# Fama–French Three-Factor Model

Last Updated :

21 Aug, 2024

Blog Author :

N/A

Edited by :

Aaron Crowe

Reviewed by :

Dheeraj Vaidya

Table Of Contents

## What Fama–French Three-Factor Model?

The Fama-French three-factor model is an asset pricing technique founded on the belief that small-cap stocks outperform the market and hence induce the size and value risks as additional factors to the market risks. It aims to provide a detailed explanation of stock returns compared to capital asset pricing model.

The model is an extension of the capital asset pricing model (CAPM). Professors Eugene Fama and Kenneth French developed this model in 1992. Researchers, as well as practitioners, use this model to evaluate and comprehend the risk and return characteristics of various equities and portfolios.

##### Table of contents

- The Fama-French three-factor model is a framework for asset pricing that builds upon the capital asset pricing model (CAPM) by include both value and size risk elements in addition to the market risk factor.
- It determines a stock market investment's future risk and potential return.
- This model was developed in 1992 by two American economists who received the Nobel Prize for contributing to economic sciences.
- Hence, the three factors used in the model are firm size, the excess return of the market, and book-to-market values.
- When the economists tested the model on different sets of portfolios, it predicted approximately 95% of the returns.

### Fama-French Three-Factor Model Explained

The Fama-French three-factor model is an extension of the old CAPM method, but it also provides an estimated value based on market factors, namely, the value risk, size risk, and overall market risk. It defines an equation that investors can use to determine the future rate of return on a given asset or investment.

Small-cap shares tend to offer better returns than large-cap shares. Based on this observation, US economists developed the Fama-French three-factor model paper, which widely replaced the capital asset pricing model. The CAPM only considered market risk, but the Fama-French three model adds size and value risk to the equation. Both economists believed that investors with a long-term vision would receive a higher return, which would eventually overcompensate for their short-term losses.

Moreover, the Fama-French three-factor model data is based on three elements;

- Overall market risk
- The outperformance of small companies compared to large companies
- And the outperformance of low-value stocks compared to high-value stocks.

The study conducted by the economists expressed a 95% outcome in a diversified stock portfolio. Economists need help deciding the reason for the outperformance tendency between market efficiency and inefficiency. In market efficiency, market participants define it through excess risk value and a higher cost of capital. Conversely, market inefficiency arises when market participants incorrectly price assets, ultimately resulting in an excessive return. Thus, as per the definition of the Fama-French three-factor model, small-cap and high-value companies frequently beat the market as a whole, which is the basis for their strategy.

Therefore, it offers a broader perspective than the conventional CAPM and has grown to be a vital instrument in asset pricing and portfolio management.

### Formula

The shorthand equation of the Fama-French three-factor model is -

*Return = Rf + Ri + SMB + HML*

Here,

Return - the portfolio's rate of return

Rf - risk-free rate offered by a treasury bill or bond

Ri - market risk premium

SMB (small minus big) - performance of small-cap stocks compared to large-cap stocks

HML (high minus low) - performance of high-value stocks in contrast to low-growth stocks

The expanded Fama-French Three Factor model formula is -

*R = Rf + B1(Rm – Rf) + B2(SMB) + B3(HML) + a*

Here,

B1, B2, B3 - each model factor's market coefficient

Rm - total market return

a - investment alpha

The market coefficients (B1, B2, B3) are key elements in the equation that separate it from the CAPM in the complete equation.

### Examples

Below are two examples of the Fama-French three-factor model -

#### Example #1

Suppose David is a new investor; he wants to invest in a stock, but first, he wants to understand the risk and return. Hence, David accumulated all the data and learned to employ the Fama-French three-factor model. He studies the firm size, excess return of the market, and book-to-market values of the stock upon calculating the return, and he is sure that although multiple risk factors are involved, he would still be able to gain a reasonable return from the investment.

David is also planning for long-term wealth creation, which also runs parallel with the Fama-French model. Thus, stating that for every short-term loss, an investor is rewarded with a long-term gain. Therefore, David took a long position in the stock he was interested in finally investing. It is a simple example. However, the calculation of the model is complex and relies on data analysis.

#### Example #2

In another hypothetical example, suppose Jane, who is a wise investor, comes across a stock that people are saying has huge potential to grow. Still, Jane is skeptical about it, so she decides to employ the Fama-French three-factor model. Again, Jane analyzed the firm size, risk, and return and understood that the market rumor was wrong and people should refrain from investing in it. As a wise investor, she spread the news in the investor community and tried to make more and more people aware of it.

### Importance

The importance of the Fama-French three-factor model paper is -

- The model helps determine a stock market investment's potential or likely rate of return.
- It is a better model than the CAPM, considering many factors not included in the preceding model.
- Moreover, the model is expanded to four and five-factor models and explains more than 90% of the diversified portfolio returns.
- Though it is based on many assumptions, compared to CAPM, which only used one factor of market risk, this model is based on three market risk factors.
- Therefore, it is comparatively more accurate than its predecessor and helps investors predict future investment returns precisely as it is adjusted for outperformance tendencies.

### Fama-French Three-Factor Model vs Fama-French Five-Factor Model

- The Fama-French three-factor model data uses three factors in determining the stock returns. In comparison, the Fama-French five-factor model uses five factors for the exact determination, adding two new factors: profitability and investment.
- It is considered a successor to the CAPM method. In contrast, the five-factor model is an updated version of the three-factor model.
- Although created by the same economists, the three-factor model was developed in 1992, but the five-factor model was revised and introduced in 2014.
- The three-factor model explains the changes in stock returns. Meanwhile, the five-factor model provides a detailed explanation of stock returns.

### Frequently Asked Questions (FAQs)

**1. What is the purpose of the Fama–French three-factor model?**

Primarily, the model is known for determining the return for a stock market investment. Still, its main purpose is to cover all types of risks a stock investment can suffer. Then, after taking it into account, it offers an adjusted return rate that is more accurate and provides a better prediction of future gain.

**2. What are the problems of the Fama–French three-factor model?**

The problem with the three-factor model is that it does not include low volatility and momentum of the underlying stock, and even in the updated five-factor model, there are certain technical drawbacks of including more factors. Many economists have mixed opinions on the main implication method.

**3. Why is the Fama–French three-factor model better than the CAPM model?**

Earlier, the CAPM method was widely used for predicting an investment's return. Still, the Fama-French three-factor model indicated that CAPM does not account for multiple risk factors in the return and risk determination and included the value risk and size risk in the model. It is also stated that it is an update to the old CAPM method. Both models play a quintessential role in an investor's research. The Fama French was further modified for a five-factor model.

### Recommended Articles

This has been a guide to what is Fama–French Three-Factor Model. We explain its formula, examples, importance, & comparison with Five-Factor Model. You can learn more about financing from the following articles –