows that the final result limits many value stocks and is relatively less than the computed CAPM outcome. The small-cap and value stocks are observed to scale downward for the three-factor Model. The Three prime factors of this modeling are: 

  • Market premium
  • Small minus big
  • High minus low

 Simply put, one can articulate them as the size of firms, book-to-market values, and excess return outperformance in the market. 

SMB scales for the trading companies that generate high returns from small market caps. At the same time, HML gauges those firms that generate higher returns through value stocks, i.e., higher returns than the market.
To account for a brief understanding of each, let's dive in…

1. Market Risk Premium

It is the difference between the Calculated returns and the market risk factor. These factors hold exceptional value from the investor's perspective as it accounts for better outcomes as paid for the risk-free rates and volatility.

2. SMB or Small Minus Big

It is a side effect that relies on the market capitalization of an organization. It's observed that from the long-term perspective, small caps tend to have better returns than large ones, and this statement is the very foundation of SMBs.

SMB factor plays a vital role in gauging the return gap of small and big cap organizations. After clarifying SMB, the beta coefficient is calculated through linear Regression (β). All positive and negative values of the coefficient are accepted.

3. HML or High Minus Low

HML is a tool to account for the spread in returns between firms, organizations, or companies. As the term already states, it scales between a low book-to-market value ratio and companies with a splendid book-to-market balance.

Once the HML is identified, linear Regression can calculate the coefficient. Again both positive and negative values can be undertaken.

The rationale for HML is a book-to-market ratio that enables better returns than the lower one in the long run.

Fama-French-Model scope

The Model's three factors are the hot topics of academic debates as these factors rely entirely on market growth and efficiency. The Efficient Market Hypothesis gives a green mark to the market efficiency scenario, which esteemed investors also accept.

When the market is efficient enough, the performance gets proportional to the rising risk quotient with the value stocks as it gets under the surface due to rising capital cost and market risk.

When the market faces inefficiency, the market price of stocks is not valued. This makes the excess return value adjust itself from the long-term perspective.

The Model suggests that esteemed investors with at least 15 years of experience will get over their short-term losses. If measured collectively, the underperformance and volatility they faced for the shorter spans will vanish in the long run.

While conducting this research, Fama and French came up with the result that the size and value factor, along with the beta factor, 95% of the returns can be gauged and explained for any stock portfolio.

Provided that the investors can gauge 95% of return in the stock portfolio than with the market, they can easily create a portfolio that can assure at least above average returns and eradicate the value and market risks.

Risks, like the unpredictability of book-to-market ratio, size sensitivity, market sensitivity, and value stock sensitivity, can all be predicted and eradicated to reach somewhere near the expected average.

The Fama-French Three-Factor Model Formula

Let's discuss the factors of the French fama model and its formula to see how it helps to account for the returns.

1. Formulation of the Fama factor

Mathematically, the Fama Factor is expressed as:

r = rf +ß 1(rm – rf) + ß2(SMB) + ß(HML ) + Ɛ

Terminologies of the expression 

  • r = Expected rate of return
  • rf = Risk-free rate
  • ß = Factor's coefficient (sensitivity)
  • (rm – rf) = Market risk premium
  • SMB (Small Minus Big) = Historic excess returns of small-cap companies over large-cap companies
  • HML (High Minus Low) = Historic excess returns of value stocks (high book-to-price ratio) over growth stocks (low book-to-price ratio)
  • Ɛ = Risk

2. The application of the French Factor factor

While formulating the Model for accounting for the returns, you consider four constants. And here is how and what they imply.

  1. (Rf): The risk-free return factor provides you with the amount of money you can make by taking zero Risk. One should take this for the initial stage for other sorts of Investment.
  2. (Rm): The risk-based returns are an alternative to risk-free returns. Here returns are based on the SMB as they are size-based returns. Also, they are measured by HML for the value-based stock returns as they depend on the value over growth performance.
  3. The beta coefficient: The composition of market investment is measured by this constant once the SML and HML are determined.

Fama-French Three-Factor Model Vs. Five-Factor Model

In asset pricing, Fama and French introduced the Three-Factor Model, which aimed to provide a more comprehensive understanding of stock market returns. Later, in 2015, they expanded this model into the Five-Factor Model by adding two more factors, Investment and Profitability. These additional factors were introduced to adapt to changing market conditions.

However, researchers and economists have diverse opinions on the significance and complexity of this expansion. The table below summarizes the key aspects and criticisms of the Three-Factor and Five-Factor Models.

Three-Factor Model Vs. Five-Factor Model

Aspect Three-Factor Model Five-Factor model
Original Factors Market Risk, Size, and Value (SMB, HML) Market Risk, Size, Value, Investment, and Profitability
Rationale for Expansion To enhance the model's explanatory power in modern markets Adaptation to changing market conditions and behavior
Model Complexity Simpler, based on three primary factors More complex with five factors
Stock Market Explanation Focuses primarily on explaining stock market returns Adds focus on Investment and Profitability as determinants
Criticisms Some economists prefer simplicity for stock market explanations Complexity may lead to challenges in interpretation
Efficiency vs. Effectiveness Debate over whether additional factors always lead to greater effectiveness Some argue that simplicity is more effective for understanding stock market returns

Importance of the Fama-French Three-factor Model

Besides being an expanded version of the Capital Asset Pricing Model (CAPM), the Model has paved possibilities for better outperformance. The contributed factors have increased accountability for outperformance.

Also, the risk factors have enabled investors to eradicate probable size and value risk. The Model has made small companies gauge more returns than large ones, and the value companies lead the growth companies in the long run.

The searches have stated that this Model can brief the returns for the latest 90% of companies with indifferent Portfolios. Following the CAPM crucial assumption. i.e., The Riskier investments need higher returns, and the Model has become even more reliable.

The other Expanded formulation of the three-factor Fama French model, four and five-factor has brought a lot more return explanation to the table.

The Fama and French three-factor models are helpful to investors by putting light on the extra volatility and periodic underperformance that happens in the short term, affecting the returns.

Investors with a long-term time frame of 15 years or more get paid back for losses they suffered in the short term.

The Model explains about  95% of the return in a diversified stock portfolio. This further assists the investors in working on their portfolios in a way that will get them at least an average expected return, considering all the risks involved.

The Model assists investors in keeping up with a diversified portfolio. The stock market is, for sure, a volatile entity; you need to keep a watch on it all the time and scale the patterns.

But if you can keep up with a diversified portfolio, you can always stand safe irrespective of whether the market is bullish or bearish.

Bottom Line

The Model explains great returns for nearly 95% of diversified portfolios, better than the computed average of 70% through CAPM. Capital assets pricing modeling is a model designed to determine the rate of return from an asset.

A Capital Asset Pricing Model considers the size, value, and market risk factors. It gives good returns for both small and value factors.

An established relationship makes accountability sound, as one only needs to find the value of β, which can be known once SMB and HML are known.

SMB accounts for the return gap of small and big cap organizations, while HML gauges spread in returns between firms, organizations, or companies.

From the investor's eye, the Model provides a pre-explanation of risk factors and how one can gauge the returns.

This Three Factor Model is considered more compliant than the five-factor one because it offers a more straightforward and understandable explanation. It also has expanded versions like the five-factor adopted in 2014.

This Model comprises two other prime aspects besides the three mandatory ones. The Model is a factotum for the potential investors of the market. In the long run, Value-based companies overtake growth-based companies if they consider the Fama-French Model.

Researched and Authored by Antra Sharma | LinkedIn

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